Partial and complete explanations

1. Any explanation for an event E that does not go all the way back to something self-explanatory is merely partial.

2. A partial explanation is one that is a part of a complete explanation.

3. So, if any event E has an explanation, it has an explanation going all the way back to something self-explanatory. (1,2)

4. Some event has an explanation.

5. An explanation going back to something self-explanatory involves the activity of a necessary being.

6. So, there is an active necessary being. (4,5)

I am not sure I buy (1). But it sounds kind of right to me now. Additionally, (3) kind of sounds correct on its own. If A causes B and B causes C but there is no explanation of A, then it seems that B and C are really unexplained. Aristotle notes that there was a presocratic philosopher who explained why the earth doesn’t fall down by saying that it floats on water, and he notes that the philosopher failed to ask the same question about the water. I think one lesson of Aristotle’s critique is that if it is unexplained why the water doesn’t fall down it is unexplained why the earth falls down.

A cosmological argument from a PSR for ordinary truths

Often in cosmological arguments the Principle of Sufficient Reason (PSR) is cleverly applied to vast propositions like the conjunction of all contingent truths or to highly philosophical claims like that there is something rather than nothing or that there is a positive contingent fact. But at the same time, the rhetoric that is used to argue for the PSR is often based on much more ordinary propositions, such as Rescher’s example of an airplane crash which I re-use at the start of my PSR book. And this can feel like a bait-and-switch.

To avoid this criticism, let’s suppose a PSR limited to “ordinary” propositions, i.e., the kind that occur in scientific practice or daily life.

1. Necessarily we have the Ordinary PSR that every contingent ordinary truth has an explanation. (Premise)

2. That there is an electron is an ordinary proposition. (Premise)

3. It is possible that there is exactly one contingent being, an electron. (Premise)

4. Necessarily, if no electron is a necessary being, then any explanation of why there is an electron involves the causal activity of a non-electron. (Premise)

5. Let w be a possible world where there is exactly one contingent being, an electron. (By 3)

6. At w, there is an explanation of why there is an electron. (By 1, 2 and 4)

7. At w, there is a non-electron that engages in causal activity. (By 4, 5 and 6)

8. At w, every non-electron is a necessary being. (By 5)

9. At w, there is a necessary being that engages in causal activity. (By 7 and 8)

10. So, there is a necessary being that possibly engages in causal activity. (By 9 and S5)

So, we have a cosmological argument from the necessity of the Ordinary PSR.

Objection: All that the ordinary cases of the PSR show is that actually the Ordinary PSR is true, not that it is necessarily true.

Response: If the Ordinary PSR is merely contingently true, then it looks like we are immensely lucky that there are no exceptions whatsoever to the Ordinary PSR. In other words, if the Ordinary PSR is merely contingently true, we really shouldn’t believe it to be true—we shouldn’t think ourselves this lucky. So if we are justified in believing the Ordinary PSR to be at least contingently true, we are justified in believing it to be necessarily true.

Necessary Existence, now in the US

Josh Rasmussen's and my Necessary Existence book is now released in the US.

Pruss and Rasmussen, Necessary Existence

Josh Rasmussen's and my Necessary Existence (OUP) book is out, both in Europe and in the US. I wish the price was much lower. The authors don't have a say over that, I think.

The great cover was designed by Rachel Rasmussen (Josh's talented artist wife).

From particular perfections to necessary existence

This argument is valid:

1. Necessarily, any morally perfect being can morally perfectly deal with any possible situation.

2. Necessarily, one can only morally deal with a situation one would exist in.

3. So, necessarily, any morally perfect being is a necessary being.

That said, (1) sounds a bit fishy to me. One may want to say instead:

4. Necessarily, any morally perfect being can morally perfectly deal with any possible situation in which it exists.

But that’s actually a bit weaker than we want. Imagine a being that can deal with one situation and only with it: the case where it has promised to eat a delicious cookie that is being offered to it. But imagine, too, that the being can only exist in that one situation. Then (4) is satisfied, but surely being able to fulfill a promise to eat a cookie isn’t enough for moral perfection. So we do actually want to strengthen (4). Maybe there is something in between (1) and (4) that works. Maybe there isn’t.

There are other arguments of the above sort that one can run, based on premises like:

5. A maximally powerful being can weakly actualize any possibility.

6. An epistemically perfect being can know any possible proposition.

7. A rationally perfect being can rationally deal with any possible situation.

It is looking like moral perfection, maximal power, epistemic perfection and rational perfection each individually imply necessary existence.

If this is right, then we have an ontological argument:

8. Possibly, there is a morally perfect or a maximally powerful or an epistemically perfect or a rationally perfect being.

9. So, possibly there is a necessary being. (By arguments like above.)

10. So, there is a necessary being.

I am not saying that this a super-convincing argument. But it does provide some evidence for its conclusion.

Progress report on books

My Necessary Existence book with Josh Rasmussen is right now in copyediting by Oxford.

I am making final revisions to the manuscript of Infinity, Causation and Paradox, with a deadline in mid October. As of right now, I've finished revising five out of ten chapters.

I am toying with one day writing a book on the ethics of love.

Necessary Existence

Josh Rasmussen's and my Necessary Existence book is now complete. We just sent the final manuscript to Oxford. We're both quite happy with the book.

Necessary Existence

I forgot to post an update earlier in the month that my and Josh Rasmussen's book manuscript Necessary Existence was sent off to the publisher for review. This book contains a bunch of arguments, some of them developed on this blog, others by Josh alone, some in correspondence by the two of us, all of which contend that there is at least one concrete necessary being, where an entity is concrete if and only if it is possible that it causes something.

Is a necessary being inconceivable?

Consider this argument:

1. Obviously necessarily, if N is a necessary being that exists, it is impossible that N doesn't exist.
2. It is conceivable that N doesn't exist.
3. So it is inconceivable that N exists.

For this argument to work, we need to be able to make the inference from:

4. Obviously necessarily, if p, then necessarily q.
5. Conceivably not q.
6. So, not conceivably p.

Suppose that p just is the statement that necessarily q. Then (4) is uncontroversial. If the above argument form is good, then so is this one:

7. Conceivably not q.
8. So, not conceivably necessarily q.

But why can't we conceive both of not q and of necessarily q? Why should the ability to conceive of one thing, viz., the necessity of q, preclude the ability to conceive of another, viz., not q?

The principle that conceivability is defeasible evidence of possibility may seem relevant, but I don't think it establishes the point. That I can conceive of necessarily q is evidence of the necessity of q. That I can conceive of not q is evidence if the possibility of not q. So, if both, then I have evidence for two contradictory statements. Nothing particularly surprising there: quite a common phenomenon, in fact!

Suppose A and B are contradictory statements. It may be that evidence for A is evidence against B. But is evidence for A evidence against there being evidence for B? If it is, it is very weak evidence. Likewise, even given the principle that conceivability is evidence for possibility, the argument from (7) to (8) is very weak, much weaker than the inferential strength of this principle.

To summarize: The strength of the inference from (1) and (2) to (3) in the original argument is about equal to the strength of evidence that the existence of evidence for A provides against the existence of evidence against A. But the existence of evidence of A provides very little evidence against the existence of evidence against A. So the original argument is a very weak one. It would be improved if the conclusion were weakened to the claim that it is impossible that N exists, and then I would focus my attack on (2).

Attempted murder

Every wrong act is wrong because it wrongs someone or something. Say that an act is fundamentally self-wronging provided that it is wrong because it wrongs oneself. It's controversial whether there are fundamentally self-wronging acts, but I think there are. However, attempted murder (as long as it's not attempted suicide) is not a self-wronging act. But now imagine that Bob is the only contingent being in existence, and Bob attempts to murder someone else (of course, to do that he will presumably have to have a false belief that there is another contingent being). Bob commits attempted murder, which is not a fundamentally self-wronging act. Hence it wrongs someone or something other than himself. Only concrete beings can be wronged. So there is a concrete being other than Bob. Since Bob is the only contingent being in existence, there is a concrete necessary being.

Existential commitments of First Order Logic

In First Order Logic (FOL), we have two oddities: (a) if "b" is a name, then it's a theorem that b exists, and that (b) it's a theorem that something or other exists. We might conclude that since theorems hold necessarily, everything that exists, exists necessarily. Or we might be embarrassed and reject FOL, going for some version of free logic.

Maybe, though, what we should say is that just as ordinary language sentences have presuppositions, a language can have presuppositions. Presuppositions make communication easier. Instead of a nurse's making the convoluted request "If you have an age, please tell me your age; otherwise, please tell me that you're ageless", the nurse can simply presuppose that you have an age and ask: "How old are you?" It's not particularly surprising that presuppositions might also make reasoning easier. It can be easier to reason on the presupposition that there is something, and on the presupposition that names have reference. So FOL has presuppositions. No need for embarrassment: the presuppositions make things simpler for us, much as it's easier to work with commutative groups than groups in general.

Of course, if a language L has presuppositions, then we shouldn't expect its theorems to hold necessarily. Rather, a theorem is something that necessarily follows from the presuppositions. We can without embarrassment say that it's a theorem of an appropriate dialect of FOL that Obama exists, since the only modal conclusion we can make is that, necessarily, if the presuppositions of the dialect are true, Obama exists.

We could search for a logic without presuppositions. That's a worthwhile quest, and leads to exploring various free logics. But we shouldn't go overboard in worrying about the metaphysical consequences if we don't find a good one. Likewise, we shouldn't worry too much if we can't find a satisfactory quantified modal logic. These are just tools. Nice to have, but people have done just fine with modal and other arguments for centuries without much of a formal logic.

Four arguments that there must be concrete entities

An entity is concrete provided that it possibly causes something. I claim that it is necessary that there is at least one concrete entity.

Argument A:

1. The causal theory of possibility is true.
2. So, necessarily there is at least one concrete entity.

Argument B:

3. Necessarily, if there is time (respectively: space, spacetime, laws), there are concreta.
4. Necessarily, there is time (respectively: space, spacetime, laws).
5. So, etc.

Argument C:

6. Every possible fundamental fact can be reasonably believed (respectively: known).
7. Nobody can reasonably believe (respectively: know) there are no concreta.
8. Necessarily, if there are no concreta, then that there are no concreta is a fundamental fact.
9. So, etc.

Argument D:

10. Necessarily, if there is nothing concrete, the only fundamental contingent fact is that there is nothing concrete.
11. Necessarily, some fundamental contingent fact has a potential explanation.
12. Necessarily, that there is nothing concrete has no potential explanation.
13. So, etc.

And since, plausibly (though controversially),

14. If it necessary that there is a concrete entity, there is a necessary concrete being,

it follows that there is a necessary concrete being. And this some call God. :-)

Current task

In case anybody is interested, these days I'm working on a book with Josh Rasmussen arguing there is at least one necessary being (definition: an entity that is concrete and exists necessarily; an entity is concrete if and only if it is possibly a cause), based in part on the arguments on necessarybeing.net. We've got about 40000 words so far:

$ wc -w chapter?.tex
3019 chapter1.tex
7945 chapter2.tex
12295 chapter3.tex
9255 chapter4.tex
435 chapter5.tex
6676 chapter7.tex
4547 chapter8.tex
44172 total

I'm in the middle of chapter 8, which is a variant of my Goedelian ontological argument, with a special focus on the negative formulation.

From necessary abstracta to a necessary concrete being

Start with the Aristotelian thought that abstract entities are grounded in concrete ones. Add this principle:

1. If x is grounded only in the ys, then it is impossible for x exist without at least some of the ys existing.

Consider now a necessarily existing abstract entity, x, that is grounded only in concrete entities. (Some abstract entities may be grounded in other abstract entities, but we want to avoid circularity or regress.) Thus:

2. x is a necessarily existing abstract entity.

Add this premise:

3. There is a possible world in which none of the actual world's contingent concrete entities exist.

This isn't the more controversial assumption that there could be a world with no contingent concrete entities. Rather, it is the less controversial assumption that these particular concrete entities that we have in our world could all fail to exist, perhaps replaced by other contingent concrete entities.

If the concrete entities that ground x are all contingent, then we have a violation of the conjunction of (1)-(3), since then all the actual grounders of x could fail to exist and yet x is necessary. So:

4. There is at least one necessary contingent entity among the entities grounding x.

An Aristotelian argument for a necessary concrete being

All of the quantifications in the following are to be understood tenselessly. Consider these premises:

1. If y is an entity grounded solely in the xs and maybe their token relationships, then it is impossible that y exist while none of the xs exist.
2. All y is an abstract being, then there are concrete xs such that y is grounded solely in the xs and maybe their token relationships.
3. There is a possible world in which none of the actual world's concrete contingent beings exist.
4. There is a necessarily existing abstract being.

Alright, then:

5. Suppose there are no necessary concrete beings. (For reductio)
6. Let y be a necessarily existing abstract being. (4)
7. Let the xs be concrete entities such that y is grouned solely in the xs and maybe their relationships. (2 and 6)
8. The x are contingent. (5 and 7)
9. Possibly none of the xs exist. (3 and 8)
10. Possibly y does not exist. (1,7 and 9)
11. y does and does not necessarily exist. (5 and 10). Which is a contradiction.
12. So, by reductio, there is a necessary concrete being.

Premise 2 is a basic assumption of Aristotelianism. Premise 1 is more problematic. Note, however, that it is very plausible that this computer could not have existed had none of its discrete parts (CPU, screen, etc.) existed (i.e., ever existed, since the quantifications are tenseless). An object can have its parts get gradually replaced, but by essentiality of origins it must at least start off out of some of the stuff it started out of. And so it must have at least some of its constituents (at some time) in any world where it exists.

Further, premise 1 follows from the thought that when y is grounded solely in the xs and maybe their token relationships, then there is nothing more to the being of y than the being of the xs and maybe their relationships. But the token relationships of the xs couldn't exist if the xs never existed.

Premise 3 is very plausible. It must, of course, be distinguished from the much more controversial claim that there could be no contingent beings. Premise 3 is, on its own, compatible with the thesis that necessarily something contingent or other exists, as long as there aren't any contingent things that necessarily exist.

If premise 3 is the sticking point, but S5 is granted, an alternate argument can be given. Very plausibly, there is a possible world w containing a concrete being c with the property that all the concrete beings of w modally depend on w, i.e., they couldn't exist without c. (For instance, maybe they are solely grounded in c and its properties, or maybe c is a common part of them all, or maybe there is nothing but c.) Then running our argument in that world we conclude that c is a necessary being in w, and, by S5, actually.

An Aristotelian argument from a necessary being to a necessary concrete being

Suppose that none of the participants in World War II had ever existed. Then it would have been impossible for World War II to occur. Why? Because World War II's existence is solely grounded in the existence, activities, properties and relations of the participants, and

1. If an entity x's existence is solely grounded in the existence, activities, properties and/or relations of the Fs, then it is impossible for x to exist without at least one of the Fs existing.

Now add this Aristotelian axiom:

2. If x is abstract, then x's existence is solely grounded in the existence, activities, properties and/or relations of concreta.

Finally, add this:

3. Every being is either concrete or abstract.
4. There exists a necessary being.
5. There is a world where no one of the contingent concrete beings of our world exists.

One might try to give the number three as an example of a necessary being to support (4).

Now, let N be the necessary being of (4). If N is essentially concrete, we get to conclude that there is a concrete necessary being. If N is essentially abstract, then N is grounded in the existence, activities, properties and/or relations of concreta. If some concreta are necessary, we conclude that there is a concrete necessary being. So suppose all concreta are contingent. Then the beings that N is grounded in don't exist at the world mentioned in (5), which violates the conjunction of (1), (2) and the necessity and abstractness of N. So, no matter what, it follows from (1)-(5) that:

6. There is a necessary concrete being.

Necessary being survey

Josh Rasmussen has a very interesting survey on propositions related to the existence of a concrete necessary being.

An argument for a necessary being from healthy wonder

1. (Premise) A constitutive part of wondering why p is a desire to know why p.
2. (Premise) A healthy wonder has only healthy desires as constitutive parts.
3. (Premise) Some people have a healthy wonder why there are contingent beings.
4. (Premise) A desire for an impossible state of affairs is not healthy.
5. So, some people have a healthy desire to know why there are contingent beings. (1-3)
6. So, it is possible to know why there are contingent beings. (4 and 5)
7. (Premise) Necessarily, if someone knows why p, then there is an explanation of why p.
8. So, it is possible for there to be an explanation of why there are contingent beings. (6 and 7)
9. (Premise) If there is no necessary being, there cannot be an explanation of why there are contingent beings.
10. So, there is a necessary being. (8 and 9)

First Order Logic and an ontological argument

[I also posted this on prosblogion.]

I want to give this argument in part to provoke a bit of discussion of the role of FOL in philosophy. I don't think the argument carries great weight, in large part because of Objection 2 (see the end).

1. (Premise) The inferences allowed by classical First Order Logic (FOL) combined with a modal logic that includes Necessitation are valid.
2. (Premise) If every being is contingent, then possibly nothing exists. (A material conditional)
3. Necessarily something exists. (By 1)
4. So, there is a necessary being. (By 2 and 3)

The proof of (3) is as follows. Classical logic allows (Ex)(x=x) to be inferred from (x)(x=x). Since (x)(x=x) is a theorem, so is (Ex)(x=x), and hence by the rule of Necessitation, we have: Necessarily (Ex)(x=x). And thus (3) follows. And of course Necessitation is a part of standard modal systems like M, S4 and S5.

I think (2) is intuitively plausible. Here is one way to try to argue for it:
5. (Premise for reductio) Premise (2) is false.
6. (Premise) The non-existence of non-unicorns does not necessitate the existence of unicorns.
7. Every being is contingent and it is necessary that at least one thing exists. (By 5)
8. Necessarily, if no non-unicorns exist, then at least one thing exists. (By 7)
9. Necessarily, if no non-unicorns exist, then at least one unicorn exists. (By 8) 
Since (9) contradicts (6), our reductio argument for premise (2) is complete.

(I am grateful to Josh Rasmussen for simplifying my original argument.)

Now, the weak point in the argument, I think, is premise 1, and specifically the assumption of classical FOL which allows the derivation of (Ex)F(x) from (x)F(x). In a free logic, this wouldn't happen.

But it is still an interesting fact, and a real cost to contingentism (the view that all beings are contingent), that it requires one to abandon classical logic or modify Necessitation. After all, there is some non-negligible prior probability that classical logic and Necessitation license only valid inferences.

Moreover, there is the question of why one should go for a free logic? If one's reason for going for a free logic is precisely that FOL licenses the derivation of (Ex)F(x) from (x)F(x), then one runs the danger of begging the question against the anti-contingentist, in that the derivation is valid (in the sense that necessarily if the premise is true, so is the conclusion) if there is a necessary being.

Objection 1: There is likewise a cost to the non-contingentist who is prevented from adopting those logics on which it is provable that possibly nothing exists.

Response: The non-contingentist who accepts such a logic can still make the move of distinguishing metaphysical and narrowly logical necessity. She can then say that the logic gives an account of narrowly logical necessity. Therefore, all that is shown in such a logic is that it is narrowly logically possible that nothing exists, but not that it is metaphysically possible that nothing exists. On the other hand, it is much harder for the contingentist to make the analogous move of saying that (3) is true in the case of "narrowly logical necessity". For it is widely accepted that if there is a distinction between metaphysical and narrowly logical necessity, the narrowly logical necessity is stronger of the two. Thus, if one accepts (3) with "narrowly logical necessity", one accepts (3) with metaphysical necessity, too.

Objection 2: There are other good reasons to accept free logic, besides the fact that FOL licenses the derivation of (Ex)F(x) from (x)F(x). Specifically, FOL+Necessitation implies that:
10. Necessarily (Ex)(x=a)
is true for every name a.

Response: This objection almost convinces me and is one of the main reasons why I think that while my argument lowers the probability of contingentism, it is not very powerful.

I do think there are two speculative responses to the objection, which is why I think my argument still has some weight.

i. The truth of (10) for every "name" a shows that FOL's "names" do not correspond in function to names in natural languages. In particular, they show that when translating natural language sentences into FOL, one can only employ FOL's "names" for necessary beings. This shows a significant limitation of FOL--namely, that FOL has no way of translating sentences like "Socrates is mortal." However, the fact that a logic has no way of translating a sentence does not mean that the logic's inferences are invalid. There is probably no standard formal logic that can translate all sentences of natural language.

ii. Another move in defense of FOL+Necessitation is that we should see the inclusion of non-dummy names in a language L as embodying existential assumptions about the referents of these names. Consequently, when we give the Tarskian semantics for a modal logic built on top of FOL, the recursive clauses for "Necessarily s" and "Possibly s" in a language L under an interpretation J should respectively read:
- Necessarily: If e(L,J), then s.
- Possibly: e(L,J) and s.
Here, e(J,L) is the conjunction of all metalanguage claims of the form "a* exists" where "a*" is a metalanguage name for the entity that the L-name "a" refers to under J, if L contains any names, and is any tautology otherwise. Then my initial argument needs to be run in a language with no names.

Towards a necessary being

Start with these premises:

1. It is a contingent fact that there are contingent beings.
2. No one can believe that there is nothing.
3. Necessarily, if p, then it is possible that someone believes that p.

It follows from (2) and (3) that:

4. It is not possible that there is nothing.

For if it were possible that there is nothing, then at some world there would be nothing, and it would follow by (3) and S4 that it is possible that someone believes that there is nothing, contrary to (2). But (4) is equivalent to:

5. Necessarily, there is something.

But by (1), there is a possible world with no contingent beings. Since (5) assures us that there is something at that world, it must be something necessary. Hence:

6. Possibly, there is a necessary being.

And by S5:

7. There is a necessary being.

We can do one better. Replace (2) with:

8. No one can believe there are no thinkers.

It follows from (3) and (8) that:

9. It is not possible that there are no thinkers.

By (1) it is possible that there are no contingent beings. Therefore:

10. Possibly, there is a necessary being who is a thinker.

And by S5:

11. There is a necessary being who in at least some worlds is a thinker.

That said, I don't know if (2) and (8) are true.