Friday, April 19, 2013


Suppose I am a plumber, and I take a section of pipe, insert a blowgun dart, and blow.  I just shot a dart out of a blowgun.  When did the pipe turn into a blowgun, though?

Did it happen when I formed the intention to use the pipe as a blowgun?  No: I do not have the power to make new material objects come into existence just by thinking about it.

When I picked up the pipe?  There are at least there is contact.  But surely it's not the right kind of contact.  It would be magic if I could make a new material object come into existence by just picking up a material object with a certain thought in mind.

When I inserted the dart?  Presumably, not any insertion will do, but one with a plan to blow.  For I could just be doing plumbing, using the outer diameter of the dart to measure the inner diameter of the pipe, and that shouldn't turn the pipe into a dart.  Again, we have some magic here--thinking about the pipe in one way while inserting the dart creates a blowgun while thinking about it another way leaves it a boring pipe.  Moreover, putting the dart into the pipe seems to be an instance of loading a blowgun rather than making a blowgun.

When I fired the dart?  Surely, that's too late.  As I lift up the pipe and point it at the target, I am surely pointing a blowgun!

Further complication: I now put the blowgun down among the pipes on the back of my truck, and next day install it in Mr. Smith's sprinkler system.  Does Mr. Smith now come to be a blowgun owner, with the rights, liabilities and responsibilities attendant on having such a weapon (blowguns are illegal in California or Canada, after all)?  Moreover, did I violate my contract with Mr. Smith, for I agreed to install pipes, whereas I installed a blowgun instead?  The last question is perhaps not so pressing--for perhaps the tubularly arranged matter I installed in his garden constitutes both a pipe and a blowgun.

One might think some of the difficulties could be removed by saying that throughout I was dealing with one object, a pipe, which acquired an extrinsic property, being a blowgun.  There need be no magic when a material object acquires an extrinsic property as a result of my thinking.  When I think about your car, your car acquires the property of being thought about by me.  But this is mistaken.  Suppose I add sights to the blowgun.  The sights come to be a part of the blowgun, but they do not come to be a part of the pipe--they are, rather, attached to the pipe.  So the blowgun seems to be a material object distinct from the pipe.

The solution to all this is to deny that there are pipes and blowguns.  There is just matter (or fields) arranged pipewise and blowgunwise.  And for convenience we adopt ways of speaking that make it sound like such objects are among the furniture of the universe.


Paul Symington said...

Possible counter example to your claim that "I do not have the power to make new material objects come into existence just by thinking about it": Assuming a materialist account of mind, perhaps some kind of material relation comes into existence when you learn something about some object.

I don't that this is possible, FWI. In fact, your claim quoted above might be support against the conjuction of realism about material objects (anti-constructivism) and a materialist view of mind.

Heath White said...

Don't we get to just run the argument again, asking this time when the object acquired the property of being arranged blowgunwise?

Alexander R Pruss said...


Yeah, that's so, I guess.


I guess so. But there is no worry about magically an object appearing. Just particles acquiring a vague mind-dependent relation.

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SMatthewStolte said...

This is a quibbling point, but … if the legal question is really a problem on the assumption that there are pipes and blowguns, then it remains a problem on the assumption that there aren’t. (For the purposes of the law, I doubt — but I could be wrong — that the term ‘blowgun’ could be replaced with ‘the xs arranged blowgunwise’.)

Of course, it isn’t really a problem for the law. Courts will rule (make a Declaration) one way or another and set some sort of precedent — items put to such and such purpose, say, shall not be construed as blowguns for the purpose of the law — and that will be that. So the legal example is not really an example of the problem.

As far as I can tell, no situation with practical import could exemplify this problem. So the problem is purely theoretical. This is not to say that it is a nonproblem.

Unknown said...

Matthew --

Suppose we decided that there were no pipes or blowguns. But of course, unreflective commonsense tells us that there are pipes and blowguns. So we've dealt a blow against commonsense.

That blow could have practical import when we start considering other questions where commonsense is also an issue. For example, the question of whether morality is real or if its just an opiate for the masses. Commonsense says it's real. But if we strike a blow against commonsense (and so, to some degree, lose confidence in commonsense), then the appeal to commonsense no longer as strongly supports the realness of morality.

It seems to me that this sort of weakening of our grounds for morality --- and similar weakening in other cases (say, the case against solipsism, or the case for the validity of logic or religious experience) --- these sorts of weakening can become a practical problem for someone who's not aware of the other good reasons to take a certain (correct, healthful, sane) view on these issues.

Unknown said...

Let's deny that identity is constant across time. So before the sights are connected onto the pipe, the pipe is the blowgun. After the sights are added, the pipe and the blowgun are two distinct things.

Speaking tenselessly: the pipe is not the blowgun. They are two distinct things. Despite that, there is a limited period of time during which they are not distinct but rather are the same thing.

This solution seems to avoid the problems that Dr. Pruss raised against the existence of pipes and blowguns. Also, it supports the view that pipes and blowguns do exist.

But why should we deny that identity is constant across time? Well, let's look at the claim that identity is constant across time:

Constancy of Identity Across Time (CIAT)

For any x and y, if at some time, x is y, then at every time where x or y exists, x is y.

As near as I can tell, this thesis CIAT is not a mere truth of logic. Also, if it is true, then it's necessarily true.

But that's a problem. There may or may not be some necessary truths out there that are not truths of logic ... but we typically call these 'brute necessities' and regard them as bad things. All things being equal, the more brute necessities your theory has, the worse off your theory.

So if CIAT is true, it's a brute necessity, and we do not like brute necessities. Therefore, until we find some good reason to believe CTAT, we should deny CIAT.

So the rational course of action is to deny that identity is constant across time. Once we've denied that, the door is left wide open to solve the present problem about pipes and blowguns by believing that the pipe and the blowgun are the same object at one time but different objects at a later time. This solution works.

Now, the alternate solution is that there are no pipes or blowguns. But we should prefer my solution to that alternate solution, because we have some good reasons to think that there are pipes and blowguns do exist.

Unknown said...

What reasons do we have to think that there truly are pipes and blowguns? Well, here are five sources of motivation for the theory that pipes and blowguns do exist:

1. Commonsense
2. Perception (we naturally form the belief that pipes and blowguns exist when we encounter them and think about them, assuming we understand the concepts "pipe" and "blowgun"; so we have a natural belief-formation process that leads us to believe that there are pipes and blowguns; we should accept natural belief-formation processes like this as rational unless we have specific good reasons to doubt that they are rational --- which in the present case we don't)
3. Conceivability (conceivably, pipes and blowguns exist; conceivability gives evidence of possibility; so we have evidence that it is possible that pipes and blowguns exist; but very likely, if it is metaphysically possible that there are pipes and blowguns, then any material arranged pipe-wise and blowgun-wise --- and appropriately used and thought about by its maker --- is a pipe and a blowgun; so there are pipes and blowguns)
4. Rational Intuition (there's a rational intuition that if someone deliberately arranges some matter blowgun-wise and uses and regards it as a blowgun, then the matter thus arranged is a blowgun; don't believe me? well... doesn't it at least kinda seem that there's a rational intuition to this effect? if so, this this kinda-seeming provides at least some grounding for the view that there is a rational intuition to this effect; and if there is such a rational intuition, then blowguns exist)
5. Aesthetics (the universe is more interesting and variegated if there are either artifacts or else non-living compound objects in it than if there aren't either of these things; this gives us a rational reason to think that one or other of these things do exist; and if non-living compound objects exist, then some of them are artifacts; so in either case, artifacts exist; so the aesthetic consideration gives us some reason to think that artifacts exist)

Taken cumulatively, I think the motivation accruing from 1--5 for the existence of artifacts (such as pipes and blowguns) is strong. Conversely, as far as I can tell, there aren't any good reasons to disbelieve in artifacts (as I've tried to show, the specific problem Dr. Pruss raised isn't a worry; there are other objections that can be raised against artifacts, but I don't think that any of them are worries either). So we have strong motivation for the belief that there are artifacts, and no strong motivation for the belief that there aren't artifacts. Therefore, the rational thing to do is to believe that there are artifacts.

Alexander R Pruss said...

Doesn't CIAT directly follow from Leibniz's law?

Dagmara Lizlovs said...

When blowguns are outlawed, only outlaws will have blowguns.

What stops a bad guy with a blowgun? A good guy with a blowgun.

I'll give you my blowgun when you take it from my cold, dead lips.

Alexander R Pruss said...


Believing in non-simple artifacts seems to require that one accept either (i) 5D mereological universalism or (ii) (a) existential vagueness--vagueness as to whether something exists--as well as (b) the mind-dependence of some material objects. But (i), (iia) and (iib) are all implausible.

Unknown said...

Dr. Pruss ---

I can see that the following claim follows from Leibniz's Law:

For any x and y, if x = y, then at any time where x or y exists, x = y.

But that's different from CIAT. Unlike the thesis justgets stated, CIAT has the operator [At some time,] before the first [x = y] clause. So how does CIAT follow from Liebniz's Law? I may just not be seeing it.

Unknown said...

I see how we can get CIAT from the following Leibniz's Law-esque premise:

At any time: for any x and y, if x = y, then for any F, Fx iff Fy.

And you can get that premise from [Necessarily, Leibniz's Law] together with the further principle:

For any P, if necessarily P, then at any time, P.

Call this pinciple Necessarily P Implies Always P (NPIAP).

I think NPIAP is false. Why? Well, I think there are things that are true but aren't true at any time. In particular, suppose a 'tensed' proposition is any proposition P which begins with a temporal operator or which has a conjunct or disjunct which begins with a temporal operator. Call a proposition 'effectively tensed' if it is logically equivalent to some tensed proposition. I think that there is never a case of an effectively tensed proposition P and a time t and such that at t, P. I don't think time operators 'embed' like that and result in true sentences. In the past there were dinosaurs, but not: in the future, in the past there were dinosaurs. I think such constructions fail to be meaningful, so they fail to be true.

But NPIAP logically entails things like [At any time t, for any time t, for any effectively tenseless P, P or ~P]. And that's an effectively tensed proposition with a temporal operator on the front of it. So it's not true. So what entails it is false or meaningless. So NPIAP is false or meaningless. NPIAP is meaningful. So NPIAP is false.

Since NPIAP is false, it doesn't give us a reason to believe [Always: Leibniz's Law]. So I don't see why we should believe [Always: LL]. So I don't see why we should believe CIAT.

Unknown said...

Do you know of a short statement of the argument that the existence of non-simple artifacts entails that (i) or (ii) is true? Also, I'm not familiar with the "5D"in 5D Mereological Universalism. Is the 4th D time and the 5th D possible worlds?

Alexander R Pruss said...

Suppose t = now. Then if x=y at t, then x=y simpliciter. And so we can run Leibniz's law at t, no?

Michael Gonzalez said...

Pruss, let's say we accept the following commonsense (very plausible, in my opinion) beliefs:

1) Deny mereological nihilism, and say that physical objects do exist.
2) Admit that a given object can be put to many purposes (for example, I can turn a bucket over, and sit on it like a chair).
3) Recognize that moral, legal, and contractual distinctions very often hinge on intent/purpose.

So, in the case of the pipe/blowgun, it is a simple case of re-assigning an object a new purpose. A person who is expert in making blowguns from household materials might even say something like "any pipe in your house is a potential blowgun, if you just know how to use it".

It seems rather simple to me, from this commonsense standpoint. No new object is created when you decide to use object X as a blowgun rather than as a pipe. It's originally intended use goes back to the manufacturer's purposes, but the buyer may have other purposes for a given item (as anyone who does arts and crafts will tell you). Pipes do exist. They are objects arranged certain ways with certain purposes. And, while the manufacturer's purposes hold initially, the object can later be turned to some other purposes (especially if modified in some way, since the buyer now becomes a manufacturer and re-initializes).

Doesn't this seem right?

Alexander R Pruss said...

I think this is ruled out by my thought of putting sights on the pipe. The sights are a part of the blowgun but not of the pipe.
P.s. I don't think there is much point to sights on a blowgun.

Paul Symington said...

You could say that artificial objects are discovered by us and so are already there. So, the section of pipe is both a pipe and a blowgun already, which would remove the bizarre condition that one brings into existence a material object just by thinking about it.

However, this view would commit one to co-spatially located material objects, but constitution folks don't seem to mind this worry.

Also, there is still the lingering problem that although the existence of the artificial object isn't dependent on my mind to exist, artificial objects seem to be dependent on some generic mind in order to exist, since they are related in some way to intentionaliy. I think Amie Thomasson holds that such objects are dependent on some generic understanding of mind to stay in existence. She gives the example of an obscure law in some dusty law book that no one knows about. On her view, the law still exists since it is still binding, but it depends on no one's particular mind in order to exist.

Michael Gonzalez said...

Pruss: But isn't the addition of sights covered by my point about manufacture? Once you modify the item with another purpose in mind, you become a manufacturer of an item, and it now has a new "initial" purpose. But, then if someone buys it from you, and still uses it as a plumbing pipe, he has simply given it new purpose despite the "initial" bias toward being a blowgun.

It just seems to me that an item made for a purpose is not the same as items made without purpose. A mountain, for example, forms via natural processes without purposeful directedness (in my opinion). So, to call the mountain an "exercise machine", just because we can get exercise by walking up it, is not going to fly, since such designations require that the mountain was made for some purpose (in this case, the purpose of giving us something to exercise on). On the other hand, calling a manufactured thing by a label identifies the purpose for which it was initially manufactured, OR the purpose to which it was later applied instead. But in no case is a new object created, nor does the old object go out of existence.

It just seems to me that this is the commonsense, intuitive notion of adapting something from its original purpose into some new purpose, but nevertheless keeping the same object. In fact, if one were to tell the "story" of the object's "life" one would tell of its many changes-of-purpose as events in the life of a single object, no? Just as one would say Alex was a University student, but then became a professor when certain things were added to him (degrees, titles, etc), so we would say "this object started off as a plumbing pipe, but underwent several changes... heck, it was even a blowgun for part of its life, with a superfluous sight and everything!".

I don't know. Maybe I've missed the point.

Unknown said...

It looks like you're saying that [Now, P] entails [P]? I don'tdon't see how it does. For instance, I'd say using a tenseless copula in each case that (now the clay is the statue) but the clay isn't the statue. After all, the clay is older than the statue, and even (now the clay is older than the statue).

If presentism were true, then we might say that for any effectively tenseless proposition P, the proposition [Now, P] is the very same proposition as P. Then we would get the entailment from [Now, P] to P.

But (i) there is no strong reason to think that presentism is true (so if presentism turned out to rule out the existence of artifacts, then since we do have some strong reason to think there are artifacts, then we should reject presentism), (ii) there is some pretty good reason to think that presentism is false (mainly, you need a ream of presently existing 'abstract' truthmakers for truths about past states of affairs as well as a primitive predicate distinguishing these truthmakers from present SOA's), and (iii) it's not clear whether [Now P] = P is plausible even on presentism (since it looks like [now] is equivalent for some t to [at some t], and even under presentism, adding [at some t] onto one proposition does result in a different proposition).

So the presentist consideration doesn't give us a good reason to think that [Now P] = P. So we have no good reason to think that. And a la (iii) above we have some good reason to doubt that [Now P] = P. So we should not accept it, especially if it turns out that this result is inconsistent with the existence of artifacts. But if not [Now P] = P, then not: [Now P] logically entails P.

So [Now P] does not logically entail P. So setting t to Now does not give us CIAT.

Unknown said...
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Unknown said...

Hi Paul --

I think that before adding the sights, the pipe and the blowgun both exist. But I don't think the pipe and blowgun are colocated. Rather, I think the pipe and the blowgun are the very same thing until the sights are added. So to say tbat they were colocated during that period would be like saying that I and Richard Davis are colocated. But I and Richard Davis are not colocated because I am the very same thing as Richard Davis.

Does it seem to you that this reasoning defuses the colocation objection for people who hold that (at certain periods of time) the pipe is the blowgun?

Unknown said...

What if I sculpt a statue with two purposes: to be a work of art AND to have something heavy to lift for exercise. I might even give it a certain shape so I can lift it. It looks like then the statue is also a piece of workout equipment. Supposing, though, that sometime I add a handle to it. I don't intend the handle to add to the statue's aesthetic value; I just want to be able to lift my workout equipment more easily. The question is: at this point, is the statue still the workout-equipment? I think the argument is that no, it isn't, because the workout equipment has a part (the handle) that the statue doesn't.

In this case, though, the statue is still a statue, since the manufacture (me) still primarily intends the statie to serve as a work of art. That makes this different from the pipe case, since then we might say that once sights are added, the pipe is no longer a pipe because it's no longer primarily intended to be used as a pipe.

So it looks like the statue was the workout equipment, but now, after adding the handles, it is no longer the workout equipment. If you thought it was absurd for X and Y to be the same thing at some times but not all times, then you might respond by denying that X or Y (the statue and the workout equipment) ever really existed.

(I don't think that's the right conclusion --- rather, I think we should accept that two things can be sometimes identical and sometimes distinct --- but I do think it's a cool argument.)

Alexander R Pruss said...

I am assuming that what is now true is true. If not, I don't understand "now true".

Alexander R Pruss said...

Note that the statue and the weight have different modal properties. The latter can survive being squashed while the former can't.

Unknown said...

So are you reasoning:

(P1) Now x = y.
(P2) If now P, then P is now true.
(L1) So [x = y] is now true.
(P3) If P is now true, then P is true.
(L2) So [x = y] is true.
(P4) If P is true, then P.
(L3) So x = y.
(LL) If x = y, then Fx iff Fy.
(L4) So Fx iff Fy.
(L5) x = x
(L6) So x = y.

Therefore (Now x = y) --> (x = y).

I object to P2. Again: (now the clay is the statue) but (the clay is the statue) is not now true. In fact, (the clay is the statue) is never true, because the clay is older than the statue.

Michael Gonzalez said...

Richard: You seem to be committed to two absurdities.

First, your reasoning entails that for every possible use of the pipe without modifying it or adding anything to it, there are objects/entities which co-exist (along with the pipe and the blowgun, we also have the child's toy and the paperweight, etc etc).

Secondly, you seem to be saying that your P2 is false, but that is logically impossible. The proposition "P" is exactly the same as the proposition "P is true". So, take P(n) to mean "now P". Since "P" = "P is true", it must be the case that "P(n)" = "P(n) is true".

Unknown said...


Thanks for the comment!

About colocation: see my response above to Paul (posted April 22nd 10:54 am).

About your argument with P and P(n): what that argument gets you is the following conclusion:

P(n) = P(n) is true.


[Now P] = [Now P] is true.

As an instance of the schema [If P, then P], that result entails:

Q1. If now P, then [Now P] is true.

Suppose I grant your principle that for any P, P = [P is true]. If so, then I've granted the above conclusion Q1. I've even granted that Q1 is a truth of logic. Correct me if I'm wrong: You are objecting, on these grounds, that my proposition P2 is logically necessary and so it's absurd for me to deny P2?

I want to make sure I read your argument correctly. You're saying that Q1 (which, for the sake of argument, I've agreed is logically necessary) logically entails P2 --- and so since Q1 is logically necessary, that means that P2 is also logically necessary?

OK. If I've got your reasoning right, here's my response: Q1 doesn't logically entail P2. P2 says:

If now P, then P is now true.

This means the same as:

Q2. If now P, then now: P is true.

Listed together, Q1 and Q2 read as follows:

Q1. If now P, then [Now P] is true.
Q2. If now P, then now: P is true.

Q1 and Q2 have the same hypodoses (Now P), but different consequents. So they're not the same proposition. And I don't see how the first of these two propositions logically entails the second one. After all, here's a case of proposition P for which [Now P] is true but P is not true:

Q3. Every reptile is not a dinosaur.

Read Q3 with a tenseless "is". [Now, every reptile is not a dinosaur] is true, because now there are no dinosaurs. So Q3 is a case of P for which [Now P] is true. However, [Every reptile is not a dinosaur] is not true, because (tenseless "are") there are reptiles that are dinosaurs. They're just all in the past. So Q3 provides a case of P for which P is not true.

Now I'm assuming that we both accept P3 from the original post:

(P3) If P is now true, then P is true.

P3 is equivalent to its contrapositive:

(P3') If P is not true, then not: P is now true.

I showed above that Q3 is a case of P where P is not true. From this result and P3', it follows by modus ponens that Q3 is a case of P where not: P is now true. Since [P is now true] is the same as [Now, P is true], this result means that Q3 is a case of P where not: now, P is true.

Alright then. Here's our result: Q3 is both

(i) a case of P where [Now P] is true, and
(ii) a case of P where not: now, P is true.

But look at Q1 and Q2:

Q1. If now P, then [Now P] is true.
Q2. If now P, then now: P is true.

What we've just worked out is that Q3 satisfies the consequent of Q1 but does not satisfy the consequent of Q2!

So there's a value of P (namely, Q3) which satisfies Q1 but doesn't satisfy Q2. Therefore Q1 does not logically entail Q2.

As I said above, Q2 means the same as P2. So since Q1 does not logically entail Q2, therefore Q1 does not logically entail P2. If we had found that Q1 did entail P2, this would have shown us that P2 was logically necessary. But what we have found is the opposite: Q1 doesn't entail P2.

Therefore, as far as the present argument goes, we have found no reason to think that P2 is logically necessary. So I plead innocent to your charge. Even if I grant for the sake of the argument that P = [P is true], it does not follow that P2 is logically necessary; so it is not absurd for me to deny P2.

Thanks again for your two objections (about colocation and logical absurdity). I think I've cleared myself of the charges ... but I'm open to being shown otherwise.

Unknown said...

Michael, a thought: could you possibly be conflating [Now: P is true] and [[Now P] is true]? Both of them can be written [Now P is true], so it's easy to make the slip...

Unknown said...

Dr. Pruss:

On the other hand, maybe P2 is right, but P3 and P4 are ambiguous between a tensed and a tenseless reading of "is". On the tensed reading, P3 is true and P4 is false. On the untensed reading, P4 is true and P3 is false. For the argument to be sound, we need the same reading in both cases. So there's no reading on which the argument is sound.

Since you take "P is now true --> P is true" to be a priori (right?), I think you're using a tensed reading of "is" in the apodosis of P3. After all, on a the tensed reading of the "is" in its apodosis, P3 is a logical tautology; so it's unsurprising that it seems a priori. But it's hard to see how P3 could be a priori on the untensed reading.

So P3 is tensed. That means we also need a tensed reading of P4 if the argument is to be valid. So here's my objection: P4, interpreted with a tensed "is", means:

(Now, P is true) --> P.

But if P2 is correct, then the conditional just stated is false. For example, let P := There are (tenseless) no dinosaurs. We had better not be committed to any premises that entail that there are (tenseless) no dinosaurs --- because there are some. They're just all in the past. But P2 and the tensed reading of P4 entail that there are no dinosaurs. So we better not accept both P2 and the tensed reading of P4. But unless we accept both of them, then we don't have a sound argument from P1 through P4. So we don't. So we don't get [Now: x = y] --> [x = y]. So we don't get CIAT.

Michael Gonzalez said...


I appreciate your response. No offense, but you could have spared yourself a very long explanation and just said that when "is" is taken tenselessly, "P is true" doesn't necessarily entail "P is now true". Since I think B-theory is hopeless and without good motivation, I don't normally think of how "is" is used in tenseless language. That being said, I think that, even given B-theory, "is" should be taken as "at the moment of speech act (written or vocal) and as such is relativized in time.

If one accepts this, then Q3 (the statement "every reptile is not a dinosaur") is actually true. If the word "is" relativizes the proposition in time to the point at which the speech-act is occurring, then it is actually true at that point in time that every reptile is not a dinosaur (leaving aside entirely the paleontological fact that dinosaurs weren't reptiles at all, but sauropsid ancestors of birds).

So, basically, I understand now that you meant a tenseless P can be true without it being true that P(n). However, if the P in question applies to a time other than the time at which the speech act is occurring, it doesn't seem to me proper to say that P "is" true, so much as that it "was" true.

But, then, maybe it's just the fact that I think B-theory is nonsense, and that A-theory corresponds so much better to how we actually speak and think.


Michael Gonzalez said...


Oh, and, as to your response about colocation, you seem to have missed the point. The piece of pipe that you are using in your plumbing is quite plausibly NOT a blowgun. To say that it is both, is to say it is also every other thing that it could conceivably be used as, which is absurd. It isn't any of those things, until someone puts it to those other uses. Until then, it holds the identity given it by its manufacturer (see my response to Pruss at April 22, 2013 10:29am).

Unknown said...
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Unknown said...
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Alexander R Pruss said...

Whether the A- or the B-theory of time is true, I don't see what it means to say that x=y now, if it doesn't imply that x=y. What is this temporalized identity?

Unknown said...

I agree that on a reading of "is" that indexes to the time of use, P2 is true. So I think I'd agree that A-theory/presentism entails CIAT.

I'm not personally aware of much good motivation for A-theory or presentism. So the fact that A-theory and presentism each entail CIAT doesn't seem to me to give us much reason to accept CIAT.

You suggested that we most frequently and naturally think and talk using a tensed existence predicate (and don't as frequently or naturally use an untensed one). But surely that's beside the point? An A-theorist only needs to hold that there is a most basic existence predicate which is tenseless. He needn't hold that we primarily use it, sans the tensed existence predicates, in our thought or speech. So how does the question of what sort of predicate we ordinarily use, bear on the question of A-theory and B-theory? I.e., even if we do usually use tensed existence predicates, how does that count as evidence that there isn't an untensed existence predicate out there to be used?

I'd also be curious to know what you make of truthmakers for the past in A-theory. The best A-theory-consistent view on truthmakers for the past that I know of requires reams of presently existing abstract objects to serve as the truthmakers for the propositions about the past. It also requires there to be an extra fundamental predicate which these abstract truthmakers satisfy but which present states of affairs don't satisfy.

Why? Well, truthmakers for the past aren't the same things as present states of affairs. So there is some difference between them. So there is some predicate that the one class satisfies that the second class doesn't satisfy. There doesn't seem to be any good candidate for a predicate of this kind that reduces down to other predicates that are already in the fundamental language. So the predicate in question must itself be fundamental.

Of course, whenever you get a new (possibly instantiated) fundamental predicate, you also get a new brute necessity. Suppose the predicate is F. Here's our brute necessity: [Necessarily, possibly for some x Fx]. Alternatively, if we think that think F is a fundamental predicate and F-ness is a universal, then the brute necessity will instead be [Necessarily, F-ness exists].

Finally, it looks like --- given Dr. Pruss's argument --- that A-theory/presentism renders it implausible that there are any artifacts. But there are good reasons to think there are artifacts (cf my post April 20, 2013 10:06 pm). A la modus ponens, these reasons count as reasons to disbelieve A-theory.

So it looks to me that there are four problems with A-theory (reams of abstract truthmakers, a new fundamental predicate, a new brute necessity, evidence for the existence of artifacts) that B-theory doesn't face. And I'm not aware of any strong motivations for A-theory/presentism, or any serious objections to B-theory. So I feel like B-theory is the rational choice.

I know you see this differently than I do. I'm curious to know what problems for B-theory you see, and whether you think the four problems I've alleged against A-theory don't really bite.

About your other objection to my view --- the point about colocation: You're right. I did misread you. I thought you were saying that I'm committed to the view that there are infinitely many colocated objects after the pipe is cut out from the larger pipe of which it is originally a part. But instead, you were saying I'm committed to the pipe being each such object before the pipe is cut out --- in fact, while the pipe is still a part of the larger pipe.

I plead innocent. I don't accept that there exists any blowgun (or child's toy, or club, etc.) until after the pipe has been made suitable to be used as a blowgun (or child's toy, or club, etc.). So it's not a blowgun (etc.) until it's been cut out. As far as I can tell, this explanation is consistent with my stated view.

Unknown said...

Dr. Pruss --

You asked what being-identical-now is. I know of two ways to explain what a property is: by giving examples of its instances and non-instances, and by defining it in terms of more fundamental properties.

So first, for an example of an instance of being-identical-now, take the clay and the statue that is made of the clay at the time when the statue is intact. Or take the pipe and the blowgun, if the pipe has already been cut out and used to shoot a dart, but the sights haven't been added yet. For a non-instance, take the clay and the statue before the statue has been sculpted or after it has been smashed. Or take the pipe and the blowgun before the pipe has been cut out or after the sights have been added. Or heck: take the Eiffel Tower and a banana.

Now the second way: defining [... are identical now] in more fundamental terms. I'd say what it is for it to be the case that x and y are identical now is for it to be the case that now, x and y are identical.

Maybe I should go on to define this more fundamental predicate, [... are identical], that shows up in my definition of [...are identical now]? So: what it is for x and y to be identical is for x and y to be numerically distinct from all the same entities.

So now I've explain the sense of [... are identical now] in each of the two ways in which I know how to explain the sense of a predicate. Doesn't that work?

Maybe someone will think that the first of the two explanations I just offered didn't work --- i.e., maybe someone will object that he/she can't conceptually find any salient relationship (plausibly expressed by the phrase "... are identical now") which unites my alleged instances and distinguishes them from my alleged non-instances. I don't find myself in that boat personally. I think it's just about as easy to conceptually identify being-identical-now as it is to identify being-side-by-side-now or being-old-now. So maybe the objection is broader --- an objection to the existence of any properties with the form being-F-now?

But even if the first way of explaining being-identical-now didn't work, the second way still should.

Angra Mainyu said...


Are you suggesting an error theory of many common expressions?
For instance, if I say that I’m typing on a keyboard, would that be false, according to the theory?

I see the issues as issues of vagueness of human language, not reality.

For instance, regarding Heath’s point about running the argument about when the object acquired the property of being arranged blowgunwise, I don’t see why there would be any I don’t see how an object would ‘magically’ appear if there are blowguns, pipes, computers, etc., or how the matter would change. As far as I can tell, if there is a pipewise arrangement of particles used to (say) carry water, then there is a pipe. Blowguns, pipes, and the like are arrangements of particles (though that’s an empirical finding), perhaps with certain functions (though that depends on how one uses the words; common usage may not be precise enough, and/or there may be more than one such usage, etc.).

Also, these issues seem to be present in at least most of our talk about the world around us (roughly, concreta), not specially about artifacts.

On that note, we may consider words like ‘star’, ‘planet’, ‘exoplanet’, ‘asteroid’, ‘mountain’, ‘hill’, ‘river’, ‘creek’, ‘lake’, ‘ocean’, ‘sea’, ‘lagoon’, etc., and ask exactly how round an object would have to be in order to be a planet (even when the new definition, I’d say the term is not precise enough for there to be an answer to any arbitrary degree of precision), or the exact length, surface area, salinity levels, etc., that determine whether something is a sea, ocean, river, etc., and we get the same result.

But I think that there are oceans, rivers, etc., and someone who does not know about particles (or who doesn’t need such terminological precision) may properly include them in an ontology; on the other hand, if one has included ‘arrangement of particles that interact in such-and-such way’ (where the 'such and such’ is a more precise description of a river than calling it 'river’), then adding 'river’ to that ontology would be superfluous at best, and mistaken at worse (if there is a belief that somehow the river is something other than the arrangement in question).
That aside, a description in terms of the particles we know need not be the most precise description that can be provided given sufficient knowledge and computing power (e.g., in the future, some smaller particles might be found, and the particles we know of might be arrangements of those smaller particles, etc.; maybe it’s turtles all the way down, maybe not).
One may also run the argument in the case of, say, elephants, lions, chimpanzees, etc.

In any case, as I see it, none of the above vagueness is in the territory, but in our maps so to speak.

Regarding the plumber example, my take on it is:

You shot a dart out of a section of pipe. Depending on how one uses 'blowgun', one may or may not say that it was a blowgun, or a makeshift blowgun, etc., but the pipe of course didn't actually turn into anything. And if one uses 'blowgun' in a way that makes the claim that you shot a dart out of a blowgun true, then either it was a blowgun in the first place, or there is no objective fact of the matter as to when it became one (unless one stipulates it; I don’t think that there is a precise enough meaning of ‘blowgun’ shared by all competent English speakers that would yield a unique answer).

Regarding the legal question, the answer is that Mr. Smith didn't become a blowgun owner. The law uses the word 'blowgun` in a way that would not make the install pipe a blowgun (and it would be a non-issue in court). Also, no, you did not violate your contract with Mr. Smith (also, a non-issue in court).

Alexander R Pruss said...

With Sider, I don't believe purely logical vocabulary, like the existential quantifier our identity, suffers from vagueness. That leaves basically two options: an extremely wide ontology, basically 5D universalism (any partial function from worlds to filled subsets of their space-time defines an object), or a very sparse ontology. I go for the latter.
I don't want an error theory of ordinary language. Rather, I think the philosopher has a stricter, "more literal" quantifier, and this is a philosophical blog, so that's how I use it. The quantifier in ordinary language doesn't cut nature at its joints.

Angra Mainyu said...

I’m not sure I understand, but I’m getting that you don’t propose an error theory, so ordinary claims like ‘the suspect killed the victim with a pipe”, are sometimes true, and then the same goes for things like ‘there is a pipe over there’, etc.

Philosophers learn quantifiers like everyone else, but you’re suggesting (if I get it correctly) that the claims above are all false in the sense of ‘exists’, ‘there is’, etc., used in philosophy.
But if so, I wouldn’t call this philosophical sense ‘stricter’, or ‘more literal’; that would seem to indicate that literally speaking, there are no pipes, but the meaning of the word ‘pipe’ is given by common usage, and I don’t see anything in the ordinary meaning(s) of ‘pipe’ that would require an ontological commitment of something somehow above and beyond particles and perhaps a design purpose.

So, I would say that if philosophers mean something different from ordinary folk when they say ‘there are pipes’, so such claims are false in the philosophical sense of ‘there is’, but not in the ordinary sense, then the philosophical usage is not literal.

But literal or not, of course if you use expressions like ‘there is’ in a technical sense that differs from the ordinary sense, the matter of whether there are pipes, etc., is a different one from what I thought it was. I concede I don’t know what this sense is, but I would say that in the ordinary sense of the word, it’s not a problem (and if it were, it seems we would have an error theory).

Regarding whether strictly logical vocabulary is vague, my take is that it’s not ‘exists’ (in the ordinary sense) that is vague per se, but the terms used in combination with it, and as a result, the corresponding sentences (I don’t know about the technical sense of ‘exists’, though, since I'm not familiar with it).

In any case, it seems that the argument you make can still be mirrored for things other than artifacts, like rivers, lakes, oceans, planets, stars, and if the conclusion is correct in the case of artifacts (i.e., they do not exist in the technical) sense of ‘exists’, I don’t see why it wouldn’t work in the case of those alternatives.

Granted, I’m not sure what you mean by ‘exists’, so that makes it difficult for me to assess the matter, but your argument seems to appeal to ordinary usage of terms, and apparently the difficulty of pointing to a first moment at which there was a blowgun. The same kind of appeal can be used in the case of the things I mentioned above.

It can also be used in the case of biological organisms.

For instance:

There were no elephants (or chimps, etc.) on Earth 1 billion years ago. Let’s take a fixed t0 about a billion years ago, and move forward one Planck time at a time, tn=t0 + n Planck times.
What’s the smaller n at which there are elephants on Earth?

As I see it, there is no objective fact of the matter in either case; the word ‘elephant’ isn‘t precise enough in this context, and if one tries to find a first n, even hypothetically, a number of issues present themselves.
Eventually, if people were to find animals in the fuzzy the elephant/no elephant boundary, new words would be coined (probably), and the meaning of 'elephant' would become more precise, but that would be a change in meaning.

That said, I realize I may be missing something here due to the different meaning of the existential quantifier that I’m not familiar with, so perhaps there is a difference between artifacts and rivers, mountains etc., or between those and elephants, cats, etc., in which case I would ask what the difference is (i.e., why the argument would work in one set of cases but not the others, if that’s what happens).

Michael Gonzalez said...


Let me address your points backward, if I may:

1) I wasn't speaking of the pipe when it was still part of a larger pipe (I'm not sure how you got that from what I said). You said that the, sufficiently cut-down pipe is both a plumbing pipe and a blowgun. And I'd say that commits you to affirming that the object is EVERYTHING that it could be without modification. That seems patently false. The view I expressed seems more plausible: That the object had a purpose when it was manufactured, and that that initial purpose holds as a description of "what it is" until someone purposely puts it to new purpose (or modifies it, in which case there is a new "initial").

2) A-theory is the intuitively obvious position with regard to time and becoming. That our ordinary language coheres with A-theory and strongly rejects B-theory is indicative that part of our cognitive apparatus includes tensed considerations and temporal becoming. Since these same cognitive apparatus are what allow us to think metaphysically, it seems to me that the intuitively primary form (evinced by our ordinary language) should hold unless there are strong defeaters. Your "4" attempted defeaters are actually only 3 (truthmakers, predicate, and artifacts). And they don't seem to work. It is in fact true now that dinosaurs did exist. This doesn't require some special new predicate or brute necessity, it just requires that it used to be presently true that dinosaurs exist, and it is now true that that time has passed. And I see no force at all behind saying that objects don't exist on a presentist view. I've addressed Pruss' point directly, and have not encountered any defeaters so far. So A-theory seems rather unscathed by your criticisms.

3) B-theory on the other hand, faces numerous problems. For example, a person does not persist over more than one instant of time (even on a "worm" interpretation, the segments of the worm have different desires, beliefs, and even powers, which makes them fundamentally different people). Continuity of consciousness and freedom of the will both seem to go out the window on B-theory. Moreover, the basic intuition of temporal becoming (see point #2) argues strongly in favor of A-theory. We intuitively believe that the past is gone, and the present is what's real. This gives us our moral accountability, as the same person who once committed a crime or a praiseworthy action. If it is the case that that criminal or praiseworthy person exists eternally at a different location than I do, then it is not the case that I should be punished or praised for anything that other person did.

Finally, the initial motivation for B-theory (interpretations of STR) has been shown to be wrong. It was originally due to verificationism, which Einstein simply took for granted (it was the Zeitgeist of his era), but which has been shown to be not only false but self-contradictory. Philosophers and physicists have tried to recover a version of STR that isn't verificationist, and what they come up with is basically Neo-Lorentzianism, which is A-theoretical in nature.



Alexander R Pruss said...

Your remarks on persons seem to conflate B-theory with one particular eternalist theory of persistence: exdurance. What you say does not apply to perdurance (then there is one person with parts at different times; but there need be nothing wrong with slapping me on one wrist for what I did with my other hand), endurance (which acknowledges the person as wholly present at every time in her lifetime) and theories on which persons are four dimensional but have no temporal parts.

Alexander R Pruss said...


Ordinary English has surface-grammar existential commitment to all sorts of things that, on reflection, many ordinary speakers probably wouldn't want to be credited with belief in: holes, shadows, properties, average plumbers, etc. Nonetheless, when one ordinarily says that the average plumber is different from the average metaphysician, one says something true. But there is a kind of metaphor-of-reification that is being used in talk of the average plumber and average metaphysician, and I think something similar is true in the other cases.

Compare the word "fish". For centuries, the word was used inclusively of whales. When people hundreds of years ago said: "There is a big fish off the starboard bow", they said something true, even though it was a whale. But eventually biologists realized that the natural kind whose extension best matched people's usage of the word "fish" did not include whales. This does not mean that ordinary people said something false. Rather, they used the word "fish" to denote a non-natural kind, maybe fish-or-fishlike-marine-mammal (I don't think they'd consider an otter a fish, hence the "fishlike"). But when we want to do biology, that's not a useful category.

Likewise, the existential quantifier of ordinary English does not cleave nature at the joints, and while very useful in daily life, it's not so useful in metaphysics. So we replace it with a more "natural" quantifier that matches ordinary usage to a significant extent.

Alexander R Pruss said...


As for your list of things, I would believe in particles or fields (if we ended up with particle- or field-based physics) and organisms. No galaxies, planets, continents, molecules, etc. Here the avoidance of vagueness drives me. You might think that organisms involve vagueness, too. But I say it's only epistemological vagueness. Each organism (tree, human, etc.) has soul. And there is no vagueness whether something with soul exists.

Here's what I meant by gesturing at Sider's argument about vagueness and logical terms. Consider statements like: "There are exactly n objects", where n is some finite number. Such statements can be phrased entirely using purely logical vocabulary: existential quantifier, conjunction and identity. Thus there shouldn't be vagueness as to how many objects there are.

Unknown said...

Michael --

Here's a long response:

1) In your last post, you used the phrase "The piece of pipe that you are using in your plumbing." That's where I got the idea that it hadn't been cut out yet. If it had already been cut out, then how would I still be using it in my plumbing?

2) I agree that it's counterintuitive that the cut-out pipe is each of the things it might possibly be used as. So I'd say that suitability-for-use-p is not enough to qualify something as a p. It might also be necessary that at some point, someone comes along and actually uses the object (or at least thinks about using the object) as a p. If that's right, then the cut-out pipe is not (say) a club, unless eventually someone comes along and thinks of it or uses it as a club. So as far as Dr. Pruss's scenario lets us know, my view implies that the cut-out pipe is just a pipe and a blowgun --- not a club, a baton, a baseball bat, and so forth.

3) You said, "A-theory is the intuitively obvious position ..." Is there a certain proposition P such that (i) it is intuitively obvious that P and (ii) it is intuitively obvious that the sense on which P is obvious is one on which it logically entails A-theory? If so . . . then which proposition P is like that? If you think there is one, could you please write it out?

Take the propositions [There are no pterodactyls on earth] and [The past is not real]. Maybe each of these propositions is intuitively obvious. But so long as the "is" in them is tensed, these two propositions are 100% compatible with B-theory. As a B-theorist, I have no objection to the claims [There are (now) no pterodactyls on earth] and [The past is not real (now)]. The propositions in question would be incompatible with B-theory if the "is" in the relevant sentences was tenseless ---- for of course, B-theory entails that that there are (tenselessly) pterodactyls and the past is (tenselessly) real. So if when you say "A-theory is intuitively obvious," you're relying on the sort of propositions I've just mentioned, I think your position faces two problems: (i) it's not obvious that those propositions are tenseless, and yet if they are tensed then they aren't incompatible with B-theory and (ii) A-theory itself strongly suggests that the propositions are in fact tensed.

But you never said you were relying on that sort of proposition for your claim that A-theory is intuitively obvious. I don't mean to impute them to you. I'm just asking, which intuitively proposition(s) do you rely on? (Again, could you please write out the intuitively obvious proposition which obviously entails A-theory?)

4) You said,

"That our ordinary language coheres with A-theory and strongly rejects B-theory is indicative that part of our cognitive apparatus includes tensed considerations and temporal becoming. Since these same cognitive apparatus are what allow us to think metaphysically, it seems to me that the intuitively primary form (evinced by our ordinary language) should hold unless there are strong defeaters."

Angra Mainyu said...


I don’t think that nominalizations imply ontological commitments; for instance, I would say that there are green apples (which is true, also speaking in ordinary English), and I think that’s enough to properly say that there are apples that instantiate the property of being green (i.e., I don’t think we need to add an entity ‘property of being green’).

Regarding the whales, I do agree that the claim was true, and that the meaning of the word ‘fish’ was different. I don’t know that ‘whales’ or ‘fish’ are natural kinds, though.

In any case, regarding the vagueness of the concepts, it seems it applies to the words as used by scientists as well; in other words, even in that sense, as far as I can tell there is no first Planck time at which there is a whale, or a fish.

I get the point that you replace the usual quantifier with one that cuts nature at its joints (or reality, etc.), but I’m not sure what that alternative quantifier means.

Regarding the other cases, thanks for the explanation. So, the issue is not about artifacts only, but about a large number of other things. There is still the question of, say, particles, and elephants. Regarding particles, it seems to me that if there are turtles all the way down, the same argument would apply to particles as well, and I don’t think we’re in a position to tell at this point.

As for elephants, etc., I don’t agree that there are souls, and if there aren’t, the same argument that applies to mountains, planets, rivers, etc., would apply to elephants as well. But I’ll try to to run the argument assuming there are souls later.

Regarding Sider’s argument and the number of objects, my view is that the vagueness may well be in the ordinary term ‘object’. But even assuming the term ‘object’ does not have such vagueness, other terms do, so there may not be a fact of the matter as to the number of elephants, mountains, etc.

Unknown said...

So the argument seems to be:

(Q1) Our ordinary language strongly coheres with A-theory.
(Q2) Our ordinary languages strongly rejects B-theory.
(Q3) Facts Q1 and Q2 are strongly indicative that part of our cognitive apparatus includes tensed considerations and temporal becoming.
(Q4) These same cognitive apparatus are what allow us to think metaphysically.
(Q5) So (from Q3 and Q4) the intuitively primary form (evinced by our language) should hold unless there are strong defeaters.

I'm having a hard time with this argument. What do you mean by "coheres" and "rejects" in Q1 and Q2? Do you just mean that typically, when we think/speak in a spoken natural language like English and we use some word synonymous with "is", we express a tensed rather than untensed predicate? Do you mean that we typically affirm sentences that are true on their tensed readings but which would not be true on any 'untensed' reading if there were such a thing as an untensed reading? Do you mean that we do not typically affirm sentences that are true on an 'untensed' reading but which are not true on a tensed reading?

If that is not what you mean by "coheres" and "rejects," then what do you mean?

Anyway, I see why Q3 is almost certainly correct, given Q1 and Q2. Q4 also looks good. I agree that our overall cognitive apparatus is what allows us to think metaphysically.

What I don't get is Q5. My first problem is, I am not sure what Q5 means. You say "...the intuitively primary form ... should hold." What does it mean for an intuitively primary form to 'hold'?

Maybe Q5 is equivalent to this:

(Q5') So (from Q3 and Q4) there is a form of the "is" predicate which is intuitively primary and it is evinced by our language and we should believe that it is primary unless we have strong defeaters for this belief.

If that is equivalent to Q5, then I have three objections:

First, Q5' doesn't follow logically from Q3 and Q4. Really, I don't see how to get from Q3 and Q4 to Q5.

Second, I'd agree with Q5' if it read: "If there is a form of the "is" predicate which is intuitively primary and it is evinced by our language, then we should believe that it is primary unless we have strong defeaters for this belief." But Q5' doesn't say that. It asserts that there is an intuitively primary form of "is" evinced by our language.

I'm not sure if that is true or false, because I'm not sure what is meant here by "primary". Do you mean "expressive of the most metaphysically fundamental identity (or existence) relationship"? If so, then I find it doubtful that I have any uses of "is" in my lexicon such that it is intuitive that they are primary. It's doubtful that my ordinary intuitions go metaphysically deep enough to tell me whether what my ordinary uses of "is" express is or is not metaphysically fundamental.

Heath White said...

the existential quantifier of ordinary English does not cleave nature at the joints, and while very useful in daily life, it's not so useful in metaphysics. So we replace it with a more "natural" quantifier that matches ordinary usage to a significant extent.

Except it doesn’t match ordinary usage at all. There are “No galaxies, planets, continents, molecules, etc.” But there are pea plants, though no pea pods, and I am not sure about peas. Definitely no pipes or blowguns.

Here is an interpretation of what is going on that I believe predicts all the same results but has a much less logic-valorizing feel. The logical quantifiers range over the non-vague objects in the world, which we can label “logical objects.” This is a very small set of what we ordinarily call objects and a very small part of reality. The logician uses the English language in a highly distorted way: when he says “there are” he means “there are logical objects which are” and when he says “all” he means “all logical objects”.

Thus, in logic-speak, there are no blowguns, while in English there are blowguns. This is not because logic is an improvement on English but because it is a restriction of it.

The case that logic-speak improves on English seems to rest on the claim that English does not cut nature at the joints; this is because nature is not vague. I don’t know what the argument for the latter would be unless it were known apriori that our non-vague logic had to capture nature. At that point we are arguing in a circle.

In any case I think Wittgenstein said all this some time ago.

Alexander R Pruss said...


Yeah, the match with ordinary language isn't great. :-(

And, yes, one of my main programmatic assumptions is that at the fundamental level there is no vagueness.

Unknown said...

On the other hand, if you don't mean that by "primary," then (as my third objection) I don't see how Q5' entails A-theory. After all, B-theory is perfectly compatible with the view that a tensed "is" is 'primary' in the sense of 'first learned by children' or 'most easily, frequently, and naturally used'. B-theory just can't accept that the tensed "is" --- used without a temporal operator --- express the most primitive property/relationship expressible by any of the available ways we typically use "is".

So I'm asking you for three things: for clarification on your terms in Q1, Q2, and Q5; an explanation of how to get from Q3 and Q4 to Q5; and an explanation how to get from Q5 to A-theory.

Alright, you then explained:

"Your "4" attempted defeaters are actually only 3 (truthmakers, predicate, and artifacts). And they don't seem to work. It is in fact true now that dinosaurs did exist. This doesn't require some special new predicate or brute necessity, it just requires that it used to be presently true that dinosaurs exist, and it is now true that that time has passed. And I see no force at all behind saying that objects don't exist on a presentist view. I've addressed Pruss' point directly, and have not encountered any defeaters so far. So A-theory seems rather unscathed by your criticisms."

First, what about my fourth defeater --- the concern about an extra brute necessity?

Second, I haven't yet done much explaining of my point about truthmakers. Take the sentence "Dinosaurs used to exist." What makes that true? In virtue of what is it true? Is there some corresponding fact floating out there --- the fact [Dinosaurs used to exist] --- and the sentence "Dinosaurs used to exist" is true because it corresponds to that fact? If not, then is there some property --- say, the property of [having once coexisted with dinosaurs] --- that some presently existing thing has, and the sentence "Dinosaurs used to exist" is true because it corresponds to some presently existing thing having that property?

There's gotta be something in reality that "Dinosaurs used to exist" corresponds to and which makes that sentence true. Whatever that thing is, that's what I mean by the truthmaker for the sentence.

Non-logical sentences aren't true in a vacuum. Any such sentence that is true has a truthmaker.

Yet, if the truthmakers for sentences about the past are 'facts' or a 'properties', then think how many facts and properties of this kind there must be! Enough to differentiate between all the true and false claims that can possibly made about the past! These facts or properties are the 'reams of abstract entities' to whose existence I was claiming that A-theory is (on its best interpretation) committed. I take this commitment to comprise an objection to A-theory both because (i) all these facts add a lot of complexity to theory (viva simplicity!) and (ii) these disembodied facts and properties about the past --- with no genuinely existing past to correspond to --- seem, frankly, a little weird.

There are other problems, too. Like, there must be some law which sees to it that necessarily, for any proposition P, if now P, then in the future, there will be one of the 'past-making' facts/properties corresponding to the present fact that now P. For example, right now at 10:45 am, I am typing. In the future, the sentence "I was typing at 10:45 am" will be true. So in the future, there will have to be one of these 'pastmaking' properties or facts which sees to it that "I was typing at 10:45" is true. So there's got to be some law which sees to it that --- whatever these pastmaking facts or properties are --- the things we do now lead to some appropriately corresponding pastmakers existing in the future. This law looks like a brute necessity. So it's bad.

Unknown said...

Spelled out, that was my point from my earlier post about reams of truthmakers. Does it seem to you that A-theory isn't committed to the existence of pastmakers like I've described? If not, then in virtue of what do you say sentences like "There used to be dinosaurs" are true?

Third, the extra fundamental predicate A-theory is committed to: First, I introduced this predicate as differentiating between pastmakers and ordinary, present states of affairs. Surely you agree that there is some predicate that pastmakers satisfy but which ordinary, present states of affairs don't? (If two classes of things are different, then there is some predicate that one class satisfies and the other doesn't. So I'm just saying: pastmakers and present states of affairs are different. So there's a predicate that differentiates them.) If you do think this, then what do you think this predicate is? You said your view didn't need a new fundamental predicate --- so do you think the predicate in question is non-fundamental; i.e., reducible? Then which reducible predicate is it? What does it reduce to?

You could hold this view: pastmakers are just the same as present states of affairs, except they have an ontologically real "in the past" operator stuck on them. In that case, there is some predicate which uniquely describes this "in the past" operator --- a predicate which expresses its being what it is --- and that is the new fundamental predicate accrued by the view.

Fourth and lastly, about truthmakers: You said that you had responded to Pruss's argument. In my post on April 22 2013 11:14 am, I've responded to your response to Pruss by offering a second version of the paradox that (I thought) avoided your objection. Apologies for not flagging it "Michael" --- in a thread this long, I really should mark each post with the person it's addressed to.

Next, you argued,

"B-theory (. . .) faces numerous problems. For example, a person does not persist over more than one instant of time (even on a "worm" interpretation, the segments of the worm have different desires, beliefs, and even powers, which makes them fundamentally different people). Continuity of consciousness and freedom of the will both seem to go out the window on B-theory. Moreover, the basic intuition of temporal becoming (see point #2) argues strongly in favor of A-theory."

Forgive my ignorance: define "persist" in your first point?

I don't accept that on a worm theory, the fact that different segments of the worm have different desires/beliefs makes them different people. That's because I don't accept that any proper segment of a person-worm (as opposed to the whole person-worm) is a person. A forteriori, different segments aren't different people.

Why do consciousness and freedom go out the window on B-theory? I don't see that.

Unknown said...

Why does temporal becoming argue against B-theory? I'm a B-theorist, and I believe in temporal becoming. I don't see any difficulty holding both.

"The past is gone, the present is what's real." I grant that those are true. Do you mean that these claims are logically incompatible with B-theory? They would be, only if the "is" in them was tenseless. But an A-theorist will think that the "is" in them is tensed. So an A-theorist can't reasonably view these claims as logically incompatible B-theory. Then again, your next comment makes me think that maybe you don't see them as logically incompatible with B-theory; you just think they lead to a problem in moral theory:

"If it is the case that that criminal or praiseworthy person exists eternally at a different location than I do, then it is not the case that I should be punished or praised for anything that other person did."

Again, I don't accept that some past proper segment of me is a person at all --- much less a different person than I am.

You mentioned that the relativity-based motivations for B-theory have been debunked. I have to plead ignorant about that. For now, I'm happy just to accept B-theory on the basis of the four motivations I've listed.

Cheers, and thanks for the stimulating debate,

Unknown said...

Michael -- my last response to your thoughts is in five sections. The first at 10:26 am, the last at 10:42. I couldn't post them fast enough to get them all together, so there are other posts interspersed. Should still be easy to track, I hope.

Angra Mainyu said...


Assuming dualism, you say that the argument wouldn’t work for biological organisms because any of them has a soul, and there is only epistemic vagueness.

But I think there are a number of issues:

1. That entails that the word ‘soul’ is so precise that there is always a fact of the matter as to whether there is a soul. I don’t see why that would be so. In fact, it seems implausible to me.
If one is to learn the meaning of ‘soul’ by means of pointing to (assumed) paradigmatic examples, then different people will learn with very different examples, and come up with different intuitive grasps of the term (e.g., many would not say that trees have souls). On the other hand, if you have a definition of ‘soul’ in terms of more precise terms, I would like to ask what that is in order to assess the matter.

2. Even assuming the word 'soul’ is so precise that there is always a fact of the matter as to whether there is a soul (or two, etc.), there would still be semantic vagueness as far as I can tell, and that’s the same kind of vagueness I can see in the other objects (e.g., pipes, mountains, etc.; the vagueness is not in the territory, but in the maps).
For instance, let’s consider the elephant case. Even if elephants have souls, and even assuming ‘soul’ is precise enough so that there is always a fact of the matter as to whether a certain soul exists, there may still not be a fact of the matter as to whether an elephant exists, since there may not be a fact of the matter as to whether a certain entity with a soul is an elephant, due to the vagueness in the term ‘elephant’, and even assuming no vagueness in the term ‘soul’.

Alexander R Pruss said...


Here's one way the "logical" quantifier matches ordinary usage in a significant way. It includes all the objects that are worth caring about for their own sake, all the objects that are properly lovable in themselves. On my view, we should not love rocks, the earth, nations as such. It is appropriate to love the people of a nation, and even to love them qua constituting the nation. It is inappropriate to love Michelangelo's David, but it is appropriate to love Michelangelo for arranging matter Davidly. Artifacts are in this sense moral extensions of their makers: they are not the proper objects of love, but rather we should love their makers for producing them. And of course, given theism, peapods are also artifacts, and so we can love their Creator for arranging peas and particles/fields peopodwise. But peas (which are, I assume, embryonic pea-plants) are lovable as such. They have an a flourishing which we can further by planting them or (much more controversially) by eating them.

I don't know how lovable particles are.

Unknown said...

Heath and Pruss ---

A two-part post:

Suppose we let "Ontological Vagueness" (OV) be the following sentence:

"There is vagueness in nature."

I think I know a decent argument against OV. It starts with definitions:

One sentence is more 'expanded' than another sentence if, roughly, the two sentences express the same fact but the former sentence carves reality at more joints than the latter sentence does. For instance, suppose we move from "That's a square" to "That's a regular quadrilateral" to "That's an equiangular, equilateral four-sided polygon" to ... and so on until there's no farther to go (not even if we invent new words to do it!). We can call this the 'expansion series' for the original sentence. As we move down the series, we are moving from less expanded forms of the original sentence to more expanded forms of that sentence. If there is a last sentence in this series, then the ultimately expanded form of "That's a square" is that last sentence.

Call a sentence a vagueness-sentence if for some predicate F and noun "X", it logically entails the sentence "[~(Definitely, Fx) & ~(Definitely, ~Fx)]".

Now take a given sentence S. There may --- or may not --- be some item R in the expansion series for S which has both of the following properties:

(i) R is not a vagueness-sentence;
(ii) there is no vagueness-sentence at any point in the expansion series for R.

If there is a sentence R of this kind, then it is a 'vagueness-stopper for S'.

Now we're through with definitions. Next stage of the argument:

I take "There is vagueness in nature" to mean "There is some true sentence S for which there is no vagueness stopper." Since we've used "OV" to name the sentence "There is no vagueness in nature," we can call this latter sentence OV*. Since OV* and OV mean the same thing, therefore if we show that OV* is false, then we thereby show that OV is false.

There are exactly two ways in which OV* could be true. Either

(i) there is some true sentence S whose expansion series never ends (each sentence in the series can be further expanded) and no matter how far along it you go, you always eventually get to another item in it that is a vagueness sentence, or
(ii) there is some true sentence S whose expansion series terminates with a vagueness-sentence.

Here's an objection to (i): That's really complicated. It implies that reality is so jointy, that no sentence can carve all the joints. Because, you see, if you did reach a sentence that carved all the joints, then that sentence could be no further expanded. Contra (i), the expansion series would stop there. So (i) implies that there is no such 'omni-joint-carving' sentence.

Unknown said...

So the simplicity criterion counts against (i). There are some other, complicated objections that can be raised against (i), which have to do with necessity and aprioricity and introspective accessibility. But I won't mention those hear unless someone is curious.

There's another objection that counts against both (i) and (ii):

If the operator "Definitely ..." could be defined in terms of any other more basic operator(s), then every vagueness-sentence would have a vagueness stopper. You can see how that would go: Just take the vagueness sentence and replace each instance of "Definitely ..." (or "Indeterminately..." if you're using that as equivalent to "Not definitely ...") with its definition in terms of more basic operators. The resulting sentence would not be a vagueness-sentence, and it would not logically entail any vagueness sentence.

So (i) and (ii) imply that "Definitely..." cannot be defined in terms of any other more basic operator(s).

Well, that's bad. It's bad in three ways.

First, it implies that we have this extra, irreducible feature --- [Definitely ...] --- in our fundamental language, which if OV* was false, we could make do without. The simplicity criterion leads us to eschew such barnacles when feasible, so it leads us to believe that OV* is false.

Second, the irreducibility of [Definitely...] implies that the proposition [For any P, (Definitely P) --> P] is not a theorem of standard first-order or second-order logic. Nor is it explicable in terms of true fact more fundamental than itself. And yet ... it's necessarily true! So it's a brute necessity. So the irreducibility of [Definitely...] saddles us with an extra brute necessity. We should seek to avoid those.

Third, [(Definitely, P) --> P] is a priori. But how could it be a priori, if it's not a theorem of logic and it doesn't follow logically from any introspective observation nor any truths about accessible constituents of our own minds? Rather, the aprioricity of this claim shows that it is a theorem of logic, and hence that [Definitely...] must be reducible.

This strikes me as a strong trio of considerations against (ii) and an even stronger quartet against (i). So we have powerful reasons to disbelieve OV*. Since we have these, and since meanwhile we don't (as far as I know) have any powerful reasons to believe OV*, therefore we should disbelieve OV*. OV* and OV mean the same thing. So we should disbelieve OV. So we should disbelieve that there is vagueness in reality.

This is the first time I've written out this argument. Does it seem sound to you?

Heath White said...


I have the following difficulty. Suppose (contrary to fact) that France had some exact mathematical border. Call the property of having a shape of exactly this form, being France-shaped. Still, I would want to say, France is (vaguely) hexagonal. And in my mind, “there is vagueness in nature” means “there are some vague but true sentences” which I think is the same as, or anyway close to, “some sentences are vaguely true.”

Now about your expansion series of sentences. Is “France is France-shaped” in the expansion of “France is hexagonal”? If so, fine … but then (a) it is unclear to me in what sense these report the same fact, and (b) so long as the latter counts as (at least vaguely) true I will continue to say there is vagueness in nature, and the existence of a vagueness-stopper has nothing to do with it. If not, fine … but then I guess “France is hexagonal” has no vagueness stoppers and that doesn’t strike me as terribly problematic.

Michael Gonzalez said...

Pruss: On perdurance, it is still the case that the event is occuring eternally and changelessly, as are the events of right now. So, if I'm having thoughts and desires and beliefs at t1 and different thoughts, desires, and beliefs at t2, but neither goes out of existence, in what sense am I a single person? In what sense is it that I, who am sitting at my desk, am the same person who at another location, with different thoughts, different beliefs, and different desires is committing a crime?

As for "endurance" or any other theory that has me "wholly present" at all times; how is it that I am not having all my thoughts at once? Think of being in love with someone now, who you had previously been indifferent to. If I am wholly present, four-dimensionally, as a person, throughout all of the times of my existence, then how do I not experience both (contradictory) emotions together?

Michael Gonzalez said...

Davies: We'll need to E-mail or something, sometime, because there is absolutely no chance that (or any of my other four-dimensional parts) can respond to all of that. I'm sorry. I'm not even sure where I'd begin.

Unknown said...

Heath --

Thanks for the response. I think we may be talking at cross-purposes. In ordinary English, the word "vaguely" often means something like "more or less" or "approximately". I don't take this to be the same as the sense philosophers use for "vaguely" when they're talking about sorites series and indeterminacy and that sort of thing. When I say "there is vagueness in nature", I'm using the philosophical sense of "vagueness" --- not the 'more or less' English sense. But would I be right in thinking that when you say "there is vagueness in nature", you're using something like the 'more or less' sense of "vaguely"? If so, then I'm afraid we're saying two different things.

I'm going to assume that you're using "vaguely" in a 'more or less' sense, and see where that takes me. Thus:

I didn't mean to weigh in at all on the question of whether there is vagueness in nature in the sense in which you are using the words. I'm actually not sure in which of two senses you are using them. You might mean:

There are some sentences that are more or less true.

Or you might mean:

There are true vague sentences.

I'd agree hands-down with the first of these. But I have to ask you what you mean by "vague" in the second one. "There are true, more or less sentences"? But what is a "more or less sentence"?

At any rate, it doesn't look like these two things you might mean, mean exactly the same thing. Why? Well, the second one entails that there are true sentences, whereas (as far as I can see) the first one doesn't entail that.

About "France is France-shaped" and "France is hexagonal". Nope, the second one is not in the expansion series for the first one, because they don't mean the same thing. But why does that mean that "France is hexagonal" has no vagueness-stopper?

Alexander R Pruss said...

"So, if I'm having thoughts and desires and beliefs at t1 and different thoughts, desires, and beliefs at t2, but neither goes out of existence, in what sense am I a single person? In what sense is it that I, who am sitting at my desk, am the same person who at another location, with different thoughts, different beliefs, and different desires is committing a crime?"

Why is this any less of a problem on presentism? In what sense is it that I, who am sitting at my desk, am the same person who at another location, with different thoughts, different beliefs, and different desires was committing a crime?

But all that said, I don't really get the "in what sense am I the same person" question. There is one same person who is sitting at t0 as is standing at t1 iff there exists a person x such that (a) x is sitting at t0 and (b) x is standing at t1. (Notice that I used no identity claims on the right hand side of the "iff").

Maybe you feel a pull to the idea that where there is one person, there can be only one coherent collection of thoughts. That idea is mistaken, as the Incarnation (Christ has two minds) and the existence of persons with multiple personalities indicates. Maybe you think each of multiple personalities is a different person. That would be mistaken, I think, because multiplicity of personalities comes in degrees, surely, while multiplicity of persons does not.

Heath White said...


I am pretty sure I am using ‘vague’ in the philosophical sense. That is, there are some predicates which admit of borderline cases (‘hexagonal’ and ‘blowgun’ for example). What I believe is that some sentences that employ vague predicates (e.g. “France is hexagonal,” “I once owned a blowgun”) are true.

I also believe, though this is not critical to the argument, that ‘true’ is one of those vague predicates. But leave that aside.

If “France is France-shaped” is not in the expansion of “France is hexagonal”, I do not know what would be. I do not know how to report the same (vague) fact or state of affairs as “France is hexagonal” in any other way except perhaps by further specifying the shape, which is why I came up with my example. If there is no other way to report this fact, then “France is hexagonal” has no further expansion, and we have a series (of one) which terminates in a vagueness-sentence.

Michael Gonzalez said...


3 quick responses:

1) Presentism would say that the person back then has evolved into me, and no longer exists. I am the only "me" that exists, and am the product of all the previous experience, etc. This does not seem possible on a view where all the "me"'s co-exist. (Note: A similar point is often made with regard to theodicies about the problem of evil, since no occasion of evil is ever actually overcome, but persists eternally and changelessly).

2) My "in what sense" question was totally untouched by your example of sitting and standing. A quick definition of "person", which is often used in philosophy texts, is a "substance who possesses desires, beliefs, and powers to act in accord with those belief to achieve those desires". We could tighten that up to "a substance with beliefs and desires", and leave out the "powers" bit. The point is that the person standing at t1 has the belief that he is standing, while the person sitting at t0 has the belief that they are sitting. And this is a belief about their whole body, mind you; not just part of it. Does this not strike you as problematic? That the person is a locus of beliefs and desires and yet has an enormous number of contradictory beliefs and desires all at once!?

3) I don't think Christ did have two minds, nor did he ever indicate that he did in anything he said. But that's surely a separate discussion, so I won't try to open too many cans of worms. As for DID (dissociative identity disorder), there are two possibilities. Either there are separate personalities, in which case it would be proper to treat each as a different person (such as if one personality murders someone, while the others are unaware). Otherwise it is disorder of coherency in the single person, and that would be a form of disorder. But, on your descriptions of the various B-theories, why do we not all have this kind of disorder?

Michael Gonzalez said...

And by the way, just for the record, my point #1 applies to all truth statements. I have never understood why people think there is a problem for presentism when it comes to truth statements about the past. The idea that x "was true" just means that the world as it is now includes the fact that the world used to be some other way. There are causal effects of that (including our knowledge that x was the case), but even if it had no causal effects at all (not sure if that's possible, but even if) it would still be a fact of the world now that the world used to be another way.

Unknown said...

Heath ---

I was taking "... is hexagonal" to mean "... has, as its shape, a six-sided polygon". So I was thinking that "... is hexagonal" was not a vague predicate, since I don't think there is anything vague about having a six-sided polygon as one's shape.

Are you using "... is hexagonal" in a different way --- kinda like "... is roughly hexagonal"?

Unknown said...

Michael ---

I'll leave your argument about persons between you and Pruss. But in response to your question about truthmakers, see my two posts to you on April 23 2013 at 10:38 and 10:41 am, starting with the line "First, what about my fourth defeater" about a third of the way into the 10:38 post and ending with the line "and that is the new predicate accruing to the view" about a third of the way into the 10:41 post. I've done my best to enumerate all the problems that presentism has in terms of truthmakers, and the length of that explanation is only about the length of a single post.

Angra Mainyu said...
This comment has been removed by the author.
Angra Mainyu said...

Heath, (sorry about the spelling error).

The hypothesis about what you call “logical objects”, “logic-speak”, etc., is very interesting.
I would say that the vagueness is in the language, not in the objects (though we may be using ‘vagueness in the objects’ in a different manner, so maybe there is no actual disagreement here).

But that aside, one can try to make some assessments about existence under that interpretation. Let’s 'l-exists’, 'l-there are’, etc., stand for the claims about non-vague objects in the world (i.e., the logic-speak), whereas 'exists’, 'there are’, etc., are the usual English expressions.

Then, going by the given examples, there are galaxies, stars, planets, rivers, etc., but it’s not the case that l-there are galaxies, stars, planets, etc. But now let’s consider, say, oak trees. They exist, but do they l-exist?

The concept of a soul is I think too vague at best (if coherent at all) in this context, or else for some reason I’ve not been able to grasp it. But let’s say it’s the latter; so, the concept has no problem. Also, let’s say that l-there are souls.
Now, even though I’ve not been able to grasp the concept of a soul, I can take a look at assertions about souls usually made by those who grasp the concept, and in that manner reach some conclusions about at least some of the properties a soul would or would not have.
So, whatever a soul is, going by how people who posit souls usually use the word 'soul’, a soul has no DNA, no cells, no bark, no leaves, no branches, no roots, and in fact does not have any volume. But if an entity E has no DNA, no cells, etc., then E is not an oak tree.
Alternatively, one can point out that an acorn is not an oak tree, even if it has a soul.

So, an oak tree is not a soul, nor is it a particle, etc., so it seems to me that even assuming that particles and souls (whatever those are) are logical objects, an oak tree wouldn’t be one of those.

But moreover, it seems that the vagueness argument can be run against the oak tree as it can be run against, say, a planet. For instance, let’s start with an acorn at t0, and let tn=t0+n Planck times, etc., and then ask for the first Planck time at which there is an oak tree, etc. If that works against planets, rivers, stars, etc., it seems to work against oak trees as well.

It seems to me, then, that plausibly oak trees do not l-exist, even under all of the previous assumptions (which I don’t believe in, but for the sake of the argument).

Yet, Alexander’s points entail that oak trees do p-exist (where ‘p-exist’ means that they exist in the philosophical sense).

Given the analysis above, it seems plausible to me that either oak trees do not p-exist, or p-existence is not the same as l-existence (I don’t know what p-existence would be, though).

Angra Mainyu said...


Regarding what’s proper to love, and leaving aside other issues, it seems to me that in what Heith calls ‘logic-speech’, there are no oak trees, no acorns, etc.
The argument works against them too, so even assuming that there are souls and particles, that does not seem to get the result in question.

That said, I would like to ask for more clarification about your usage of the word ‘soul’ (if not a definition, perhaps a way in which I might try to grasp the meaning).
So far, I can (perhaps) tell a few things about what a soul is not, but I’ve not been able to go beyond that.

Alexander R Pruss said...

By "souls" I mean Aristotelian forms. And oak trees probably have them.

The vagueness is purely epistemic: is there in fact an oaken form that informs matter, and if so, how many.

I don't know if there is an answer to the question at which Planck time the oak tree came into existence, because I do not know if time is a part of fundamental reality. But there is an answer to the question of how many oak trees of a particular kind there are.

Angra Mainyu said...


I’ll try to address other issues about souls later if I can, but for now I would raise the following ones:

You say the vagueness is ‘epistemic’, but I don’t see why it’s not semantic, as in the case of pipes, planets, etc.

For instance, there is an oaken form that informs matter, but then:

1. One may ask about the first Planck time at which there is at least one oaken form on Earth, and then there is the issue about the vagueness of the term ‘oak tree’ that results presumably in vagueness in the case of ‘oaken’, and even if ‘Aristotelian forms’ is not a vague term and there are such forms.
If that does not work because of something related to time, then it seems to me that the same reply would block the argument in the case of, say, mountains, or stars.

2. Additionally, there seems to be the issue of when there is an oak tree, rather than just an oaken form. An acorn is not an oak tree, and an oaken form (even if there are such forms) is not an oak tree, under the usual conception of ‘oak tree’.

3. I don’t know whether time needs to be a fundamental part of reality for the argument to work, but I was mirroring the argument in the case of planets, stars, rivers, mountains, etc.; if the argument succeeds in showing that they don’t l-exist in those cases, then I don’t see why the case of an oak tree would be any different.
As far as I can tell, I’m running essentially the same argument.

From another perspective, if a planet is a certain arrangement of particles with certain interactions but the term ‘planet’ is vague so l-there are no planets, then an oak tree (assuming souls, etc.) would seem to me like a certain arrangement of particles plus an oaken form, with certain interactions between them, but it seems that the term ‘oak tree’ is still too vague for l-there to be oak trees (i.e., if the argument works against mountains, I don’t see why not against oak trees).

Maybe I'm missing some basic assumption here?

Heath White said...


"France is hexagonal" is a standard example of a vague sentence in the literature, where ' hexagonal' means ' roughly or approximately hexagonal.'

Note that all empirical hexagons (in geometry textbooks, and so on) would be vaguely hexagonal in this sense.

Unknown said...

Heath ---

Weird. Never came across it. At UT Austin we talked and read a lot about bald people, tall people, heaps of sand, and whether Buddhism was a religion --- but never the shape of France.

So what's an expansion for "France is (roughly or approximately) hexagonal"? Maybe start with "France is such that its shape is saliently similar to that of a hexagon." Then expand "saliently" and "similar" and "hexagon." And so on.

I don't think the resulting sentences would, strictly speaking, be expansions of "France is (roughly or approximately) hexagonal." That's because the "... is an expansion of ..." relation requires exact synonymy and our natural-English terms are typically so nuanced that you can't get exact synonymy between different phrases. So for sentences involving most natural terms, the items in my expansion list will involve non-natural terms. I don't think that's much of a problem for the theory, though, so long as phrases exactly synonymous to natural-English phrases and composed of new, non-natural terms can exist.

On the other hand, is "France is hexagonal" the sort of sentence for which we require a vagueness-stopper? It doesn't seem to have the form "~DP & ~D~P". Sentences of that form were the ones whose vagueness my argument tries to show can be 'stopped'.

So the sentence whose vagueness must be 'stopped' would be: "Neither is France definitely roughly-hexagonal nor is France definitely not roughly-hexagonal."

I'd hold that there is a further expansion for this sentence. The expansion will be very like the sentence: "Neither does France definitely have a shape that is saliently similar to a hexagon nor does France definitely not have a shape that is saliently similar to a hexxagon". But the expansion will probably not be exactly this sentence. Probably the expansion will involve some new, made-up (but meaningful and thinkable) terms.

Does that help?

Unknown said...


Here's a principle: It would be weird for there to be x and y such that there was no significant difference between x and y (other than I-existence) and yet x I-existed and y did not.

Compare a mountain and an almost-but-not-quite mountain. There's no significant difference between them. So it would be weird for one to I-exist and the other not to.

But now consider an organism and an almost-but-not-quite organism. On Pruss's view, the organism has a form as one of its parts. The almost-but-not-quite organism doesn't have one. So there's a significant difference between them. So it's not weird that one of them I-exists and the other doesn't.

I don't think I accept Pruss's background theory about Aristotelian forms, but it seems to me they can do the work Pruss wants them to do here. Yah?

Angra Mainyu said...


Thanks for that explanation. I see some difficulties in the view that Aristotelian forms do the work (even accepting they exist for the sake of the argument), such as:

1. Regarding the principle, it doesn’t seem clear to me in which sense of 'relevant’ the differences relevant.

2. In any case, and going by the example you give, I’m not sure why you think the principle is plausible. For instance:
If the l-existence of objects requires certain precision in the definition, and if that suffices (if not, I would ask for more details on the concept of l-existence), then it seems to me it’s plausibly false. For instance, let’s say a particle l-exists. Let’s say that we define ‘mountain*’ as an object that has between n and m particles (for some specified n and m), which interact in such-and-such ways, etc., and we make the definitions precise to the extent to which we can make talk precisely about particles. Then, it seems to me that mountains would l-exist, even if mountains do not and are similar.

3. Leaving that aside, the original conclusion that l-there are no mountains, etc., is based on an argument that seems to rely heavily on the vagueness of the words. But if vagueness in the meaning of the words supports that conclusion, then the same vagueness seems to affect the term ‘oak tree’, for the following reason:
Let’s start at t0 1 billion years ago and move forward 1 Planck time at at time. We may ask whether there is some first n at which l-there are oak trees (if somehow that’s blocked because of some feature of time, then the argument would be blocked for mountains as well). A crucial point here is that the term ‘oak tree’, like the term ‘mountain’, is not precise enough for that. Even if there is always a fact of the matter as to whether a particular form exists, the problem is that there would seem to be no fact of the matter as to (for instance) which is the first form that is an oak tree form, rather than the form of an almost-oak tree. So, we have forms before some n, and after it.
The question does not need to be about when some specific form, and the difference that is (in some sense, I take) relevant is not present there. Still, it seems to me that even when considering a specific form, I would say that very plausibly the difference is not present in many cases, since the form is there all along (I will address that matter in the next post).

Angra Mainyu said...


This is the continuation:

4. Accepting forms, the proposed principle, etc., and going by the non-mountain/mountain example, there is also the issue that it’s very plausible that the form is not sufficient for the oak tree (for instance) to exist. One may give a number of arguments in support of that conclusion, like:
a. An acorn is not an oak tree, yet it has its form.
b. The form of an oak tree has no leaves, bark, roots, DNA, cells, etc. In fact, it’s an object that occupies no space at all. But in the usual sense of ‘oak tree’, that thing (whatever that is) isn’t an oak tree.
In other words, an oak tree seems to be not just the form or the particles, but some kind of arrangement of particles + the form...but the arrangement is vaguely defined, like the arrangement in the case of the mountain.
So, one may run the argument from an entity with an oak-tree form but which is not an oak tree, to an oak tree, and the result is the same sort of vagueness as in the mountain case. The specific form of that tree is there all along since we start counting, so that does not make the relevant difference, independently of how one assesses relevancy in this context.
Granted, someone might claim that the form of an oak tree is an oak tree, but then that seems to not match the usual concept of ‘oak tree’ (see above), since that would seem to result in an oak tree with no DNA, cells, leaves, bark, roots, branches, and which does not even occupy any space at all. I don’t think that the ordinary term ‘oak tree’ is properly applicable to something like that.
Also, someone might try to say that the form only appears late in the development, but that would seem ad-hoc and also add further evidence against such forms (i.e., if the “pre-tree” would develop normally without the form until, so what’s the form for?). But even if one assumes that, then another problem can be raised (see below):

5. Thought experiment: how about changing from oak tree to non-oak tree while keeping the organism alive?
Granted, present-day technology does not allow that, but with far more advanced genetic engineering, it might be doable (in sci-fi, there are plenty of much more radical cases of metamorphosis, involving entities with complex minds, so at least thought experiments are easy to construct). So, it’s an oak tree at first, but then it ends up being some other plant, as a result of gradual changes. That would mean the form changed from being an oaken form to a non-oaken form. But then, one may ask when the form changed from being that of something that is not an oak tree to that of an oak tree.

Unknown said...


Thanks for the detailed post!

I was taking I-existence to be the property of being something, in the logical sense of the word "something." I.e., I-existence = being some x such that for some y, x = y ---- with the existential quantifier being the one used in logic in both instances.

I'd have a hard time defining my term 'significant' in my proposed weirdness principle. I was just using the term intuitively. Intuitive uses of terms are notoriously hard to define. But I'd say that on my usage of "significant," if one mountain was just slightly bigger than another mountain, that's not a significant difference; whereas if one mountain had a soul and the other didn't (or if one mountain was an active volcano and the other was not) that would be a significant difference.

If that's not clear, then I have worked out a gesture at an actual definition for my term "significantly different." Do let me know if you'd like me to post it.

You mentioned mountains* and mountains as a problem for my weirdness principle. I think Pruss would deny the plausibility of the existence of mountains* (as you've defined them) on the following grounds: If a mountain* is any entity composed of between m and n particles, then define a mountain** as any entity composed of between m and (n + 1) particles. There could be no good explanation as to why possibly mountains* exist but ~possibly mountains** exist, or vice versa. Therefore, either (possibly mountains* exist) and (possibly mountains** exist), or neither (possibly mountains* exist) nor (possibly mountains** exist). But taking the first disjunct sets us on a path to 5D Mereological Universalism, which is implausible. So we take the second disjunct. So it's not possible that any mountain* exists.

(I've never read Pruss saying all that. I'm putting it forward as something which I'd guess he might say --- but I could be very wrong about that.)

So I don't think the mountains* example is a problem for my weirdness principle. From the mere fact that for some mountains*, there are some mountains that are not significantly different than they (or at least, there would be some such mountains, if both mountains and mountains* could possibly I-exist), it seems to follow that there is no good reason why it should be possible for those mountains* to I-exist but not possible for any of the mountains to which they would be so similar to I-exist. So, then, it would be weird if the mountains* existed and the mountains didn't.

About your point (3), Pruss could argue as follows:

Unknown said...

"There's no sense in saying that t is the first Planck moment at which a given mountain exists, because it's apriori that if a given mountain exists at t, then it also existed one Planck unit earlier than t (when, by hypothesis, the mound of earth was one particle smaller). I.e., it's apriori that no single particle makes the difference between a mountain and a non-mountain. Therefore, since if mountains did exist, there would have to be for each mountain a first moment when it existed, it follows that there are no mountains.

"But the same argument doesn't work against things with souls. It's not apriori that if x has a soul at Planck moment t, then x had a soul one Planck unit earlier than t. So if x can't exist without a soul (and it can't), then there's no problem with saying that t --- the moment when the soul first inform's x's body --- is the first moment when x exists.

"Oak trees have souls. Mountains don't. Therefore, from the above reasoning, we have grounds to deny the existence of mountains but not of oak trees."

Note that "oak trees have souls, mountains don't" plays the role of a premise in this argument. The argument doesn't give evidence that oak trees, but not mountains, have souls. So to take this line, Pruss would have to hold that he has independent reason to think that oak trees, but not mountains, have souls. I suspect he affirms very happily that he has some such reasons. (For instance, oak trees can flourish; mountains can't. Oak trees are alive; mountains aren't.)

Pruss could also give this argument against the existence of mountains:

"If mountains exist, then why not mountains' (composites of mountains and the stones on top of them)? If mountains' exist, then why not mountains'' (composites of mountains' and the stones around their feet)? And so on and so on, until you get the result that for any filled regions of spacetime, there is some material object occupying exactly the union of those regions of space time. This result as implausible! So modus ponens to the whole argument! Ergo, mountains don't exist."

Again, the argument does not work against things with souls. Why? Well try the question: "If an oak tree (a composite of an oak tree form and some matter) exists, why not a soul-less oak tree body?" In this case, the two things compared (a matter-soul composite and a soulless aggregate of matter) are so very different that it's not obvious that the second one should exist if the first one does.

I'm not sure whether Pruss would think that an acorn is an "oak tree" in the English sense of the term. He might. After all, Catholics (and many non-Catholics) accept that a fertilized human ovum is a human.

But suppose he doesn't accept that (or, at any rate, suppose you don't accept that). Pruss could just say, "Right. 'Oak tree' doesn't express a natural kind. But there is a natural kind --- one for which we don't have any ordinary English phrase to express it --- which informs both acorns and oak trees (and nothing else). Things of that kind are things that I say I-exist."

Neat point about the transformation of a living oak tree into, say, a living beech tree. I think Pruss will say that there is some precise moment (God knows which) at which the oak form stops informing the matter and the beech form begins to do so. Maybe the moment is selected randomly, or maybe God or some angel freely chooses it. Or maybe there's some law that monitors a certain quantity called 'oak-body-likeness' and 'beech-body-likeness' and sees to it that the form is switched exactly at the moment when the tree-body's beech-body-likeness becomes greater than its oak-body-likeness. Who knows. At any rate, at some precise time the switch does happen. I don't see any reason why Pruss may not say that.

Do you?


Michael Gonzalez said...


I can just briefly respond that not only is there a causal/explanatory connection between the events of the past and the current situation of the world (thus making the current world a "truthmaker" for statements about the past), but also the statement "x was true" has clear meaning, and does not intuitively reduce to "x is true at t(n)". These are not precisely the same concept, and the basic intuition people typically have is that the former, not the latter, is the accurate description of past events.

You talk about needing to correlate past-statements with abstract objects, but I don't see why this is necessary or even helpful. Abstract objects are, plausibly, always necessary in their existence. But necessary objects are a subset of the eternal objects, and so all of history would be composed entirely of necessary events which were eternally ordained. That's surely not what the presentist has in mind when she says "x happened in the past, and is no longer happening". They just mean that, it used to be true that "x is happening", but it is no longer true. And, before that, it was perhaps true that "x will happen", but that ceased being true when x started happening. You relativize the statements, and it's all very clear (and coheres with how we actually talk, outside of philosophical discussions about the nature of time).

Angra Mainyu said...


Thanks for your detailed reply as well.

I was (trying to) match Heath’s proposed concept of existence in ‘logic speak’. Based on his use, it seems x l-exists if and only if x exists and the term ‘x’ is not vague. So, it seems to me that may define mountains*, pipes*, etc., which are as precisely defined as particles.
So, if particles l-exist, it seems to me so do mountains*, pipes*, etc., even if mountains, pipes, etc., do not l-exist (but exist and the referent of ‘mountain’ and ‘mountain*’ overlaps almost entirely).

Regarding the concept you propose, I don’t know that the quantifier used in logic has a different meaning from the usual one, despite the use of the expression ‘logic speech’ to denote different meanings in this thread; I take it that your definition need not match Heath’s concept of ‘exists’ in what he named ‘logic speech’.

However, since you’re indicating a difference in meaning (which would explain that there are mountains in the ordinary sense in English, but not in the sense you propose), either we disagree about whether there are mountains in that sense, or I’m not groking the concept you propose.

I get that intuitive usages are very difficult to define; thanks for the explanation. Going by what you said, I’m not sure why the principle is intuitive to you. At least, I don’t find it intuitive in 'logic speak’, as I understand ‘logic speak’.

In any case, it seems to me the vagueness remains in oak trees, since the language is vague, even if there are forms, for the reasons I gave in the earlier reply.

Regarding mountains**, the definition is such that every mountain* is necessarily a mountain**, but not vice versa (since a number between m and n is also between m and n+1). But it seems to me that they would both l-exist.

In any case, I don’t see these matters as substantial matters of ontology, but of terminology (and, by the way, I’m using ‘substantial’ intuitively as well, I think in a way somewhat along the lines your use of ‘significant’, if I got it right). For instance, whether there are Aristotelian forms would be a substantial matter. Whether or not there l-are mountains is not. There are mountains anyway, and whether l-there are mountains seems to be a question of whether the term ‘mountain’ in ordinary English is precise enough to satisfy the requirements of some more or less obscure technical definition; it’s not about what actually exists.

Angra Mainyu said...

Regarding mereological universalism, I think the matter is here about l-speech, not about actual speech, so I don’t know whether it would be implausible.
But as for mereological universalism in ordinary speech, I would reject the argument from vagueness precisely because of vagueness. The argument supposes that if something exists, then something very similar exists too, etc. But such arguments have the problem of vagueness in our language. For that matter, we may start with a bacteria of species X, say that if something is of species X, so is something extremely similar, and then end up (via incremental changes) concluding that all sorts of other bacteria (of very different species) are also members of species X. That wouldn’t work.

I see the question of whether there, say, there are nose-mountains (i.e., an object composed of a nose and a mountain) as a question primarily about the (also somewhat vague!) ordinary concept (or rather concepts) of ‘object’, and whether such arrangements match such concept.
On that note, I would say that the word ‘object’ has more than one more or less common meaning. In what is perhaps the most common usage of the term ‘object’, it doesn’t match it (so, there is no such object as a nose-mountain), but there is a universal usage that is also not uncommon, and under which there are nose-mountains (but that does not mean that everything exists under that broad concept of object; there might or might not be, say, actual objects composed of n planets for any n, depending on whether the universe is finite).

I do recognize that my stance on this is uncommon, but I think the matter is a semantic one, though there may well also be a substantial psychological matter involved, regarding a potential common human instinctive concept of object (or more than one).

On the issue of the composites of mountains and a stone above them, etc., I think the analysis of the nose-mountain I gave above explains my take on those issues. But let me know if you find something unclear.

As for the argument against the existence (or is it against the l-existence?) of mountains based on removing one particle, etc., I don’t think it works, because in ordinary English (as has been accepted), mountains exist, and in l-speak, there is no concept ‘mountain’ in the first place (it’s not precise enough for l-speak). On the other hand, if a mountain* l-exists, it does not follow that if a particle is removed, a mountain* l-exists. Briefly, that argument against mountains seems to be mixing ordinary concepts with l-speak.

Angra Mainyu said...

As to the soul arguments, I would say the vagueness argument still works, for the following reasons:

1. We may still run the argument as follows:
Let’s say that there is a first moment t0 at which a soul of an oak tree exists. So, at t0-1 Planck time, the oak tree does not exist. But at t0, the oak tree does not exist, either. Only the soul of the oak tree exists. But the soul of the oak tree is not the oak tree. Else, we would have an oak tree with no DNA, no leaves, no bark, no roots, and which occupies no space. But that does not match the ordinary concept of ‘oak tree’. So, an oak tree would be a combination of a soul and some particles, but the term 'oak tree’, like the mountain, would not be precisely defined, due to vagueness in the definition of the particle arrangement.
As for whether an acorn is an oak tree in the ordinary sense, I’m claiming it’s not, using an intuitive grasp of the term here. Others may use their own intuitive grasp, but while I agree someone might consistently hold that an acorn is an oak tree (and I’m not making any claims about Alexander’s position on this), I would say that they’re mistaken (i.e., I’m saying it’s a mistaken position, not necessarily a contradictory one).

2. Moreover, there is also vagueness in the concept of the soul of an oak tree, because even assuming ‘soul’ is well defined and precisely so, ‘oak tree’ is not. In other words, plausibly there would be no fact of the matter as to whether some soul is the soul of an oak tree, or a non-oak tree (what would make the difference, given that ‘oak tree’ itself is a vague expression?).

3. As for the 'natural kind’ argument, those ‘natural kinds’ would be extremely similar to each other, in fact arbitrarily similar, and yet they would all allegedly l-exist, or possibly l-exist, and I see no good reason to think humans are psychologically capable of making such arbitrarily fine-grained distinctions.
Still, let’s say that this works, and so there would be such natural kinds. Then, the vagueness argument would remain a problem for oak trees.
In other words, accepting that there l-there is a natural kind for which we have no name (and arbitrarily similar ones, etc.) does not block the argument against the l-existence of oak trees, since the vagueness in the expression ‘oak tree’ would still remain, and so it seems it’s not only that l-there would be plenty of natural kinds for which we would have no name (which isn’t particularly problematic), but also, l-there wouldn’t be oak trees.
So, l-speak would still be very different from ordinary English when it comes to the existence vs. l-existence of oak trees.

4. Regarding the genetic engineering example, I would say that a problem there is that that account gives us a moment of radical shift in souls (one goes, another one enters), whereas the changes in everything observable are incremental, not radical. The questions is then what does the soul do?
From another perspective, let’s say that we stop the transformation one Planck time before the soul would change in one case, and in the other, one Planck time after it. Then we have genetically almost identical organisms (or identical), which are pretty much the same in every respect, but have different souls.
It would seem to work as an argument against the plausibility of souls. An alternative is a soul transforming too (not that I find that plausible), but then one may argue from vagueness as before.

Unknown said...


Consider this argument:

P1. There are true sentences about the past.
P2. For any true sentence S, there is something x to which S corresponds and it is in virtue of corresponding to x that S is true.

Now take the true sentence "In the past, there were dinosaurs." Call this sentence S. P1 and P2 entail that there is some thing x to which S corresponds and, in virtue of corresponding to which, S is true.

Stated very roughly, the argument against presentism is that there isn't anything that this entity x could plausibly be.

Do you accept P2? If so, then which entity do you say x is?

I don't think it matters for the argument whether we use sentences like "In the past, P" or "At time t, P". I'm happy with either.

Thanks again for the discussion --

Michael Gonzalez said...


Hey, I'm grateful to have a good, stimulating discussion! I just don't usually have time for very long posts. I appreciate your patience and your insight.

If by "something" in P2 you mean "some object" then I would reject P2. For example, I think statements about Wednesday can be true without corresponding to any object at all (surely you don't think there's an abstract object corresponding to "Wednesday" which is nothing more than a cultural norm in a particular language and tradition).

I think the more salient thing to say, however, is that the commonsense notion of "was" is that at some point in the past it would have been true to say "is", but that that point in time has passed. On B-theory, every event is equally real, no matter "when" (where on the t-axis) it occurs. This is not intuitively correct and contradicts the idea of temporal becoming. I notice that you want to believe in temporal becoming but also hold to B-theory. Well, I'm sorry, but that doesn't seem possible. On B-theory, everything that is true, was true, or will be true, is eternally and changelessly true. Things don't go out of being at all, nor do things come into it.

Your thoughts?


Alexander R Pruss said...


There is an oak iff some oak form (or soul) informs some matter.

There is no vagueness as to whether the informing relation occurs.

Now, maybe there is vagueness whether a given form is an oak form. (After all, Wikipedia says there are 600 species of oak, and there are presumably many more possible species.) But that's OK, because the Sider argument only concerned purely logical vocabulary. The Sider argument was that there has to be a definite fact of the matter as to how many entities there are, not as to how many entities of a particular kind there are.

Unknown said...


"Based on [Heath's] use, it seems x l-exists if and only if x exists and the term ‘x’ is not vague."

Suppose that there are two noun phrases, one vague and one precise, but they refer to the same thing. For instance, X is both that square ("that square" is precise) and that squarish shape ("that squarish shape" is vague). Doesn't your definition of I-exist entail that X both I-exists and doesn't I-exist?

I was taking "I-exist" to work so that a given entity I-existed iff it was in the range of the most basic logical quantifier. I'll use "B-exist" from now on to mean that, so as not to confuse it with the original sense (your and Heath's sense) of "I-exist".

Don't get me wrong: I think that mountains do B-exist. Dr. Pruss thinks they don't. I'm trying to explicate/defend Pruss's position, not mine.

So yeah: Pruss has to say that either mountains don't exist (in the ordinary English sense) or else that there's a difference between B-existence and ordinary English existence.

You asked why my weirdness principle was intuitive to me. Here's an argument, with premises marked "P#" and lemmas that follow logically from premises marked "L#" and the conclusion marked "C":

P1. For any predicates F and G, if it's possible that some F B-exists but it's not possible that any G B-exists, then there is some good reason why it should be possible that some F B-exists but not be possible that any G B-exists.
P2. For any predicates F and G, if there is no significant difference between what it is for something to be an F and what it is for something to be a G, then there is no good reason why it should be possible that some F B-exists but not be possible that any G B-exists.
L1. (From P1 and P2) Hence, for any F and G, if it is possible that some F B-exists but not possible that any G B-exists, then there is some significant difference between what it is to be an F and what it is to be a G.
P3. For any x and y, if there is no significant difference between x and y, then there is no significant difference between what it is to be x and what it is to be y.
L2. (From P3) So if there is no significant difference between X and Y, then there is no significant difference between what it is to be X and what it is to be Y.
L3. (From L1) If it is possible that X B-exists but not possible that Y B-exists, then there is some significant difference between what it is to be X and what it is to be Y.
L4. (From L2 and L3) So if there is no significant difference between X and Y, then then not: (it is possible that X B-exists but not possible that Y B-exists).
L5. (From L4) So if there is no significant difference between X and Y and it is possible that X B-exists, then it is also possible that Y B-exists.
P4. For any x, if it is possible that x B-exists, then x B-exists.
L6. (From P4) So if it is possible that X B-exists, then X B-exists; and if it is possible that Y B-exists, then Y B-exists.
L7. (From L5 and L6) So if there is no significant difference between X and Y, and X B-exists, then Y B-exists.
C. (From L7) Therefore, for any x and y, if there is no significant difference between x and y, and x B-exists, then y B-exists.

Unknown said...

This conclusion C is very like my weirdness principle --- stronger than it, really.

I made an error (which you pointed out) in defining mountains* and mountains**. I should have said that if a mountain* is any entity composed of between m and n particles, then a mountain** is any entity composed of between (m + 1) and (n + 1) particles. My argument (in fact, all the arguments from the last post) should be run with B-existence instead of I-existence.

If these questions of what I-exists and what B-exists and what exists in the ordinary English sense of "exist" are just matters of terminology, rather than questions about what actually exists, then what would a question about what actually exists look like? I think Pruss and I both hold that there is a certain fundamental sense of "existence" (which we take to be B-existence) that carves nature at the joints. I.e., for any x, if x B-exists, and the fact that x B-exists does not follow logically from some other simpler fundamental fact, then the fact that x B-exists is itself a fundamental fact. So we're asking: "What 'exists' in the fundamental sense?" Or you could also put it like this: "There's a certain natural-English sense of 'exist' on which I and God and fundamental particles exist but on which Sherlock Holmes and average Americans and the points earned by a team in a football game don't exist. What are all the things that exist in that sense of existence?" It seems to me that these are questions about what really is, and not questions about semantics.

Would you consider whether or not there B-are mountains a substantial question? I do. I don't take B-existence to be a product of obscure technical definition. I take it to be the single most basic sort of existence that there is out there.

I think you're right that the argument that modus tollenses mereological universalism doesn't work if we are using "exist" in a vague way. But I meant the argument to be about B-existence, and I take B-existence to be non-vague.

About nose-mountains: my question would be, Do they B-exist? I think so. Pruss thinks not. I think our disagreement is a dispute about how things really are.

I'm not sure I follow your objection to the sorites argument against mountains. The argument goes like this (with Q# for premises, L# for lemmas, and C for the conclusion):

Q1. If there are mountains, then possibly, there is some mountain that was constructed from particles and a non-mountain by adding particles to that non-mountain, one by one.
Q2. Necessarily, if there is some mountain that was constructed from particles and a non-mountain by adding particles to that non-mountain, one by one, then there is some first moment when that mountain exists.
Q3. Necessarily, if there is a first moment when that mountain x exists, then there is a non-mountain y that exists one moment earlier, and only one particle makes the difference between x and y.
L1. (From Q1, Q2 & Q3) So if there are mountains, then possibly, there is a mountain x and a non-mountain y such that only one particle makes the difference between x and y.
Q4. However, necessarily, there is no x and y such that x is a mountain and y is not a mountain and just one particle makes the difference between x and y.
C. (From L1 and Q) So by modus tollens, there are no mountains.

Unknown said...

The "is" and "are" predicates should be interpreted as "B-is" and "B-are". Do you object to this argument? If so, which premise do you reject --- or which inference? (I'm personally inclined to reject Q4 --- roughly, I'm inclined to the view that there is a mountain/non-mountain pair that differs by only one particle, but there is no matter of fact about which pair this pair is --- but I'm not really certain what the right reaction to the argument is.)

About your Planck argument about oak trees (you numbered it "1"), I see two possible responses on behalf of Pruss. First response: There is an absolutely definite matter of fact as to exactly which particles the oak form informs and at exactly which moment it begins to inform them. Second response: There is no matter of fact about exactly which particles are in the body of the oak tree, but there it is still absolutely definitely true that there is exactly one matter-form composite and exactly one oak tree; it's just indeterminate which particles are parts of that one matter-form composite.

I don't think your objection will work if Pruss takes either of those lines.

I suspect you're right (though I'm not absolutely certain) about the terms "oak tree" and "acorn" --- in the ordinary English sense of the term, no acorn is an oak tree. But this isn't devastating for Pruss. He can talk about oak trees* (organisms that have the form that adult oak trees do) instead of oak trees and claim that acorns are oak trees*. Similar for human beings and fertilized eggs, I suppose. As for abortion and such on this view, presumably if there are forms, then our moral duties line about with the question of when the organism gains the human* form; not when the organism enters the range of our fairly arbitrary natural usage of the word "human".

If acorns aren't oak trees, then you're right: there will be times when it is vague whether a certain matter-form composite is an oak tree.

I apologize. I don't follow your argument numbered "3". You say "those 'natural kinds' would be extremely similar". Which natural kinds are you speaking about there?

Your point about observed changes being incremental is interesting. But I wonder, what about the first moment a given human being phenomenally entertains reddishness (i.e., has an experience that is at least somewhat 'reddish')? That seems to be a radical shift --- suddenly, reddishness is present, but one instant prior, there was no reddishness there at all. This case wouldn't be a problem for your objection on the assumption of property monism, but it does seem to be a problem on property dualism.

I agree that it seems a little strange for there to be a sudden radical shift in souls at a certain instant. Maybe Pruss just bites the bullet here? Or maybe he denies that there is an absolutely definite time at which the event takes place? The second option would mean that there is no definite matter of fact about how many oak* trees exist at a given moment of time. But that's OK on the B-theory of time (the "B" in "B-theory of time" is not related to my term "B-exist"). He could still maintain that there is a definite matter of fact as to how many oaks* exist (in the tenseless sense of exist).

Unknown said...

Another response would be this: Deny that the genetically altered oak tree ever loses the oak* form. You can make it as physically like a beech tree as you like. But really, it remains what it started out as: an oak* tree.

It might no longer be an oak tree (for the natural English sense of "oak"), but it might still be an oak* tree --- i.e., an organism that has the same form that (typically) adult oak trees have. It seems to me that it's oak* trees, not oak trees, that Pruss's theory is really about. (Unless maybe he accepts some semantic theory that forces "oak tree" and "oak* tree" to mean the same thing.)

Cheers --

Unknown said...
This comment has been removed by the author.
Unknown said...

Michael --

In P2, I mean "something" in the sense of "anything that, strictly speaking, is real". I take it that in this sense, neither Sherlock Holmes nor 'the average American' nor a point earned by a team in a football game is 'something'. But God and you and I and angels and fundamental particles each are 'something'.

I also think that compound objects like mountains, as well as artifacts like pipes, are each 'something'. Pruss denies this. I also think that properties and facts and thoughts and concepts are each 'something'. I.e., certain properties are real things that actually exist. Philosophers are (and usually have been) divided about whether that's right.

So do you accept P2 on this reading of "something"? If so, what is x?

I don't accept the objection to B-theory in the last paragraph of your recent post. You seem to be saying that B-theory commits me to holding that the sentence "Things go out of existence" is false. Well, I think the sentence "Things go out of existence" is true. For instance, "John goes out of existence" means [There is some moment such that during it, John exists but after it, John doesn't exist].

This is fine on B-theory. B-theory is compatible with the claim that at t1, John exists, but that at every moment later than t1, John doesn't exist. So B-theory is compatible with the truth of "John goes out of existence".

You say there's an intuition that the past isn't as real as the present. I'm not sure if I have that intuition or not. Suppose I did. Then I'd take the sentence "The past isn't real" to mean "Now, the past isn't real".

But that's fine. I agree that now, the past isn't real. As a B-theorist, I hold that the past is real and yet that now, the past isn't real. That's not a contradiction. In terms of its logical form, it's like saying that the correct answer to the math problem is 7 and yet that in Jil's opinion, the correct answer to the math problem isn't 7. No problem there. Jil is wrong, but so what?

The only things that are real now are the things that exist now. Obviously, the past isn't one of those. The past isn't real now. But [The past isn't real now] doesn't logically entail [The past isn't real].



Angra Mainyu said...


Thanks for that definition.
Aside for the vagueness issues, etc., it would result in, say, the possibility of something being an oak tree even before it’s an acorn; in fact, any kind of interaction with small numbers of particles would seem to count. In my view, that’s not in line with what ‘oak tree’ means.
But leaving that aside, on the other issues, it seems to me that there is vagueness in ‘matter’, ‘oak tree’, and perhaps to some extent ‘entity’ (unless the different usages of ‘entity’ are different enough to be clearly separated and one or more are precise enough; but that’s not entirely clear to me).
That said, if ‘entity’ is used in a way that is precise enough to for there to always be a fact of the matter as to whether some arrangement of stuff is an entity, then I don’t see any problems with the view you propose, but I don’t see any problems with mountains*, or pipes*, either, in terms of numbers of entities (I take no stance for now on whether there is an ordinary usage of ‘entity’ that is precise enough for that). In other senses of ‘entity’, there may not be a fact of the matter as to how many there are.
In any event, I don’t see anything odd, puzzling, etc., here. On that note, the cases of no fact of the matter about the number of entities or about the number of entities of a certain kind X strike me as relevantly similar, since in both cases, the issue seems to depend on the precision of the definitions of ‘entity’, or ‘entity of kind X’, etc., and it seems to me that issues are in both cases issues about the maps, not about the territory so to speak (unlike, say, the issue of whether there are Aristotelian forms; that seems to be a question about the territory, not about the maps).

Angra Mainyu said...


Regarding the definition I proposed, I was trying to match Heath’s.
He said that:

1. “There are” (in what he calls ‘logic-speak’) means “there are logical objects which are”.
2. “Logical objects” are the non-vague objects in the world.
3. “There is vagueness in nature” means “there are some vague true sentences”.

Based on that, it seems to me that logical objects are defined in terms of the vagueness of the sentence. At least, that’s how I understood the above, and that’s why I gave that definition. But it seems I misspoke by speaking loosely.
So, thanks for the correction, and let’s see if I can approach the interpretation I had in mind better.
Let me put this in another way: For every sentence of the form ‘X exists’ let’s define ‘X k-exists’ to mean ‘“X” has no more than 9 letters, and X exists’.

S1: Phosphorus k-exists.
S2: Hesperus k exists.

Then, S2 is true, and S1 is false. But Phosphorous is Hesperus. Would that entail that, contradictorily, the same object (i.e., Venus) k-exists and it’s not the case that it k-exists?
Actually, there is no contradiction, because even though loosely speaking one can say that something k-exists, strictly speaking a claim like “Hesperus k exists” is not only a claim about Hesperus, but rather, it’s a conjunction between a claim about Hesperus, and a claim about the term ‘Hesperus’.
I was thinking that something like that was what Heath had in mind, and that’s what I meant to say in the definition, though I didn’t write it properly. But after further consideration of his posts, I’m now less confident in having grokked what he meant.

As to your definition: “ was taking "I-exist" to work so that a given entity I-existed iff it was in the range of the most basic logical quantifier.”. I'll use "B-exist" from now on to mean that
But that’s not clear to me. What is ‘the most basic logical quantifier?’
I’m familiar with ordinary usages of ‘exists’, ‘there are’, etc. (and, btw, I think there is more than one), but I’m not sure what you mean here by ‘the most basic logical quantifier’.

“So yeah: Pruss has to say that either mountains don't exist (in the ordinary English sense) or else that there's a difference between B-existence and ordinary English existence.”
He accepts that mountains exist in the ordinary English sense, but I don’t think he needs to take a stance on that issue, since “B-exists" is your terminology.

Regarding your argument, the concept of ‘significant difference’ might be a difficulty as well, because it seems to me it may well be vague (which does not make it unusable in all contexts, but in this context, I’m not sure it’s precise enough for the task at hand).
However, as I mentioned I don’t know what you mean by ‘B-exists’ (you provided a definition, but I’m afraid I haven’t understood it yet), so I’m not in a position to evaluate the argument properly.

Angra Mainyu said...


I do think that there is a sense of ‘exists’ in which Sherlock Holmes does not exist, and neither do average Americans, though you do, and fundamental particles might (I do think that electrons exist in that ordinary sense, for instance, but I don’t know whether they’re fundamental, or whether any particle is so. I take no stance on whether it’s turtles all the way down), though I would not agree that God exists, under any of the usual philosophical definitions of the term ‘God’ (this clearly is not a disagreement about the meaning of the words, though).

I also think that in that ordinary sense, there are pipes, mountains, etc. I don’t think that there is always an objective fact of the matter as to whether, say, some stuff we point out is a mountain, and thus there might not be an answer about how many mountains there are. But that is something about terminology, language, etc., as far as I can tell.

On the other hand, Alexander says that in ordinary usage, there are pipes, etc., so there seems to be no disagreement there.

It might be that there is a disagreement between you and him about whether in some the existence (no pun intended) of some sense of ‘exists’ which somehow cuts nature at its joints, pipes exist or not.

However, that does not mean that there is a disagreement about what really is. For instance, two people may agree to the sentence ‘there is a common sense of ‘exists’ that cuts nature at its joints’, and even agree to use ‘exists’ in that sense, and yet still use ‘exists’ in different manners (i.e., the fact that two people say that a sense of ‘exists’ is the most fundamental does not mean that they have in mind the same sense).

Of course, it might also be your disagreement is about something other than terminological issues. I don’t know. It’s a matter that we might try to test in different ways.
For instance, a possible one (it’s not exhaustive; i.e., the test is not guaranteed to work, but it’s a reasonable shot) you’re apparently implying that Alexander’s claim that there are no pipes in some sense of ‘there are’, is false. I would ask you the following question here: how do you think the world would look different (if at all) if his claim (as you interpret it) were true?

Regarding that sorites argument, I reject premise Q2. I would say that there is no objective fact of the matter, using ‘mountain’ in the usual way, as to whether some intermediate objects are mountains.

Angra Mainyu said...

Clarification: I reject Q2 in any ordinary usage of 'mountain', etc.; I'm not familiar enough with "R-exists" to make a proper assessment, so I was going with ordinary English as I understand it (but I do not know whether "B-existence", etc., matches any ordinary usage. I would need more info about "B-exist", etc.)

Angra Mainyu said...


With regard to the argument about the first moment at which there is an oak tree, I think my exchange with Alex may clarify some of the matters sufficiently (see the exchange for more details); let me know if you have more questions about them.

As for abortion and the like, I would disagree. I think this would be a matter for another discussion, but briefly, I would assess moral issues intuitively, and it seems intuitively clear to me that there is nothing immoral about, say, destroying a human embryo or even a human form (assuming I can destroy it) in order to end a pregnancy, as long as the person making the decision is the mother, and all other things equal (i.e., no scenario in which aliens will nuke humanity to death from orbit if and only if Alice aborts, etc.).
The description of this ‘form’ is not such that I would assess it’s immoral to destroy it.

Regarding argument number 3, I meant that there would be (on that account) different natural kinds that are increasingly similar to one another (e.g., as trees evolved very gradually), even possibly arbitrarily similar (if one constructs hypothetical scenarios). But I can’t name the natural kinds in question because those would be the natural kinds for which we have no name yet.

As for the reddishness argument, I’m afraid I may not be following you here. What’s the conclusion you intend to draw?
In any case, I would say that the experience may be different from any other previous experience, but it does bear similarities to other color experiences (also, it’s not experienced from no experience to having that experience in a Planck time (perception does take some time, even if very little)).
In any even, I don’t think experiencing red from the first time involves a radical change in a human being. But the case of the tree is even simpler, since they don’t experience in the complex ways in which we do.

In any case, the difficulty is as follows:
Let’s consider T(t0), the starting point tree, which is a tree of type A and has a type A soul; T(t0+m0 Planck units) is the tree at the end point of the transformation, which is a type B tree and has a type B soul, and the transformation takes, say, 10 years approximately.

If the soul changes at some specific temporal point, there is some m1, such that (say) at t0+m1 the soul is a type A soul, and at t0+m1+1 is a type B soul. Let’s say (for instance; this is not crucial), that m1£m0/2). Then, the tree at t0+m1 will be far more similar in any observable respect to the tree at t0+m1+1 than the tree at t0+m1+1 will be similar to the tree at t0+m0.
Yet, the Aristotelian soul is supposed to be causally effective. Moreover, it’s supposed to be crucial, causally speaking (what explains its behavior, etc.).

Denying that there is an absolute first time at which the event takes place would be problematic as well it seems to me, since at every time between the two extremes (tenselessly or not), there is one tree (not more), and thus one soul, and souls are definite, etc.

But moreover, my argument here only needs that at some time there is a soul of type A, and that 1 (or, say, 2 or 3) Planck units later there is a soul of type B; what happens in between (if anything) is not a matter that needs to concern us. For that matter, we may extend the intervals to, say, a microsecond, or a millisecond.

Unknown said...


You're right. "B-exists" is my terminology. Alexander has never used it. So why do I say that Alexander denies that mountains B-exist?

I believe Alexander denies that the most basic logical quantifier ranges over mountains. So since B-existence is the sort of existence possessed by all and only the things over which the most basic quantifier ranges, therefore Alexander's view entails that mountains do not B-exist.

This validity of this reasoning depends upon the premise that Alexander and I are picking out the same quantifier when he says "the most basic logical quantifier" and when I say "the most basic logical quantifier". You commented that two people might separately define some sort of existence as "the most fundamental sort of existence" and yet not have defined the same sort of existence, because they didn't mean the same thing by "fundamental".

That's a good point. The same point could apply to the phrase "the most basic logical quantifier." If Alexander and I were not using the phrase "most basic logical quantifier" in a sufficiently similar way, then we might not be picking out the same quantifier. In that case, Alexander's stated view would not obviously be committed to any claims at all about B-existence.

But as it happens, I do think that Alexander and I mean the same quantifier when we say "the most basic logical quantifier". So I do think Alexander's view is committed to the B-nonexistence of mountains.

Suppose I'm right about this. So what? How can Alexander and I explain what we mean by "basic" in this context? Or suppose I'm wrong. Still, how can I explain what I mean by 'basic' or by 'B-existence'?

Here are some possibilities:

(A) In the ideal theory of the world, there is exactly one quantifier that has the following feature: Every quantifier that appears in the ideal statement of that theory is defined in terms of it, but it is not defined in terms of any other quantifier. This is the basic logical quantifier.

(B) There is a relationship among our human concepts which is --- or, at any rate, is analogous to --- the mereological relationship of parthood. Or else, this holds not of parthood but rather of set-membership. Or perhaps of some complex relationship that reduces to parthood and set-membership and/or other mathematical and causal relationships --- but is still at least analogous to set membership and parthood. For example, the concept of being colored stands in this relationship to the concept of being red. The concept of moving stands in it to the concept of speeding. Call this relationship R. We have exactly one concept with the following feature: we often express it by the English predicate "... exists" and it does not stand in the relationship R with any other human concept besides itself. B-existence is the content of this concept.

Unknown said...

(C) There is exactly one entity which is a part of everything. This entity is existence. The predicate "... B-exists" expresses existence, much as "... is red" expresses redness (if there is such a thing as redness) and "... are two things" expresses twoness.

(D) B-existence is the property of being --- strictly speaking --- ultimately metaphysically real (rather than being merely something that we talk about as though it were real, for the sake of convenience).

(E) Whether or not there is any sort of existence which has the properties I have ascribed to it in (A) through (D), nevertheless, B-existence is the sort of existence that is most likely (epistemically speaking) to have those properties.

That's about the best I know how to do in defining B-existence and the most basic logical quantifier. In my opinion, B-existence does does dovetail closely, though not exactly, with most ordinary English uses of the word "exists." But that's a separate claim.

So in summary: I think that Alexander thinks that pipes don't B-exist, in the above sense of B-existence. But I think that pipes do B-exist.

I think you're right to object to Q2 from my sorites argument from the last post. But what about the following, tighter argument? (The premises are R1, R2, R6, and R10.)

R1. There is no integer such that in virtue of being exactly as large as or larger than it is, it is enormously large; whereas any integer just 1 less than it would not be enormously large.
R2. If R1, then there is no enormously large integer n such that the integer (n - 1) is not enormously large.
R3. So there is no enormously large integer n such that the integer (n - 1) is not enormously large.
R4. Suppose N is an enormously large integer.
R4.1 So (N - 1) is an enormously large integer.
R4.2 So (N - 2) is an enormously large integer.
R4.(N-1) So 1 is an enormously large integer.
R5. Therefore, if N is an enormously large integer, then 1 is an enormously large integer.
R6. But 1 is not an enormously large integer.
R7. So N is not an enormously large integer.
R8. So for any n, n is not an enormously large integer.
R9. So there are no enormously large integers.
R10. But if there are any integers other than 1, then there are all the traditional integers; and some of the traditional integers (say, a googleplex) are enormously large.
C. Therefore, there are no integers; or at least, no integers other than 1.

I'm curious if you object to any of these inferences and premises (and on grounds independently of disbelieving in the existence of integers tout court)? If not, and you accept the conclusion, then I suspect a similar argument could be constructed against the existence of mountains.

(Personally, I'm inclined to reject R2.)

Cheers --

Unknown said...


About abortion: Pruss commented that matter-form composites can be loved for their own sake. If he means that all matter-form composites are like this, then one might reason as follows (S# are premises, L# are lemmas):

S1. If S loves x, and it is S's power to cause an enormous positive differential in x's degree of flourishing, then S should be strongly motivated to cause that differential.

S2. If x is a fetus, then x's becoming a human child (say, of at least age 1-year) would result in an enormous positive differential in x's degree of flourishing.

L1. So if S loves x and x is a fetus and it is in S's power to cause x to become a human child, then S should be strongly motivated to do so.

S3. If there is an entity x which can be loved for its own sake now, and it is intimately connected to S, and S knows about that entity and its intimate connection to him or her, then S should love x.

S4. Any matter-form composite can be loved for its own sake now.

S5. Any human fetus is a matter-form composite.

L2. So any human fetus can be loved for its own sake now.

S6. Any gestating human fetus is intimately connected to its mother.

L3. So any gestating human fetus is an entity which is closely connected to its mother and which can be loved for its own sake now.

L4. So if any mother of a gestating human fetus knows about that fetus and its intimate connection to her, then she should love it.

L5. So if any mother of a gestating human fetus loves that fetus and it in her power to cause that fetus to become a human child, then S should be strongly motivated to do so.

C. So any mother of a gestating human fetus who knows about that fetus and its intimate connection to her should be strongly motivated to cause that fetus to become a human child, if it is in her power to do so.

This conclusion suggests that mother's should be strongly motivated not to abort the fetuses they carry. The premises seem plausible to me, but what do you think?

My point about reddishness was that to begin to undergo reddish phenomenology for the first time is a non-incremental change (at least, given property dualism). You had said (April 24th, 11:23), "the changes in everything observable are incremental". I was trying to offer a counterexample to your claim.

Thanks for the point about forms being causally efficacious. I hadn't thought about that. That does suggest that the oak tree shouldn't retain the oak* form even at the end of the process of transformation, when it's physically behaving like a beech tree. I think it also causes a problem for the idea that when the tree is near the middle of the transformation, its form is definitely oak* or definitely beech*. At the middle of the transformation, it neither definitely behaves like an oak nor definitely behaves like a beech. But you'd think that if it definitely had an oak* form (or a beech* form), and forms are causal, then the tree would definitely behave like an oak (or like a beech)!

In Alexander's last post to you, he committed that there might be vagueness in whether a given form was an oak form. So in the case of the oak tree changing into a beech tree, can't he say that while there is exactly one form, it's indeterminate whether that form is oak or beech? I think that avoids your objection about "how many" souls there are.


Unknown said...

Edit to my comment today at 9:16 pm:

In the "(B)" description, I should have said "and no concept besides itself stands in relationship R to it" --- not what I actually said, which was "and it stands in relationship R to no concept besides itself."

I got that quite backward. I was trying to make out the concept of B-existence to be the mereologically simplest existence concept, not the most complex one.

Unknown said...
This comment has been removed by the author.
Angra Mainyu said...


Regarding B-existence, etc., it seems Alexander hasn’t used the expression ‘the most basic logical quantifier’, either. He mentioned a ‘ “logical” quantifier’ (quotation marks in his post), and that was in a reply to Heath, who introduce terms like ‘logic speak’, etc., and he talked about “logical vocabulary” as well (including the existential quantifier), so maybe it’s something similar to what you have in mind. I don’t know.

As to the alternatives, I’m afraid I don’t know enough to understand some, and tend to disagree with others.

(A) I’m not familiar with that theory, if you’re referring to a specific one. If not, I may be missing your point.

(B) I’m not inclined to agree that there is such relationship between human concepts (I don’t know whether there is; I don’t see it as clear). More precisely, I’m not sure what it would look like (i.e., similar how? etc.).

(C) I don’t think existence in an entity (though maybe we use ‘entity’ differently, but I’m not sure). My take on this is that to exist is a verb, and sometimes we talk differently by means of nominalizing. I don’t think this nominalization is ontologically committed. But in any case, I’m afraid I don’t understand an expression like ‘Existence is a part of everything’.

(D) I don’t think existence is a property, in any sense of ‘exists’ I’m familiar with.

(E) The difficulties I get in understanding the previous points, etc., affect this one as well.

Still, even if you and Alexander have a shared concept of existence, you may have a disagreement in your theories about what that concept means, rather than in your intuitive views of what actually exists, in a common sense of the word ‘exists’.

While there might be a disagreement between your respective positions beyond the disagreements about the meaning of words, I’ve not seen it so far; in particular, I’ve not been able to find ways in which the way would differ if (what you’re saying is true, e.g., that B-there are mountains) vs. (what Alexander is saying, e.g., that in some sense there are no mountains).

For instance, let’s say that Bob says that there is a being who can effortlessly impose his will in the whole world (i.e., a being who can run the world effortlessly), and Alice denies it that there is any entity (say) capable of transmitting information faster than light in the universe. Based on that, I can tell that there are clear differences between Bob’s beliefs about some issues, and Alice’s.

But I’ve not been able to figure out what difference your disagreement (if there is one) would make.

Unknown said...


Suppose in world w1 there's just one organism. For each natural number n > 1, in world wn, all the matter in the world has the same arrangement as in w(n-1), except that the matter that is arranged organism-wise in w1 is arranged just marginally less organically in w(n) than it is in w(n-1). Eventually --- say, by w10^80, we reach a world in which there is no organism.

Isn't this a sorites series from worlds with 1 organism to worlds with 0 organisms? So on your view, aren't there some worlds in this series where it is indeterminate how many organisms (and hence, how many entities) there are?

Angra Mainyu said...


On the ‘enormously large’ argument, I think ‘enormously large’ is used to mean somewhat different things in different contexts, and most if not all of them are vague. So, I would reject that premise R1 has sufficiently clear terms for the kind of mathematical argument at hand.

That aside, I would say that of course there are integers in the set of positive integers (for instance), or the set of integers, or the set of real numbers, the category of mathematical objects etc.; but I don’t consider those ordinary claims to be ontological claims, in the usual sense of the words.

In other words, I don’t think one should include integers in one’s ontology, or try explain their existence, etc.; we’re just talking about state of affairs in some abstract scenario that involves certain also abstract structures, etc., not about the world ‘out there’ so to speak (even though some mathematical objects like the natural numbers are abstracted more or less directly from what we observe around us; the integers are an extension, and then there are other extensions, etc.). However, I do think that ‘there are infinitely many prime integers’ is true, in the ordinary sense of the words (e.g.., as mathematicians use them).

The comparison of existence of mountains and existence of integer, in my view, has the problem that claims of existence of mountains are (by default) about the world ‘out there’, so to speak, whereas I don’t see ‘there are infinitely many integers’, etc. (again, as the term is used in math) as similar.

I realize my view on this are probably unusual.


Angra Mainyu said...


On the issue of abortion (and I’m afraid I can’t address so many topics properly, but briefly):

1. Alexander said he does not know how lovable particles are, so it seems to me that he only claimed that all entities that are the proper objects of love are among those that exist in the logical sense, but he did not claim that all objects that exist in that sense are the proper objects of love.

2. Even if it were the case that all such objects can properly be loved, that does not mean that’s it’s improper not to love some of them. It might be that there are objects that it’s not improper to love, and not improper not to love, either (so, loving them would be permissible but not obligatory).

3. The issue of ‘intimately connected’ in S3 and S6 is unclear to me. What counts as ‘intimately connected’? Are particles in our bodies intimately connected to us? What about frozen embryos? Regardless, I think general ethical claims/theories/etc. are tested against particular cases rather than the opposite, so if an embryo counts as connected in such way, then by means of assessing the matter in particular cases, I would intuitively conclude that the claim is false. I don’t see that a woman would have a moral obligation to love an embryo. In particular, it would strike me as wrong to demand that she love an embryo, and more so in case of rape.

4. There is the issue of other cells, like sperm cells, or ova. If living organisms have souls, it seems even unicellular organisms that are much simpler than, say, human sperm cells (let alone ova) do. But that suggests that so do ova, or sperm cells. Why not?
At least, it’s not clear why that wouldn’t be so, or why it would be so for an embryo.

5. S2 seems false as a general statement. For instance, let’s say that the woman lives in abject poverty, or that she has a painful transmissible and lethal disease, or the fetus has a disease and will die horribly if it’s born (e.g., due to incest), or will die of hunger, or be close to death out of hunger, etc.), or generally that if born, it will have a horrible short life, etc.
I guess the vagueness of ‘flourishing’ might be getting in the way, but if so, I would tend to reject the premise due to its being too vague for the purposes of that discussion.

Angra Mainyu said...


On the issue of reddishness, thanks for clarifying.

My impression is that said perception counts as a small change in the mind of a person, not a radical one, and also perception is incremental even if very fast. Of course, if there is no temporal density, there are some discontinuous changes, but my point is that they’re very small, in my view, whereas the changes supposedly brought about by the new soul should be big.
Then again, terms like ‘big’, ‘incremental’, etc., are also... vague (we can’t escape that, it seems), but in any case, the issue is that the changes would be much less than what a change in soul would suggest.

In any case, even if the reddishness example count as non-incremental, the argument still can be run on the lines of the type A/type B soul, which does not depend on the answer to the reddishness case.

So, it seems the soul would probably have to transform from an oak soul to a non-oak soul. And yes, that would be vagueness about how many entities of some kind exist, not necessarily about how many entities exist, but as I said in my reply to Alexander, I see the issues as relevantly similar, and neither one as more puzzling, odd, etc. than the other (though I don’t see either of them as puzzling, odd, etc.; I explained my take on the matter in a bit more detail in my reply to his post).

Unknown said...


You mentioned that you don't think "enormously large" is sufficiently clear to be used in a mathematical argument. Doesn't an argument go through just in case its premises are true and the inferences are valid? So if S1 and the other premises are true, doesn't the argument go through, no matter how clear or unclear its terms are? Which do you think S1 is --- true or false?

Also, isn't there at least one intuitive use of "enormously large" on which (given the right comparison class) it is very clear that googleplex^googleplex^googlepex is an enormously large number? Can't we use that use of "enormously large" and that comparison class in order to interpret and evaluate the statements in the argument?

About (A):

I suppose I am referring to a specific theory --- something like "The Complete Theory of the World," the theory that most scientists and philosophers and explorers are (corporately) seeking. We haven't found that theory yet, but presumably it's out there.

To be a little more rigorous, I should probably speak not of 'the best theory of the world' (Goedel's Incompleteness Theorems raise serious difficulties for the idea that there is a single finite theory that describes everything in the world), but rather 'The Best N-theory of the World." An N-theory is any theory that entails all the truths there are whose complexity is less than degree N. 'Degree of complexity' will probably be defined in terms of something like the number of entities and properties that the truths in question describe; or else in terms of the number of logically irreducible semantic constituents of those truths.

The best N-theory of the world might be something like the theory that scored the best, overall, in the following areas:

(i) it uses the fewest axioms;
(ii) it relies on the fewest inferences rules;
(iii) its axioms are the best supported by intuition and/or perception and/or other whatever other mechanisms there are which justify properly basic beliefs;
(iv) its inference rules are the most intuitively valid;
(v) it entails no falsehoods;
(vi) it is consistent with its own success (i.e., it doesn't entail that it is a bad theory).

So in (A), I'm claiming that there is a certain quantifier q such that for any sufficiently high degree of complexity N, q is used in the ideal statement of the best N-theory of the world and, moreover, every other quantifier used in the ideal statement of that theory is defined in terms of q but not vice versa.

What's an 'ideal statement' of a given theory? One way to get at this would be in terms of the structure of apriori entailment among human thoughts. I can take a shot at defining this, if you would like.

It's not crucial that there be a single best N-theory or a single ideal statement. There could instead be a best class of theories and a best class of statements. Then the basic quantifier would be the one shared among that class.

Unknown said...

The notion that there is a best N-theory of the world (for each N) out there isn't something I'm making up completely from scratch. One of the prominent theories about what 'laws of nature' are makes use of this idea, and in discussions about physics, you often hear references made to 'the final theory' --- a hypothetical 'complete' theory of physics which, so to speak, does all the work there is to be done. That sort of thing is along the lines of what I mean by 'the best theory of the world'.

If we did have such a theory, and there was a quantifier in it of the sort I've described, we'd probably have good reason to think that the quantifier it used was the one that 'carved reality at its joints'.

For the record, I think we can pretty much get there --- here and now --- just by doing metaphysics. But the only way I would know to demonstrate that point would be to argue for something like a certain complete theory of metaphysics, and this isn't the venue for that.

As for (B): What do you make of the theory that some concepts have the same content as logical complexes of other concepts? For instance, [... is a polygon and has four sides] is a logical complex of [... is a polygon] and [... has four sides], and [... is a quadrilateral] has the same content as this logical complex?

If you accepted that theory, then I'd say that B-existence is the content of the concept x such that it is natural to express it with the predicate "... exists" in English and there is no logical complex of other concepts that has the content that x does.

If you don't accept that theory, then do you find it sufficiently reasonable that you can apply my move (E) to it --- i.e., pretend that it's true and then figure out which existence concept its truth means that I am speaking about?

In terms of (C): The idea is based on a certain theory of what qualitative identity comes to. Two things are qualitatively identical if they have all the same 'internal' properties. They don't have to stand in all the same relationships. For instance, two spheres could be qualitatively identical even though one was right next to me and the other was in France.

So we have this notion of an internal property. But what is an internal property? I take it to be a property of how a thing is 'on the inside', roughly speaking, as opposed to a property of how a thing is related to something.

The best theory I know that makes this distinction rigorous is one on which internal properties are literally parts of their instances. So then things that are qualitatively similar, are qualitatively similar in virtue of sharing some parts.

In that case, B-existence is the simplest internal property. It's part of everything, and it accounts for the simplest and thinnest respect there is in which any two things can be qualitatively identical --- in fact, the only respect there is in which all things whatsoever are qualitatively similar with each other.

Unknown said...

(D) What about the idea that existence is the least determinate determinable? For instance, being red17 and red12 are both determined by being red; being red and being blue are both determined by being colored; being colored and being sweet are both determined by being spatially extended; and being spatially extended and being conscious are both determined by existence.

Existence is the lowest node on the branching tree that explains the relationships among all the different properties. It is the commonality that accounts for why all the properties behave similarly to a certain degree (for instance, they all obey the rules of logic).

Besides the question of whether existence is a property, what do you make of the predicate "... is, strictly speaking, ultimately metaphysically real (rather than just something we speak about as though it existed, for the sake of convenience)"? Even if that predicate doesn't express a property, I'd still say that "... B-exists" is coextensive with that predicate. So grok the one, you grok the other.

You asked what difference it would make whether there did, or did not, B-exist a certain mountain (given that all the particles would be there, arranged the same way, in either case). Two answers: First, the very fact that there did, or did not, B-exist said mountain would be a difference. But of course, that reply (though, in my opinion, true) is not very helpful for task of glomming onto B-existence.

So, second: I can't give another answer to what difference there would be if all the particles were arranged the same, but I can give a different sort of answer. Probably at some very basic level, the laws of nature that determine the probabilistic causal connections between things make reference to such matters as how many things exist (for a certain sense of exist) in a given spatiotemporal area and whether or not certain particles compose any existing thing. For instance, it may be that there is a fundamental law that promotes the existence of as many things as possible. The more closely and intricately related things are, the more candidates there tend to be for existing things. So then, that's why we end up with a universe in which so many things are closely and intricately related (like galaxies and organisms) as there are in our universe: a certain basic law promotes such organization in order to maximize the number of existing things.

Unknown said...

B-existence is whatever sort of 'existence' those laws are concerned with. On the present hypothesis, if mountains and so forth could not B-exist, then this law would not see to it that any organization resulting in mountains and so forth took place. So if mountains and so forth could not B-exist, there might be very few interesting structures of closely and intricately related things at all in the world.

You mentioned the question of contexts (existing out there, existing in mathematics). When I say "Something exists" in what I take to be my B-existence sense, I don't take myself to be deliberately talking about things 'out there' (interpreted in a spatial sense) or deliberately talking about things 'in mathematics'. I just take myself to be talking about what's real --- what there really is, wherever, however, whatever that may be. So then, for instance, I'd be hesitant to say that the doctor I met last night in my dreams exists, but I'd have no similar hesitation about the doctor I met yesterday in person. Basically, if I have no good reason to think 'it's not real' (points in sports, average Americans, dream people, fictional characters), then I happily affirm its B-existence.

Two more stabs at what I mean:

(F) The nation of English usages of "exists" is a monarchy, not a republic. They aren't all equal and 'equally good'. There's structure among them. There is one of them at the top.

You could, in principle, explicate the sense of any other English use of "exists" in terms of B-existence, but not vice versa. You could use the concept of B-existence while lacking any of the other English existence concepts, but not vice versa.

(G) There is, in some sense, the way the world really is, independently of how speak about it. It is because the world is that way, before we talk about it, that the things we say are false or true.

B-existence is in line with this sense of is. If anything --- anything at all --- really is (in this sense) a certain way --- any way at all --- then it B-exists.

Average Americans, for example, aren't (in this sense) any way at all, independently of our conventions of speech. They are merely products of our conventions.

Not sure if any of this helps. Thanks again for the conversation.


Unknown said...

PS -- I hope it doesn't seem like I'm making [B-existence] out to be some difficult, reclusive, arcane, technical concept. I take it to be a very natural sense of the English word "exists" --- the most natural one. On my view, most things most people speak of as "existing" do B-exist. Tables, desks, chairs, food items, messes, shadows, people, minds, regions of space ... the whole shebang.

It's just when you find out that something that you speak of as "existing" is, in some sense, 'not real' that then you have reason to call its B-existence into question.

"Oh! We spoke as though 'the sky' exists, but really, when you think about it, you can tell there isn't such a thing. It would have to be located somewhere if it really existed, and where, exactly, could it be located?"

"We speak as though 'the average American' has 2.2 kids, but really there's no such thing as 'the average American' or his 2.2 kids. They are not people who exist."

"We may talk as though there are 'imaginary numbers' --- multiples of the square root of -1 --- but they aren't real. They're just useful fictions for taking shortcuts in proofs."

"Yikes. What an insight. It turns out that not even nonpositive numbers and fractions and irrationals are real. There are only natural numbers!"

"You got all emotional when Boromir died in that movie, but you do know that the Lord of the Rings universe isn't real . . . right? I mean, it's not out there somewhere, existing in its own separate space-time continuum."

Lots of philosophers say similar things about compound objects and abstract objects. They say "They're not real; they don't really exist." I disagree with them, but I think we're using "real" (hence, B-existence) in the same sense.

Giving these examples in hopes they help show what I mean by B-exists --- or at least what I think I mean!

Angra Mainyu said...


To clarify, I don’t think that ‘enormously large’ is good enough for that particular kind of mathematical argument. But for instance, someone might say (though the use of ‘enormously’ might be somewhat unusual) that the function x^(0.00000001) grows faster than (log(x+2)^(10^1000)), so even if in any of the cases we can actually compute presently the latter is greater, there is some enormously large x for which the former is greater. Normally, one would say ‘for sufficiently large x’, but I think the above would be understood.

That aside, if the term ‘enormously large’ is not precise enough to make assertions in a context in which that level of precision is needed, then it’s also not precise enough to say whether some such assertion, sentence, etc., is true or false.

The issue is not limited to mathematics. For instance, one may argue as follows:

Q1: There is no entity E in the history of Earth such that E is an elephant and was alive at some time t0, but there were no elephants on Earth 1 second before t0.
Q2: There were no elephants on Earth 1 billion years ago.
C: There are no elephants.

I would say ‘elephant’ is precise enough for describing the world around us, in most cases. It’s not precise enough for a description that involves the history of life on Earth for billions of years and is precise to the level of seconds, so it would be improper to use it in a context requiring that amount of precision.
Now, if someone presses the matter and asks me whether Q1 is true or false, I would say that since 'elephant’ is not precise enough for being properly used in that context, the same goes for saying that Q1 is true or false.

Similarly, ‘enormously large’ may be precise enough in some contexts, but not in the context of an argument that addresses the set of all natural numbers, considering them one by one, at least in most common usages of ‘enormously large’.

As for (A), I don’t know that there is such ‘complete theory of the world’. Even if it existed in science and/or in ontology (which I don’t know), I would not include a theory about quantifiers in a theory about the territory (i.e., about the world around that, in an ontology, etc.).

In any case, we don’t need to settle that, since I don’t see how that would help me assess whether there is a disagreement between your respective positions beyond a disagreement about the meaning of some terms.

Angra Mainyu said...


Thanks for the conversation as well.
I’m afraid this is getting too long for me to address in the amount of available time. I’ll try to address some of your points now, but I don’t know for how long I can keep up.

When I say 'chimpanzees exist', or I say (talking about a set) 'A maximal element with property P exists', it seems I take myself to be talking about different domains, one the world 'out there' (the territory, so to speak), the other one an abstract, ideal category.

I don't know what to make of the 'really' exists. If someone asked me whether the maximal element really exists in a metaphysical sense, I would say I don't think I understand the question well enough, though in a common sense of 'really', the claim I made is really true (but then, I would say the same about claims within fictions).

Maybe we have different concepts of "exists", or more likely different theories about what we mean by 'exists', but in any case, I'm not closer to getting B-existence I'm afraid.

That said, you make the point that B-existence would be the most natural concept in English. But Alexander seems to agree that in the most common concept in English, mountains, etc., exist. Moreover, if there would be an observable difference in terms of the stuff we see (as you suggested), the fact is that Alexander does not deny that there are mountains, etc., in the usual sense, and does not take his claim to have any implications (as far as I can tell) for our ordinary observations.

So, I still don’t see that there is a disagreement other than a disagreement about the meaning of some terms.

Angra Mainyu said...

By the way, I think the claims about imaginary numbers, fractions, negative numbers, etc., vs natural numbers are misguided.

I think a claim that there is an imaginary number x such that x^2+1=0 is true, but moreover, trying to make a difference there between natural numbers and the others looks like saying numbers are in the territory so to speak, or in other words which numbers would go into an ontology, 'really' exists in some metaphysical sense, etc. (in the examples, the natural numbers),whereas others don't, whereas in all cases we have as our domain of discourse some abstract scenarios; it's true that the natural numbers are abstractions more closely linked to our daily experience (grossly oversimplifying, e.g., there are 3 apples over, let's consider a number 3), whereas others are more or less distant extensions, but that does not justify the claims in my view.

Unknown said...
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Unknown said...


Thanks again for this long discussion. I sympathize with the feeling that the length and breadth of our dialogue is making it hard to keep keeping up. So I hope you won't be offended if I keep this post very brief ... even at the price of not responding to all the excellent points you made in your last post.

The Best Theory wouldn't necessarily make claims about the most basic quantifier. It's just that a certain quantifier would actually be used in stating the theory. I.e., the ideal statement of the theory might contain an axiom like "Ex Fx". The "Ex" quantifier which literally is a part of that axiom would express the 'basic' quantifier.

It would be really surprising if there wasn't a family of best theories like this. Why? Well, if each of the best theories there are uses two quantifiers neither of which is defined in terms of the other --- say, a C-quantifier and a D-quantifier --- it seems that theory will have to include at least one additional axiom (not a definition) stating something about the relationship C-existence and D-existence. (Does C-existence entail D-existence? Or vice versa? Or neither? And in virtue of what are they both species of 'existence'?) That extra axiom adds complexity to the theory. So since simplicity is one of the measures of how good a given theory is, it seems that the best theories will not contain such an extra axiom.

I think Pruss and I agree that B-existence is the basic sort of existence, for much the same sense of "basic", but we disagree as to how closely "B-exists" matches the most natural English predicate "exists". So I affirm and he denies that pipes B-exist; we both affirm that they exist; and I affirm but he denies that [They exist] entails [They B-exist].

I think I'd be happy to say that the B-existing things are all things such that neither are they are fictional nor would we be outright mistaken to believe that they exist. So on my view, Pruss's view entails that mountains are fictional --- i.e., they exist but are fictional. (I don't know whether on Pruss's view, Pruss's view entails that result, because I don't know what Pruss thinks about being-fictional.)

About your elephant argument, suppose we reverse it:

(C') There are elephants.
(Q2) There were no elephants on Earth 1 billion years ago.
(Q1') Therefore, not: (There is no entity E in the history of Earth such that E is an elephant and was alive at some time t0, but there were no elephants on Earth 1 second before t0).

It seems like it is proper to assert each of C' and Q2, and it seems plausible that the inference from C' and Q2 is logically valid. But if its proper to assert each of some premises, and a certain inference from those premises to a certain conclusion is logically valid, then mustn't it be proper to assert that conclusion?


Dagmara Lizlovs said...

Is there going to be anything left of this dead horse when y'all are done beatin' it?

Unknown said...

Why, of course not. That would be wasteful.

Angra Mainyu said...


Don’t worry, I’m not offended at all. I’ve been brief in my previous reply to your comprehensive analysis as well, due to a lack of time. :)

That aside, as I see it, it may well be that for every model of physics (for instance) comprehensible by humans given enough time to study it, and perhaps with the aide of some set of computers C, there is one that makes slightly better predictions, even if comprehending it might need more time and/or the aid of better computers. If so, plausibly there is no best theory (since every theory would have to have a model like that, or entail it, but a better model is nomologically possible).

That’s only one alternative under which there is no best theory. There are other reasons. So, I’m not convinced that there is a best or a class or set of best theories.

But let’s say for the sake of the argument that there is a best theory, or set of theories, etc. That assumption isn’t helping me see a disagreement that is not about the meaning of the words (even about the word ‘fictional’ perhaps). Maybe it’s just that I do not have enough information about your respective views to see it, so I’ll leave it at that.

On the elephants issue, you mention that the inference is valid. It seems it would need additional premises about time, or connecting ‘history of Earth’ with the statements about time, etc., to be a valid inference.
Usually, many such premises are left implicit, and that’s no problem. I left all other premises implicit too in my example as well, but I was arguing against that kind of argument, and I didn’t need to make any of the other assumptions explicit in order to explain my take on the matter. On the other hand, in the case of your reverse argument, it seems to me that it’s improper to assert all of the premises together, one one factors in some of the implicit premises.

For instance, some of the premises one might use in an argument similar to the reverse argument would be (there are alternatives, but they seem to have the same difficulty):

R1: There were no elephants at any time prior to 1 billion years ago, and t0 is a time prior to 1 billion years ago.
R2: There are elephants at any time from t1 to the present day, which is later than t1.
R3: There is some natural number n, such that t0 + n seconds is later than t1.
R4: For every natural number m between 1 and n, there is some time t0 + m seconds.

...and so on. But I don’t need to go on in this context, since I think that it’s improper to assert R1,R2, R3 and R4 in the context of the same argument; the word ‘elephant’ does not have enough precision to be used in combination with something like R3&R4, in the same argument (they might be proper separately).

As I said, I recognize that it’s an uncommon view.

Unknown said...

Hi Angra,

Have you ever, by chance, encountered David Lewis's essay "New Work for a Theory of Universals"? In it he gives cases that motivate a concept of 'being natural' in the metaphysical sense of 'natural'. I'd say that probably what Pruss and I mean (though, of course, I'm more confident to speak for myself than for Pruss) is that there is a certain "... is something" predicate which is the most, or even only, metaphysically natural one.

Summary of B-existence:

(1) Most natural sense of "exists," for David Lewis's sense of 'natural'
(2) Equivalent to [is real]
(3) Content of simplest [existence] concept humans possess
(4) Sense of "exists" that expresses the mereologically simplest 'existence' property
(5) Only sense of "exists" expressed by any syntactically simple predicate in The Best Theory
(6) The thinnest, least rich of all qualities
(7) The most determinable determinable
(8) Equivalent to [existing and not fictional]
(9) Roughly equivalent to [is a feature of the world, independently of our thoughts and speech]
(10) The property most epistemically likely to satisfy all or most of (1) through (9)

That's probably the best I can do right now at spelling this out.

Perhaps if either you think there is no such sense of "exists" or else you are unsure whether or not there is such a sense, then you could interpret disagreements (like mine and Pruss's) about what really exists as conflicts between the views [There is a sense of "exist" that satisfies (10) and on it, F's 'exist'] and [There is a sense of "exist" that satisfies (10) and on it, no F's 'exist']?

About arguments and elephants:

P1. Each sentence, on each meaningful use, expresses some proposition.
P2. In a given context, each proposition is either true or false.
P3. Each premise in your elephant argument has a meaningful use, even in the context of the elephant argument.
L1. So for each premise in your elephant argument, there is --- in the context of the argument --- a meaningful use on which it expresses a proposition.
P4. None of these propositions is false in the context of the elephant argument.
L2. So all of them are true in the context of the elephant argument.
P5. The conclusion of the elephant argument follows from its premises by valid inferences.
P6. Any conclusion that follows by valid inferences from premises that are true in a given context is itself true in that context.
C. So the conclusion of your elephant argument is true in the context of the elephant argument.

I'm referring to the version of the elephant argument you alluded to in your last post --- the one with all the premises spelled out. I'd be curious to know at what point you get off-board with the argument I've just given.

Maybe you'll say that it's not proper to assert each of my just-stated premises P1 through P6 in the context of the same argument? Well, maybe. But isn't it simpler to say that it is proper to assert them, and so any conclusion they entail is true?


Angra Mainyu said...


While I’m not familiar with the theory, as far as I can tell your points (2), (3), (8) seem to clearly indicate that you’re talking about the ordinary concept of ‘exists’, in English (not sure about (9), though; our thoughts are real (i.e., there is an actual entity thinking); and there are other potential issues with )(9)). The same goes for some of your previous points.

So, (I think) I get that.

But it seems to me that there is agreement here in that the usual sense of ‘exists’, mountains, cars, planets, stars, oceans, exist.

On the other hand, there may be a disagreement on whether the usual sense (explained in (2), (3) and (8)) is the same as the meaning used in philosophy, and then on whether in that sense, mountains, planets, etc., exist.

So, maybe there is disagreement on whether two different meanings are at play, or only one.

Even so, my impression would be that the usual, intuitive grasp of ‘exists’ is similar in different competent English speakers (that is somewhat tentative, though), and if so, I don’t see any significant differences (with regard to existence) in the picture of the portion of the world around us that you have and that he has, at least with regard what exists in the usual sense of the expression when asserting existence of planets, stars, pipes, etc. (though this might be because my knowledge of your respective pictures is very limited; but based on the exchange so far, I don't see that difference).

Angra Mainyu said...


Regarding the elephant argument, I’m not sure if I’ve been unclear (and if so, how to make my position more clear), but I would still take issue with (among others) P3, and say it’s improper to use the word ‘elephant’ in the context of an argument containing premises like R3&R4.

In other words, I don’t think the word ‘elephant’ is precise enough as a description of features of an environment described to the precision of seconds and over billions of years of Earth’s history.

If you like, there is a mismatch between the precision in the description required to in order to use some of the premises, and the (lack of) precision some of the other premises have.

I’m not entirely sure ‘not meaningful’ is the right term but rather not sufficiently precise, so I would reject P3 without denying it (i.e., I would refrain from accepting it; there is some vagueness here in ‘meaningful’, so I’m not sure whether it applies).

The same applies goes for claim P1, and ‘proposition’. I do not know that in that context, all of the expressions involving elephants required to make the argument express some proposition. Can propositions be vague?
If not, then that would be a problem for the view that sentences express propositions, so I would say that they can.
But if propositions can be vague, and in some context, there are different degrees of precision in the assertions in a way that making assertions would result in absurdities not resulting from anything but the imprecision of the terms, are propositions still being expressed?

For instance, we may as well consider the usual ‘heap’ argument. One grain of sand is not a heap. But some number M make up a heap. However, when people make ‘heap’ assertions, they’re (normally, in the usual senses of the word) not making assertions with sufficient precision to distinguish between the classes ‘heap’ and ‘things that are not heaps’ to the precision of one grain of sand.

In that context, would the claim ‘If m grains of sand are not a heap, neither are m+1‘ express a proposition?
I would say it’s improper to assert that, so I’m inclined to say probably not, but if one has a theory of propositions so that there are improper propositions, then I don’t know. Regardless, I would still say it’s improper to use the vague concept ‘heap’ in such a context (independently of whether they express propositions).

Similarly, when people make ‘elephant’ assertions, they’re not making assertions with sufficient precision to distinguish between the classes ‘elephants’ and ‘things that are not elephants’ when the variables (i.e., the objects to be classified) range over the last billion years, in steps lasting no more than one second.

I’m afraid I don’t know how to explain my take on this matter better.
As for the alternative conclusion you propose, I’m not sure which one is it. Could you clarify that, please?

Unknown said...
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Unknown said...

Hi Angra,

Continued thanks for the fascinating discussion. This is starting to shed some light for me on how one's theories of propositions and sentences might affect one's views on vagueness.

What I took to be the conclusion to your elephant argument, as referenced in my (C) in my last post, was Q1' from my post before that:

Q1' = "Not: (There is no entity E in the history of Earth such that E is an elephant and was alive at some time t0, but there were no elephants on Earth 1 second before t0)."

I was recommending that we accept P1 through P6 from my last post, and so accept Q1'. The easiest way I see to accept Q1' is to say that yes, there is some entity which is the first elephant in the history of the Earth; but there is no fact of the matter as to precisely which entity E is.

You're taking a different approach: rather than accepting P1 through P6 (in the context of the argument in which they occur), you refrain from accepting P1 and P3 (at least in that context). My question was: Why do that (refrain from accepting P1 and P3) rather than do what I propose (accept Q1')?

In response, you asked,

"Can propositions be vague? ... [I]f propositions can be vague, and in some context, there are different degrees of precision in the assertions in a way that making assertions would result in absurdities not resulting from anything but the imprecision of the terms, are propositions still being expressed?"

I can always tell you what I think the answers to these questions are, but of course, what the right answers are depends on the right answer to the question of what is the correct theory of what vagueness is and what propositions are and how truth (correspondence of propositions to reality) works. Oh deary. I doubt we'll manage to delve through all that here!

But in brief, my own opined answers: Yes, propositions can be vague. However, there is never a case where genuine absurdities result merely from differences in the degrees of the precision of various terms that are used in the assertions that are taken as premises in some argument. So in the elephant argument, we accept Q1'. It is not an absurdity. As for the heap sentence "If m grains of sand don't make a heap, then m + 1 grains of sand don't make a heap", I think that if the heap sentence is not meaningful, then that is because the heap sentence (precisely) expresses a metaphysically impossible state of affairs rather than because of any imprecision in the heap sentence's terms. The background theory for this take on the issue would be that all meaningful sentences express possibilities. I'm not sure whether that background theory is true. If that background theory is not true, then the heap sentence is meaningful but false.

Thoughts? I feel like I've got a long way to go to really understand all this. The present conversation is helping me better understand what the questions are whose answers I cannot give.


Angra Mainyu said...

Hi, Richard,

You’re welcome, and thank you as well.
I’m afraid I have limited time at the moment, but briefly, on the background theory you mention, I would argue that it’s false, on the following grounds (among others):
1. The sentence ‘Humans exist, or humans do not exist’ seems to be true. If you put it in terms of propositions, it expresses a true proposition (though I think there is vagueness, but that aside). But then, it seems its negation is false, not meaningless. But the negation seems to express an impossible state of affairs.
2. If there is any problem with the example in 1., let’s consider instead the sentence ‘2 + 2 = 4 or it is not the case that 2 + 2 = 4‘.
3. The sentence ‘A moral error theory is true’ seems to be meaningful. At least, I seem to have no difficulty understanding it. But if it’s false, it’s necessarily false (or expresses a necessarily false proposition, etc.). And if the sentence is true, then the sentence ‘It’s immoral to torture cats for fun’ is false, and necessarily so, or in terms of propositions if you like, it expresses a false proposition (and necessarily false), etc.
4. Given that most philosophical theories are incompatible with other theories, generally speaking, this theory would render most philosophical theories not false, but meaningless. But that does not appear to be the case.
5. The sentence ‘The background theory that all meaningful sentences express possibilities’ seems meaningful. But, then, it seems that so is the denial of that sentence.

So, it seems that there are meaningful sentences that express impossibilities.

Side note: while I hold that this one is not a counterexample, the sentence ‘Jesus was a human preacher, with no superhuman powers or knowledge.’ is clearly meaningful. I hold it’s true, whereas Christians and Jesus mythicists consider it false. But if you hold that Christianity is necessarily true and the background theory in question is true, then based on that you ought to conclude that the sentence is meaningless, rather than false (the sentence and/or the proposition, etc.).

I will try to address the other points when I have more time.

Unknown said...
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Unknown said...

Hi Angra,

Certainly all those examples seem meaningful. So does "There is a round square." The concern would be that this seeming is illusory --- the sentences seem meaningful but are not.

I do take the mere fact that something seems meaningful to provide some rational grounding for the belief that the thing in question really is meaningful. But in most cases such grounding is defeasible. So my concern is that there might be more evidence/grounding for the contrary view (i.e., the view that such sentences are not meaningful) than their mere seeming of meaningfulness provides for the view that they are meaningful. In that case, it would be rational to disbelieve that they are meaningful.

Do you know of any reason to think those impossible sentences are meaningful, besides the fact that they seem so?

One way to cash out the theory that they are not meaningful: to be meaningful, a natural-language sentence must express some sentence in Mentalese. But no metaphysically impossible sentences exist in Mentalese. That is why --- for a certain sense of 'conceive' --- metaphysical impossibilities are inconceivable. We cannot conceive of them because such conceiving involves consciously entertaining Mentalese sentences that correspond to the states of affairs we are trying to conceive of, and in the case of metaphysical impossibilities, the requisite Mentalese sentences just aren't there. I think this theory has some plausibility because: (A) it explains why we have trouble conceiving of certain hypothetical situations, even when we seem to understand the sentences describing those situations, (B) it explains the observed and intuited links between conceivability and possibility, and (C) it permits a simple theory of modality according to which every proposition P is a Mentalese sentence & (possibly P) iff (P exists).

We could also say this: There are at least two natural-English senses of the word "meaningful". A sentence is meaningful-sub1 just in case each word in the sentence is meaningful and the words are arranged with acceptable syntax. A sentence is meaningful-sub2 if it expresses some sentence in Mentalese. So impossible sentences are meaningful-sub1, and when they seem meaningful, they are seeming meaningful-sub1. But they do not seem (and in fact are not) meaningful-sub2. But meaning-sub2 is what is required for truth and falsity. So when we have the intuition that impossible sentences are meaningful, this intuition is correct: such sentences are meaningful. Nevertheless, they are not meaningful --- not in the sense required in order to be true or false.

(About the Jesus sentence: I'm a descriptivist about proper names, so such claims don't come out as necessarily false on my view. I'd say that for such sentences, there is a Mentalese sentence expressed by the claim.)

Angra Mainyu said...


‘Square’ seems to mean that it has four sides; ‘round’ seems to mean that the distance to the center is constant. In non-Euclidean geometries, there are round squares, and so clearly that’s meaningful. And in Euclidean geometry, to say that a figure is a round square is to say that it has the properties I mentioned above. It’s false, as it can be established within an Euclidean framework.

You ask why I think that those sentences are meaningful, beyond the fact that they seem so. But that they seem so clearly is decisively strong. I can intuitively tell I understand the words in question, and I can communicate those words to others. I can see how other people successfully communicate using those sentences.
Moreover, when I claim that those sentences are meaningful, it seems very clear that I’m saying something meaningful, and that you understand what I’m saying. But the theory in question seems to entail that the claim that such theory is false, is a meaningless claim (at least in the sense that it’s neither true nor false). That claim seems clearly false to me, though I don’t know what other kind of evidence of meaningfulness you may be asking about, or what might be stronger than that. What kind of evidence would you be looking for? (I will try a moral example below, just in case).

That aside, the theory in question seems to imply that the negations of necessarily true sentences are not false sentences. Would you agree with that?

As for the suggestion that that would explain our difficulty for conceiving some hypothetical situations, I think the term ‘conceive’ is unclear in this context, but in any case, I think the cost of the theory that are meaningless (which is the cost of rejecting something that seems obviously true) is simply far too heavy. For that matter, one may explain things by means of assortments of error theories, even Matrix-like scenarios, etc., but those hypotheses would be just too implausible. (additionally, that would seem to be ontologically committed to propositions, a view I don’t agree with, but leaving that aside).

I’m not an expert on the Mentalese hypothesis, but if it renders such sentences meaningless, I would say that it’s false, since it’s too clear that they’re meaningful. With regard to the sub-2 sense, I’m not sure that distinction is a natural English sense of ‘meaningful’; that seems to assume that the Mentalese hypothesis is correct.

About the Jesus sentences, I’m not familiar enough with your descriptivist view, but how about the following sentence?
The person the term ‘Jesus’, as usually used in religious contexts, refers to, never had any superhuman powers or knowledge.

Also, what about moral disputes?
The case you brought up earlier (i.e., abortion) may illustrate the point:
Let’s say that I claim that in most cases, having an abortion in order not to reproduce because one does not want children is not immoral. I take it you disagree. But do you believe that that moral claim is neither true nor false?

Angra Mainyu said...


I will more or less briefly address the second option that you offer, namely that the sentence "If m grains of sand don't make a heap, then m + 1 grains of sand don't make a heap". More precisely, I will address the hypothesis that “for all natural numbers m if m grains of sand don't make a heap, then m + 1 grains of sand don't make a heap” (at least, that’s what I meant in that context), is meaningful but false, that would entail that there is a certain number m(heap, sand) such that m(heap, sand) grains of sand do not make a heap, but m(heap, sand)+1 do.
That, however, does not seem plausible (and similar considerations apply to elephants by the way), for a number of reasons. I will address some of them.
1. Before I address the term ‘heap’, there is the question of what counts as a ‘grain’ of sand, and the same even goes for ‘sand’. Vagueness is ubiquitous. But let’s leave those issues aside, at least for now.
2. The term ‘heap’ is a term in the English language, and its meaning is determined by usage. For instance, people might as well start using ‘heap’ to mean ‘two or more items of a certain kind’, and even though that too would have its own degree of vagueness, it’s clear that three grains of sand would make up a heap, but that would be because the meaning of the word ‘heap’ would change. For that matter, they might use ‘heap’ to mean ‘elephant’.
So, the meaning of ‘heap’, and thus also the number m(heap, sand), is the result of usage among English speakers.
But here’s a difficulty. When a person learns how to use the word ‘heap’, they usually do so by watching others use it. And they see some examples of heaps, and some examples of things that are not heaps. In particular, a person may have encountered some examples of heaps of sand, or they might apply the word 'heap’ in the case of sand, by similarity.
Yet, each person has encountered different cases, not exactly the same. Given that, and given also that different people have slightly different minds, it seems almost certain that there will be some interpersonal differences in their dispositions to use the words. So, it seems that even if each person P determined by her usage a single m(heap, sand, P), the number would vary for different P. I don’t see a way around that. One may try majorities, etc., but then a question is how the majority is computed, and then what determines that, as well as the relative weighs of the views of each person, etc. (i.e., by whose concept is the relative weight determined?).
But there is a another difficulty, namely that even each individual person probably does not have a concept that is sufficiently fine-grained to establish a single m(heap, sand, P). She might even have several very similar concepts of ‘heap’ that she’s willing to use in different contexts, and none of them establish a single such m (so, there might not even be a set of such numbers relative to each person, let alone a general one).
But regardless of whether she has one or several vague concepts, it seems plausible to me that the usage of the word ‘heap’ by person P is not precise enough to determine a number m(heap, sand, P).
As I see it, it’s very probable that there are certain amounts of sand that would be deemed ‘heap’ or not depending on factors like what other amounts of sand surround them. For instance, if it’s 1 grain here, one grain there, and some greater amount X, then P might be inclined to call X a heap, whereas she might call it ‘not a heap’ if surrounded by much greater amounts. Or maybe it’s the other way around, for some P. It’s hard to tell. But there may even be other factors, like how people surrounding P may appear to be using ‘heap’ at that particular time, etc.
If that is not so, how do you think that a single, arbitrarily precise concept of heap (or, for that matter, ‘elephant’) is formed, not only for each individual but for a community? (and how are the boundaries of ‘community’ determined?

Angra Mainyu said...


I would say that the case of the term ‘elephant’ is relevantly similar to the previous one, though slightly different. For instance, some people are recognized as experts (say, biologists, or a subset), and most people might be willing to defer to their usage to some extent. But even then, there are issues like who counts as a relevant expert, how the different person’s usages are weighed, etc., and of course the issue of vagueness in the usage by a single person is there as well.
So, it seems to me that the issues I mentioned, in one way or another, are present too.

Dagmara Lizlovs said...

All this started over what constitutes a blowgun!! It's a good thing you guys don't write gun laws! By the way, your dead horse just won the Kentucky Derby so you can stop beating it now, or are we going all the way to the Triple Crown? :-)

Alexander R Pruss said...

Well, a blowgun is a particularly nice case of an artifact, because it can be just an ordinary piece of pipe that's used for a particular purpose.

Dagmara Lizlovs said...


Let's enter this dead horse in the Preakness so we can beat it some more. I think it has a chance. :-)

By the way, as soon as our new gun laws take effect in Maryland, I know where I can get a really good blowgun. And no, it's not just a piece of pipe, I think that the interior is something of a converging diverging nozzle instead of a straight pipe. And then there are boundary layer issues and differences between laminar and turbulent air flows. Do you have an Aerospace Department at Baylor to run this by? :-)

PS: When blowguns are outlawed, only outlaws will have blowguns.

Alexander R Pruss said...

A serious problem with a variable diameter blowgun is that the dart skirt won't seal in the wider sections or else there will be too much friction in the narrower sections.
An expanding skirt might help, but there might be friction issues. Though I think some blowguns are ptfe coated inside, which no doubt helps.
I think the place to concentrate the engineering would be dart design.

Unknown said...

If artifacts don't exist and guns get outlawed ... then I would pay a lot of a nonexistent money for a really good nonexistent blowgun.

ozero91 said...

This reminds me of Dennet's "two-bitser" argument. Sort of throws a wrench into materialist explanations of intrinsic intentionality.