A sketch of a proof of a version of Goedel's incompleteness theorem

Consider a first order language (FOL) L that, in addition to the standard ingredients of FOL, including equality and a store of names and predicates, has the following:

• A binary function +.
• A names for every symbol of the language. I will suppose that the name for the symbol "s" is "'s'". (Double quote marks are meta-language quotation; single quote marks are L-quotation.)
• A binary predicate Quotes.

The intended interpretation of L will have as its domain the collection of all strings of finite length, including the empty string, of symbols from L. In the intended interpretation, "+" is string concatenation, so that if "a" denotes the string "xx" and "b" denotes the string "yy", then "a+b" denotes the string "xxyy". Finally, in the intended interpretation, a and b satisfy Quotes if and only if a is of the form "'a'+'b'+...+'m'" and b is of the form "'ab...m'".

Introduce the abbreviation Substring(u,v) for the expression: ∃x∃y(v=x+u+y).

Introduce the abbreviation Begins(u,v) for the expression: ∃x(v=u+x).

Introduce the abbreviation FirstQuotes(u,v) for the expression: ∃x∃y∃w (~SubString(''', x) & u=x+w+y & Quotes(w,v) & ~Begins('+',y)).  Informally, this says that v is the first expression that is quoted in u.

Introduce the abbreviation FirstQuoteSubstituted(u, v) for the expression: ∃x∃y∃z∃w(FirstQuotes(u,y) & Quotes(w,y) & u=x+w+z & v=x+'()'+y.  Informally, this says that v is what you get if you replace the first quoted expression in u with "()".

Introduce the abbreviation SelfSubstitutes(u) for the expression: ∃x(FirstQuotes(u,x) & FirstQuoteSubstituted(u,x)).  This says that the first thing quoted by u is u itself with the first quoted expression replaced by "()".

Now, enriching the language as needed (I think we need one enrichment: we need a "Balanced" predicate which checks if parentheses are balanced), define the predicate or abbreviation Provable(u). Finally, form the sentence:

1. ∀x(∀z(z='*' → (SelfSubstitutes(x) & FirstQuoteSubstituted(x,z)))→~Provable(x)),

where we expand out all abbreviations, fixing up variables over which we quantify to avoid conflicts, and where "*" abbreviates:

• ∀x(∀z(z=() → (SelfSubstitutes(x) & FirstQuoteSubstituted(x,z)))→~Provable(x)).

We can then check that (1) is the one and only value of x that satisfies the antecedent of the conditional in (1) whose consequent is ~Provable(x).

Consequently, (1) is true if and only if it is not Provable. If all Provable sentences are true, then (1) must be true and not Provable. (For if (1) were false, it would be Provable, and hence true. If (1) were true and Provable, (1) would be false.)

If this works mathematically, I think it could work very nicely didactically, with some refinement.

Of course, I probably got some details wrong.  Maybe I made a bigger mistake, too.

If morbid curiosity leads you to ask what my Goedel-like sentence looks like when expanded, it looks like the following if we take "Provable" to be a primitive in L: ∀g(∀h(h='∀'+'g'+'('+'∀'+'h'+'('+'h'+'='+'('+')'+'→'+'('+'∃'+'t'+'('+'∃'+'q'+'∃'+'r'+'∃'+'s'+'('+'~'+'∃'+'m'+'∃'+'n'+'('+'q'+'='+'m'+'+'+'''+'''+'''+'+'+'n'+')'+'&'+'g'+'='+'q'+'+'+'s'+'+'+'r'+'&'+'Q'+'u'+'o'+'t'+'e'+'s'+'('+'s'+','+'t'+')'+'&'+'~'+'∃'+'p'+'('+'r'+'='+'''+'+'+'''+'+'+'p'+')'+')'+'&'+'∃'+'x'+'∃'+'y'+'∃'+'z'+'∃'+'w'+'('+'∃'+'q'+'∃'+'r'+'∃'+'s'+'('+'~'+'∃'+'m'+'∃'+'n'+'('+'q'+'='+'m'+'+'+'''+'''+'''+'+'+'n'+')'+'&'+'g'+'='+'q'+'+'+'s'+'+'+'r'+'&'+'Q'+'u'+'o'+'t'+'e'+'s'+'('+'s'+','+'y'+')'+'&'+'~'+'∃'+'p'+'('+'r'+'='+'''+'+'+'''+'+'+'p'+')'+')'+'&'+'Q'+'u'+'o'+'t'+'e'+'s'+'('+'w'+','+'y'+')'+'&'+'g'+'='+'x'+'+'+'w'+'+'+'z'+'&'+'t'+'='+'x'+'+'+'''+'('+')'+'''+'+'+'y'+')'+'&'+'∃'+'x'+'∃'+'y'+'∃'+'z'+'∃'+'w'+'('+'∃'+'q'+'∃'+'r'+'∃'+'s'+'('+'~'+'∃'+'m'+'∃'+'n'+'('+'q'+'='+'m'+'+'+'''+'''+'''+'+'+'n'+')'+'&'+'g'+'='+'q'+'+'+'s'+'+'+'r'+'&'+'Q'+'u'+'o'+'t'+'e'+'s'+'('+'s'+','+'y'+')'+'&'+'~'+'∃'+'p'+'('+'r'+'='+'''+'+'+'''+'+'+'p'+')'+')'+'&'+'Q'+'u'+'o'+'t'+'e'+'s'+'('+'w'+','+'y'+')'+'&'+'g'+'='+'x'+'+'+'w'+'+'+'z'+'&'+'h'+'='+'x'+'+'+'''+'('+')'+'''+'+'+'y'+')'+')'+'→'+'~'+'P'+'r'+'o'+'v'+'a'+'b'+'l'+'e'+'('+'g'+')'+')'→(∃t(∃q∃r∃s(~∃m∃n(q=m+'''+n)&g=q+s+r&Quotes(s,t)&~∃p(r='+'+p))&∃x∃y∃z∃w(∃q∃r∃s(~∃m∃n(q=m+'''+n)&g=q+s+r&Quotes(s,y)&~∃p(r='+'+p))&Quotes(w,y)&g=x+w+z&t=x+'()'+y)&∃x∃y∃z∃w(∃q∃r∃s(~∃m∃n(q=m+'''+n)&g=q+s+r&Quotes(s,y)&~∃p(r='+'+p))&Quotes(w,y)&g=x+w+z&h=x+'()'+y))→~Provable(g)).

If we have an explicit formula for Provable(x), we need to fix up the "'P'+'r'+'o'+'v'+'a'+'b'+'l'+'e'+'('+'g'+')'" and "Provable(g)" parts.

Occupation is just a relation

That's my new slogan.  It's aimed at philosophical views on which there is something ontologically special about occupying a location in space or spacetime.  But surely to occupy a location in spacetime is just to stand in some sort of a relation (to a location or to other objects).

Consider for instance claims like the following that many mereologists like:

• If R is any region all the points of which are occupied by x, and R* is any sub-region, then there is a part of x that occupies all and only the points in R*.

(We can also talk without invoking points, but points will be convenient.)  Consider now some parallels for other relations:

• If R is a set of propositions all the members of which are believed by x (think of belief as epistemic occupation!), and R* is any subset, then there is a part of x that believes all and only the propositions in R*.
• If R is a set of people all members of which x is a friend to, and R* is any subset, then there is a part of x such that that part is a friend to all and only the people in R*.

These are absurd, though we may non-literally talk that way.  "The part of Josh that is friends with Trent likes epistemology."

Or consider some claim that nothing can be in two places at once.  Make the claim precise, for instance in the following way:

• It is not possible that there is an object x and disjoint regions R and R* such that every part of x occupies some point (perhaps different points for different parts) in R and every part of x occupies some point (ditto) in R*.

But why think that the occupation relation satisfies this kind of an axiom?  

Here's a broad sweeping thought: Otherwise Humean philosophers who believe in all sorts of very general rearrangement principles for fundamental relations do not extend the same courtesy to the occupation relation.  

Ironically, while I am not happy with general recombination principles (that say that any recombination of possible objects makes for a possible scenario), I am happy to allow for wild and crazy rearrangements of the occupation relation--objects being in more than one place at a time, objects occupying spatiotemporally disconnected regions, etc.  If I thought there were such things as parts, I might even be open to such options as composite objects occupying locations that none of their proper parts occupy, parts occupying locations that the whole does not occupy, etc.

Actual infinity

I am occasionally asked what I think about actual infinities.  Mainly because of a Grim Reaper argument, but also because of the bob argument here, I do think there is a problem about certain kinds of actual infinities.  But not all of them.  The Grim Reaper argument, as well as the bob argument, only tells against one kind of actual infinity: an actual infinity of causal influences on a single event.  So while one could conclude that actual infinities are impossible, a more conservative move is to conclude that it is not possible for an infinite number of causal influences to be in the past history of any event.

This limited anti-infinitism means that I do not need to worry about arguments in favor of actual infinities such as the following:

• The actual existence of an infinite future.
• The actual existence of mathematical infinities.
• The intuitively very plausible possibility of a simultaneous infinity of objects.  At least, it's plausible to me.

In fact, my worry is not so much about an actual infinite as such, but about infinitely many causal influences coming together.  

Initially, when I came to the Grim Reaper argument against an infinite past, I found the anti-infinitist conclusion very counterintuitive.  But now it has become clear to me that it's not: for it's not that counterintuitive to think that absurdities can result if an infinite number of causal influences can work together.  My pro-infinitist intuitions were based on non-causal mathematical considerations.  But I can, if I wish, retain those intuitions.  

In fact, I can even retain the intuition that there could have been an infinite past, as long as this does not imply a backwards-infinite causal chain.  Consider, for instance, a world that consists of a multiverse of universes.  The first universe is one year old.  The second universe is two years old.  The third is three years old.  And so on.  The world as a whole has an infinite past.  But as long as there isn't the wrong kind of causal dependence between the universes, such an arrangement need not imply the kind of infinity in causal influence that my arguments lead me to think is problematic.

This strengthens the Kalaam argument by showing that the premises can be weakened: the Kalaam argument only needs the kind of causal anti-infinitism that I now cautiously accept.

Micrometeorite candidates

The kids and I took apart a defective hard drive yesterday, and I used one of the magnets (in a plastic bag, which I then inverted) to fish for micrometeorites in the soil near a downspout.  I found a few plausible candidates, as well as a bunch of surprisingly pretty microscopic ferrous dust. Here is a particularly pretty area.  The pointer is pointing to a round micrometeorite candidate.  It's stuck to some probably earth-origin stuff--the hard drive magnet magnetized all the samples, so they stick together.  There is also a pretty piece of glass or crystal closer to the top edge.

I ended up preparing a slide with four candidates (one a bit dubious) mounted under a glass coverslip.  It's hard to grab pieces as they are very tiny--though big enough to see naked eye as a tiny dot--and stuck magnetically to other things.  In particular, I lost the round one in the first photo, as it just shot away when I tried to grab it with a toothpick (which looked like a big blunt log under the microscope).  Here's one that didn't get away.  It's about 60% of the size of the ball in the first picture.  You can't tell in the photo, but if you shine the light on this, it's very metallic--a nice silvery object. I ended up perfecting a method for extracting them.  First, I use the toothpick to sweep the area around it clean, looking in the microscope most of the time.  It's confusing, since the miscroscope reverses the view, but eventually the brain gets used to it.  Then I wet the toothpick with acetone.  The micrometeorite candidate sticks to the toothpick.  I then transfer it to a clean piece of glass.  Because the acetone evaporates so quickly, it's easy to just wipe the toothpick on the glass and the micrometeorite drops off.  I lost two promising samples--especially that nice big round one in the first photo--before I got the above two.

From what I've read, rounded things that look like they were partly melted are good candidates.  Here is a less rounded one that ended up on the slide of the four that I saved.  I don't know how it got there, as I only intentionally transferred three to it, if memory saves.  Maybe it accidentally got carried there.  It looks too rough-edged to be a micrometeorite.  However, I've also read that they can avoid atmospheric melting by being small, so maybe rough-edged things count as candidates, too.  It, too, has a nice shine to it, though the photo doesn't show it.

If you try to view these with bright-field microscopy, of course you just get black silhouettes.  What I did is I taped a bright LED flashlight to the microscope, pointing at the sample, and then I took timed exposures, holding the camera to the eyepiece (sometimes with some sort of adapter to keep the camera in place).  For the second two photos, I found a way of adding more light.  I took the microscope outdoors, and then reflected sunlight onto the slide with a mirror (actually, a hard drive platter--they make lovely mirrors). The photos were taken with point and shoot cameras hand-held to microscope eyepieces, with some loose-fitting adapters to make it easier. The first photo was with a Sony P100 through the 10X Huygens eyepiece that the microscope came with. The second and third photos were with a Canon G7 through a Rini 30mm telescope eyepiece, using my home-made telescope-to-microscope eyepiece adapter. Update: I wish I knew how to better identify micrometeorites. The very round one may not be one--see this article.

Reasons, intentions and explanation

The following seems prima facie quite plausible:

1. You intend that p in doing A if and only if it is a part of your reason for doing A that p might result from your doing A.

Until just about now, I was thinking that there were decisive counterexamples to this principle. Consider for instance the case of the strategic bomber who does not intend there to be civilian casualties, but chooses the time of her bombing raid in such a way as to maximize the availability of hospital space for the civilian wounded. Then that her action might result in civilian casualties is a part of her reason for performing the action at the time at which she performs it. But the time of an action is a part of what identifies the action. So that her action might result in civilian casualties is a part of her reason for performing the action she does. Yet she plainly does not intend the civilian casualties.

If this example does not convince simply because one thinks that strategic bombers really doe intend civilian casualties, consider a different example. I choose to undergo a simple operation at an excellent hospital, rather than a low-end hospital, because the operation might result in complications that are better treated at the excellent hospital. It seems to be a part of the my reasons for acting as I do—having the operation at that hospital—that the operation may result in complications.

Or so I thought. But now I think I was confused, and these counterexamples to (1) don't work. This doesn't show that (1) holds. But it would be really nice if (1) did hold—we would then have a neat reduction of intentions to reasons.

Here's why I was confused. Take the hospital example, where things are clearer. Let A be the action of asking the surgeon at the excellent hospital to perform the operation. Then the objection to (1) goes as follows: it is a part of my reason for performing A (specifically, the "at the excellent hospital" part of A) that complications may result from A. But I think not.

The problem is related to a mistake that is sometimes made in explanation, which is to make it insufficiently general. Here is a case of that. "Why did Smith eat chocolate ice cream?" "Because the choice was between chocolate and mint, and he slightly preferred chocolate." While we speak in this way, that is in fact not the right way to speak. As Wes Salmon said, irrelevance is harmless in arguments but fatal in explanations. The "he slightly preferred chocolate" implicitly contains an irrelevant claim. That he slightly preferred chocolate is equivalent to the conjunction of two claims: "he at least slightly preferred chocolate" and "he at most slightly preferred chocolate". Of these two claims, the second does nothing for the explanation of why Smith ate chocolate ice cream. It is quite irrelevant. It is only the first claim that enters into the explanation. Thus the correct explanation is that the choice was between chocolate and mint, and he at least slightly preferred chocolate. This explanation leaves out the irrelevant fact that he at most slightly preferred chocolate, a fact that makes the explanandum more puzzling if anything (explanation removes puzzlement).

We can now formulate my reason for choosing to have the operation in the better hospital more precisely. Let's say the less good hospital is the Sextus Hospital and the better is the Harvey Hospital. Then my reason for opting for the Harvey Hospital should be put as follows:

2. The chance of complications is no greater at Harvey than at Sextus, and the chance of poorly treated complications is greater at Sextus than at Harvey.

The fact that there still is a chance of complications if I have the operation at Harvey is not, then, a part of my reason for choosing to have the operation at Harvey—it is rather like the fact that the man in my example at most slightly prefers chocolate—and hence I do not have a counterexample to (1).

Now go back to the strategic bomber case. The correct way to render the bomber's reason for choosing the time of the raid is:

3. The number of civilian casualties at this time is no greater than at the other time, but the number of casualties receiving inadequate hospital treatment is smaller than at the other time.

Again, that the bombing results in the casualties is not among the reasons.

Now, since in fact it is unlikely that the bomber actually thinks the complex thought (3), we shouldn't identify reasons with actual thinkings of the listed contents.

In an earlier post I said that intentions supervene on reasons, and that an important task is to give an account of how reasons determine intentions. I currently have no counterexample to the claim that (1) is such an account. But I am also very suspicious in general of attempts at necessary and sufficient conditions, so I am sceptical that I've succeeded in (1).

It occurs to me that Kamm's triple effect cases might be counterexamples to (1), depending on how one understands reasons for action. I read Kamm's cases as cases of defeater-defeaters. If we don't count a defeater to a defeater as a reason-in-favor, then (1) survives Kamm's cases.

The unthinkable

Typically when we say that some course of action is unthinkable, we have already thought it.  Perhaps there is an equivocation, though.  Maybe what we mean is that the course of action is one that we can think about with theoretical reason, but cannot deliberate about with practical reason.  But isn't the revulsion from the course of action in fact a matter of the will?  Maybe it is a matter of the will, but not of the will in respect of deliberation?

I've seen a classic moral theology textbook say that if you've deliberated whether to commit a mortal sin, you've already committed a mortal sin.  Of course, it is presupposed here that you're aware that the action you're deliberating about is a mortal sin.  Maybe the idea is this.  Deliberation involves weighing the pros and cons of an action.  But as soon as you've realized that a course of action involves you in mortal sin, it is illegitimate to weigh the pros of the course of action.  If you do so, you're implicitly conditionally attaching your will to the mortal sin, conditionally on the pros being great enough.  It would be a mortal sin to explicitly conditionally attach your will to a mortal sin--for instance, to resolve to commit adultery if you win the lottery.  Whether the implicit conditional attachment in deliberation yields mortal sin is something I am not so sure about.  But it is surely sinful.

Of course this needs to be distinguished from a non-deliberative consideration of the benefits of a gravely wrong action.  There can be good reason to engage in such consideration.  For instance, one might try to think through the benefits of a sinful action in order to come up with a rhetorically powerful exhortation against the action, by contrasting the induced decay of soul with the temporariness of the benefits.

Quick paper craft sundial

Here are instructions for a paper craft sundial I built last night.  The hard part was doing the trigonometry for getting the gnomon to be at the right angle after folding--I hadn't done much trigonometry for a while, especially in regard to laying out a three dimensional object (the gnomon is wider at bottom than at the top).  With the script complete, construction takes about fifteen minutes.

And there is an undocumented option in the script that generated this fun illustration of the puzzles about the cognitive content of indexicals [small PDF].

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.

A puzzle about stipulation

I don't know whether Mars ever had life.

But it seems I can very easily get to know.  Let P be the property of having once had life.  Now, stipulate the predicate "is xyzzy" as follows: if Mars once had life, the predicate expresses P, and otherwise, it expresses ~P.  Use "<s>" to abbreviate "the proposition that s".  Then, plausibly:

1. (Premise) I know the proposition <Mars is xyzzy>.  (For I know that "is xyzzy" expresses P if and only if Mars has P, and I can do all the logic needed to yield the claim that Mars is xyzzy.)
2. (Premise) The proposition <Mars is xyzzy> is the proposition <Mars once had life> if "is xyzzy" expresses P.
3. (Premise) The proposition <Mars is xyzzy> is the proposition <Mars never had life> if "is xyzzy" expresses ~P.
4. (Premise) "Is xyzzy" either expresses P or it expresses ~P.
5. So, either I know <Mars once had life> or I know <Mars never had life>.  (By 1-4)
6. So, either I know the proposition that Mars once had life or I know the proposition that Mars never had life. (Expanding abbreviations)
7. (Premise schema) If I know the proposition that s, then I know that s.
8. So, either I know that Mars once had life or I know that Mars never had life. (By 6 and 7)

And so whichever disjunct is true, I know whether Mars once had life!  So, I didn't know it, but once I stipulated "xyzzy" and came to know that Mars is xyzzy, I got to know it.

The argument is valid, but the conclusion is surely false.  So what should we deny?

My inclination is either to deny that it is possible to stipulate predicates in the way I stipulated "is xyzzy" (and hence (1) is nonsense, since it uses a bit of nonsense, namely "is xyzzy", as if it were a predicate) or to allow such stipulation but not allow that sentences using the stipulated predicate express precisely the propositions that (2) and (3) claim they do.  I also feel some pull to denying (7).

An interesting move would be to deny (1) on the grounds that I once know that it is true that Mars is xyzzy, but I do not know that Mars is xyzzy. That sounds odd.

I think Jon Kvanvig may have once used something in the vicinity of this puzzle, but I could be wrong.

Gestures and speech acts

1. (Premise) Every lie is an assertion.
2. (Premise) Every assertion is a speech act.
3. (Premise) Some gestures are lies.
4. Therefore, some gestures are assertions.
5. Therefore, some gestures are speech acts.

The conclusion of this argument should be obvious, but apparently it is controversial.

Evidence for 1: That lies are assertions is the least common denominator of standard accounts of lying ("A lie is an assertion of something one disbelieves", "A lie is an assertion of something one believes to be false", "A lie is an assertion of something one believes to be false and intends to deceive by means of", etc.)  

Claim 2 seems obvious: assertion is a paradigm of speech act, the speech act most studied.

Claim 3 is of course the center of the argument.  But it's easy to see.  Sam swears to tell the truth, the whole truth and nothing but the truth.  He is asked if the man he saw with the knife is in the court.  He says "Yes."  He is asked to point out the man.  He deliberately points to the defendant while fully aware that the man he saw with the knife was the prosecutor, because the prosecutor paid him off.  Clearly, Sam is lying.  But he is doing so by pointing, and pointing (in our culture) is a gesture.  

Moreover, notice that Sam's action violates his oath to tell the truth, the whole truth and nothing but the truth, which also shows that his pointing is a kind of telling.

Analemmatic sundial

I wanted to make something for Instructables' clocks contest, and I settled on a sundial.  I then opted for an analemmatic sundial, where the gnomon is vertical and its location changes.  I haven't made the sundial yet, but I have written a perl script that generates plans for one, with all the dimensions.

This will make a nice educational project to do with kids.  Here are complete instructions.

You can then draw it in chalk on a driveway (and then maybe paint it permanently), and then stand on the correct date (along the vertical center line) with your body being the gnomon.  Or you can just print out the design on a piece of paper, point it correctly, and hold a pencil upright on the correct date (along the vertical center line) to get the time.  You can even use it as a solar compass if you know what time it is.  You hold the pencil upright on the correct date, rotate the sundial until it shows the correct time, and use the "N" arrow.

Theists can't be anti-libertarians

Strong anti-libertarians believe that choices need to be determined by our motives in order to be free.  Weak anti-libertarians believe that choices need to be probabilified, with a probability greater than 1/2, by motives in order to be free.

Strictly speaking, one could be a libertarian and a weak anti-libertarian.  But it would be odd.  As a weak anti-libertarian, one would say something like this:  When I am choosing between two equiprobable options, I am not free.  It's just chance how I choose.  When I am choosing between an option A whose probability is greater than 1/2 and another option B, I may be free if I choose A, but I won't be free if I choose B.  And that would be a weird thing for a libertarian to say.

Theists should be neither weak nor strong anti-libertarians.  Consider these two plausible premises:

1. Necessarily, whatever God chooses, he chooses freely.
2. God made at least one choice that it was possible for him to have made otherwise.

I actually think premise 1 is true for any agent: I think non-free choices are impossible.  But that's very controversial, and the special case of God is much more clear.  If non-free choices are possible, surely God isn't going to be making any such--that would surely be contrary to an important aspect of omnipotence.

Premise 2 is I think a part of standard religious views.  For instance, Catholics are committed (by the First Vatican Council) to the claim that God isn't necessitated to create.  Christians more generally tend to think that God has chosen to redeem us, but did not have to.  It would, I think, be difficult to reconcile omnipotence with a denial of 2--we can perhaps allow that doing wrong or doing the impossible are things an omnipotent being can't do, but surely some alternate options are needed for omnipotence.  Moreover, merely conditional "had he willed otherwise, he would have done otherwise" options won't be enough to do justice to omnipotence.

We can also argue for premise 2 as follows.  Intuitively, there is a possible world w* which has no contingent beings in common with our world.  God exists necessarily.  Hence, God exists at w*.  At w*, God must have decided something differently from what he decided in our world.  (Some differences between worlds can be due to inter-creaturely causal processes having gone differently.  But in this case because w* has no contingent beings in common in our world, the differences can't be like that.)

If one accepts 2, one has to deny strong anti-libertarianism.  And if one accepts both 2 and 1, one has to deny weak anti-libertarianism.  For suppose God is choosing between alternatives A and B and can choose either one.  Then it cannot be that both the alternatives have probability greater than 1/2.  Hence at least one of the alternatives fails to have probability greater than 1/2.  Let's say that's B.  Now consider a world where God chooses B.  That's a world where God chose something that did not have probability greater than 1/2.  But by 1, the choice was still free, contrary to weak anti-libertarianism.

It doesn't follow that theists have to be libertarians.  But they have to think that freedom is compatible with lack of determinism.

[Edited to reflect my view that all choices are free. -ARP]

Implicature and lying

Philosophers say things like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates that there is a genuine possibility of Smith's being a plagiarist." (And yet taken literally "There is no conclusive proof that Smith is a plagiarist" is true even if no one ever suspected Smith of plagiarism.) However what one implicates not only has propositional content, but also illocutionary force, and both both the content and the force are implicated. So if we want to be more explicit, we should say something like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates the suggestion (or insinuation or even assertion) that there is a genuine possibility of Smith's being a plagiarist." Which of the forces--suggestion, insinuation or assertion--is the right one to choose is going to be a hard question to determine. Maybe there is vagueness (ugh!) here. In any case, we don't just implicate propositions--we implicate whole speech acts. A question can implicate an assertion and an assertion a question ("It would be really nice if you would tell me whether...").

I used to wonder whether the moral rules governing lying (which I think are very simple, namely that it is always wrong to lie, but I won't be assuming that) extend to false implicature. I now realize that the question is somewhat ill-formed. The moral rules governing lying are tied specifically to assertions, not to requests or commands. One can implicate an assertion, but one can also implicate other kinds of speech acts, and it only makes sense to ask whether the moral rules governing lying extend to false implicature when what is implicated is an assertion or assertion-like.

And I now think there is a very simple answer to the question. The moral rules governing lying do directly extend to implicated assertions. But just as these moral rules do not directly extend to other assertion-like explicit speech acts, such as musing, so too they do not directly extend to other assertion-like implicated speech acts, such as suggesting. The rules governing an implicated suggestion are different from the rules governing an explicit assertion not because the implicated suggestion is implicated, but because the implicate suggestion is a suggestion. If it were an explicit suggestion, it would be governed by the same rules.

That said, there are certain speech acts which are more commonly implicated than made explicitly--suggestion is an example--and there may even be speech acts, like insinuation (Jon Kvanvig has impressed on me the problematic nature of "I insinuate that...") that don't get to be performed explicitly (though I don't know that they can't be; even "I insinuate that..." might turn out to be a very subtle kind of insinuation in some weird context).

I think the distinction between the explicit speech act and the implicated speech act does not mark a real joint in nature. The real joint in nature is not between, say, explicit and implicated assertion, but between, say, assertion and suggestion (regardless of which, if any, is explicit or implicated). Fundamental philosophy of communication does not, I think, need the distinction between the explicit speech act and the implicated speech act. That distinction is for the linguists--it concerns the mechanics of communication (just as the distinction between written and spoken English, or between French and German) rather than its fundamental nature.

Use and mention

I was editing a paper I'm writing with a colleague, and I came on this phrase:

we will draw out the details of the Specific Analogy Thesis (SAT).

It turns out that the acronym "SAT" never gets used anywhere else in the paper. Question: Was it used in the displayed phrase, or was it merely mentioned? I am inclined to think that either it was only mentioned, or it was both used and mentioned. In any case, we have a nice case here where grammar allows mention without either quotation marks or switch of typeface. It looks like apposition is another marker for mentioning, especially where capital letters are used.

Now, consider this sentence as we might find it in a paper on Spinoza: "Spinoza's Independence Thesis is the controversial claim that substances are completely independent beings." Suppose that this sentence contains the first use or mention of "Independence Thesis." The sentence introduces the term "Spinoza's Independence Thesis" into the language of the paper. But the sentence is also an assertion--among other things, the writer is asserting about Spinoza's Independence Thesis that it is controversial. In the sentence qua assertion, "Spinoza's Independence Thesis" is being used. But in addition to the writer's making an assertion, the writer is performing another speech act, the speech act of stipulating a term. Maybe the way to look at it is this: one asserts of Spinoza's Independence Thesis that it is the controversial claim that substances are completely independent beings, while implicating the stipulation that "Spinoza's Independence Thesis" denotes the claim that substances are completely independent beings (note that "controversial" is present in the assertion but not the definition). Or perhaps we should say that both the assertion and stipulation are there in the sentence with equal rights.

A sufficient condition for not intending

Suppose that I do A, foreseeing that p.  Here is a sufficient condition for my action not to have p among its intentions:

• All my active reasons in favor of my acting as I did in doing A could have been operative for me, and to at least as great a degree, had I not foreseen that p.

(A reason is active provided that it not only favors my acting a certain way, but that acting in this way comes from the reason in the right way.)  This logically follows from the general thesis, which I am inclined to accept, that my intentions supervene on my active reasons in favor of my acting as I did.

Consider two standard cases.  Terror bombing: bomb is dropped on civilian-occupied area to terrify enemy civilians into forcing their government to surrender.  Strategic bombing: bomb is dropped on civilian-occupied area to hit a military target.  In strategic bombing, one could act as one did, and for exactly the same reasons as one did, even if one did not foresee the deaths of the civilians.  But in terror bombing, one couldn't.  If one did not foresee the deaths of a civilians, one of the active reasons for dropping the bomb where one dropped it would not have been available: that dropping it there will terrify civilians by killing them.  

Notice that reasons in favor of my acting as I do in doing A include reasons that concern the value of the end but also include reasons that concern how the means leads up to the end.  Why did you act as you did?  "Because it would save the patient's life" gives the one kind of reason, and "Because it would remove the tumor" gives the other kind of reason.  

The condition I offer is sufficient but not necessary.  Frances Kamm's triple-effect cases, if they work as she thinks they do, show that the condition is not necessary, unless one distinguishes between reasons directly favoring the action, and includes only those in the sufficient condition, from reasons that act as defeater-defeaters.  Another kind of case is given by Neil Delaney's targeting cases, where the presence of civilians is evidence that the military target is there.  Or consider a case where I modify the manner in which I act in light of my foresight that p.  For instance, I expect that there will be civilian casualties, and so I drop the bomb early enough in the raid that I will have time to do a second pass once the smoke clears and drop medical supplies.  My actual active reasons for acting as I did, namely bombing at the time I did, couldn't have existed had I not believed that there would be civilian casualties.  (I could have had another similar reason still, such as that there might be civilian casualties.)

It would be nice if the sufficient condition could be made into a necessary one.  But even without being so made, I think the condition helps with a wide range of cases.  Moreover, sometimes one may be able to handle a recalcitrant case by the following strategem.  Modify the case in such a way that intuitively if the original case had an intention that p, so does the modified one, and then show that the modified case doesn't have an intention that p by using the condition. 

More remarks on the logic of commands and permissions

It's interesting that even invalid commands typically result in permissions.  I am a civilian and I successfully impersonate your commanding officer, point to my car, and say: "Blow up this car!"  You do so.  My command was invalid.  You blew up a civilian's vehicle without a valid order to do so.  Now, if it was another civilian's car than mine, you would be wronging that someone else, by blowing up a car without any valid order to do so.  Of course you wouldn't be culpable for the action, but it would still be something wrong, and the civilian might well seek compensation from the army.  But in the case where it is my car, you didn't even inculpably wrong the car's owner.  Why not?  Presumably because by issuing the order, I gave you permission.

So an invalid order can result in a permission.  Consider another case.  Your Department Cchair hands you her cellphone and tells you to phone me and humiliate me.  Suppose there is no sufficient justification for humiliating me.  That's an invalid order, since she can't validly command you to wrong me.  Suppose you do what you're told nonetheless.  You wrong me, then, and maybe even wrong your chair by making her be responsible for a bad outcome.  But you can't be accused of using her phone without her permission.

Notice, though, that in both of these two cases, the permission issued comes "labeled" with a different role than the putative order does.  The Department chair putatively orders you to use her cellphone as chair.  But she permits you to use her cellphone as a private individual (I assume it's her private phone).  As chair, she has no right to permit the use of any private individual's cellphone.  Likewise, I pretend to order you to blow up the car as your commanding officer, but the permission comes from me as a private individual--it can't come from me as your commanding officer because I am not your commanding officer.

So, typically, a command, valid or invalid, issued by an individual x under some role R results in permission by x in x's role as a private individual.  But not always, not even in the case of a valid order.  "The colonel has ordered you to blow up my private car.  I hereby, acting under protest, order you to blow up my private car."  In this case, I didn't give you permission as a private individual to blow up my private car, which has the normative consequence that I may be entitled to compensation from the service for the unpermitted destruction of my property.

This means that the issuing of permission as a private individual needs to be logically separated from giving an order under some other role R.  Normally, by giving an order in an official capacity I implicate private permission, but this implicature can be canceled, say by an "acting under protest" qualifier.

But now we have an interesting question: Likewise, normally by giving an order in role R, I also permit the commanded thing in role R.  Is the connection here just a matter of contingent implicature, so that (a) even if the order is invalid, the permission remains, and (b) the order can be validly given without the permission?

The answers to both questions are negative, I think.

First take (a).  The most obvious counterexample.  I impersonate a commanding officer and order you to shell an enemy installation.  I invalidly command as your commanding officer, but you do not thereby receive your commanding officer's permission, since I am not your commanding officer.  Maybe, though, (a) is true in the special case where the putatively commanding party actually fills the role?  I don't think so.  Suppose that as a an American sergeant I order my men to initiate war against Canada.  Do my men have sergeant permission to make war on Canada?  Certainly not: initiating a war exceeds the authority of a sergeant both in respect of command and in respect of permission, and there is no such thing as sergeant permission to make war on Canada--there may be such a thing as presidential permission to make war, but surely not sergeant permission.  So R-permission doesn't follow automatically from an invalid R-command.

Now take (b).  Can one give a valid order in role R without giving a permission in role R?  I think not.  I don't have a very precise argument, but the basic idea seems to be something like the following (adapting stuff I heard from Mark Murphy).  By attempting to give in role R an order to A, I am attempting to create a normative situation where you have reason in light of your authority connection with R to A.  Creating such a normative situation requires the wiping away of any relevantly R-connected reasons not to A that I can wipe away qua occupier of R.  Without that wiping away, there is no attempt to create the right kind of normative situation, and hence there is no valid order given.  Besides, I can't think of a counterexample to the claim that valid R-command entails valid R-permission.

So the relevant deontic statuses can be rather logically complex.  As CEO, I order you to build a bridge.  You seek all the relevant legally required permissions.  I didn't realize this when I gave the order, but the bridge is close enough to my house that vibration from the construction would endanger my china collection.  Suppose the law requires permission from all private individuals affected by vibration from construction and you failed to seek my permission.  Because I didn't know about the issue, you can't just presume on my private permission, but you do presume, and my china is destroyed.  Then you didn't wrong me qua CEO, but you did wrong me qua private citizen.

Suppose, however, that the law allows you to build as long as you get permission from nine tenths of the citizens affected by any particular kind of harmful effect.  You get permission from the other nine tenths of the relevant citizens, so you don't bother to ask me.  Assuming that I am validly under the authority of this law, and that the law is just, it may well be that you haven't wronged me.  But neither have I permitted the damage to my china.  So you're permitted vis-à-vis me-qua-private-individual to cause the vibration, but you do not have my permission as a private individual to cause the vibration--rather, the law gave you the permission.

Suppose that the vibration causes both property damage and health damage, and that the law requires everyone's permission in respect of health damage, but only nine-tenths' majority permission in respect of property damage.  Then by causing the vibration you (i) don't wrong me qua CEO; (ii) do something not permitted vis-à-vis me-qua-private-individual in respect of health damage; and (iii) have the relevant permissions vis-à-vis me-qua-private-individual in respect of property damage.

There are, no doubt, neater ways of spelling out these normative statuses.

Remarks on the logic of commanding and permitting

Disjunctions

If I command you to do something, I thereby permit you to do it. But suppose I command you to do A or B or both. Then it seems that not only do I permit the disjunction, but I also permit each disjunct.

It is, I think, necessary that if I command you to do something, I also permit you to do it. Working out why exactly would be interesting.

But I do not think it is necessary that if I command you to do A or B or both, then I permit you to do A and I permit you to do B. Imagine a case where you are under all sorts of orders that I have no authority to override and which I do not know all of, but I know that you're not both prohibited from doing A and from doing B. I might then say: "Do A or B or both. Of course, stay within the scope of your other orders." If one of your other orders is never to do B, you can't say that my disjunctive command permitted you to do B. If this is right, then it's not part of the fundamental logic of commanding and permitting that by commanding a disjunction one permits the disjuncts.

Interesting question. Is it ever morally licit to issue the command to do A or B or both, when B is morally illicit? It is, I take it, always wrong to command or permit something wrong (I distinguish permission proper from waiving punishment). If commanding a disjunction always involves permitting the disjuncts, it follows that one may not licitly command a disjunction when one of the disjuncts in it is wrong. But if it is possible to command the disjunction without permitting each disjunct, then it may be licit to command a disjunction one disjunct of which is wrong, though not a disjunction both disjuncts of which are wrong. We can imagine a situation where very bad things will happen (to you and to your subordinates) if you refuse to issue an order you were commanded to issue, and the order is to do A or B or both, and B is morally wrong. In that case, it may be licit to say: "I command you to do A or B or both. And I forbid you from doing B." You've fulfilled your order to the letter and haven't commanded or permitted anything wrong. Still, in ordinary contexts, commanding A or B or both carries the implicated (and still real) permission of doing A and of doing B and of doing both.

Conjunctions

Suppose now I command you to do both A and B. Interestingly, while it does follow that I permit you to do both A and B, it does not follow that I permit you to do A. I may only be permitting you to do A if you're going to do B as well. So commands are not closed under logical entailment. For if they were, then in commanding A and B, I would be commanding A, and hence also permitting A.

Reasons and intentions

1. If an action has an intention, that intention is always a part of the full rational explanation of the action.
2. Only facts that are identical with or grounded in the agent's reasons are found in a rational explanation of an action.
3. Therefore, the intentions in an action are identical with or grounded in the agent's reasons for the action. ("The Grounding Claim")

Here, grounding is a relation stronger than supervenience. I think the Grounding Claim is very plausible even apart from the little argument for it. One nice thing about the Grounding Claim is that it helps demystify intentions. Once we get clear on the reasons for an action, there is nothing more to intentions.

The Grounding Claim is very abstract, but it has a concrete and controversial consequence:

4. It is possible to have two agents who differ in the foreseen consequences of an action but who do not differ in intentions.

This follows from the fact that a foreseen consequence only affect the reasons for an action when the agent cares about the consequences in some sense, and mere foresight does not entail care. When one agent finds out about a consequence of an action that she doesn't care about—either because the consequence is morally irrelevant or because the agent is morally insensitive—this does not by itself affect her reasons. Thus, two agents can have the same reasons but foresee different things, at least if they are things they do not care about. This, in turn, shows:

5. Foresight is not the same as intention.

The challenge for a theory of intention, then, is to figure out in what way an agent's intentions are grounded in (or identical with) her reasons—how to read her intentions off from her reasons.

I don't know how to do that.

Antipastism

Antipastism would be the view that the past is unreal, but both the present and the future are. I asked my six-year-old son whether he thought the past was real. He was quite sure it wasn't. One of his reasons was that we can't get there. I then asked him if he thought the future was real. He was quite unsure either way. In other words, he vaccilated between presentism and antipastism.
This is interesting, because if presentists feel a pull away from their theory, I would expect that it would often be towards an open future view on which the past is real but the future is not.
Anyway, one can take my son's reasoning and formalize it into a plausibilistic argument:

1. If you can get somewhere, it's probably real.
2. You can get to the future. (It's easy, just wait a moment.)
3. So the future is probably real.

In an earlier post, I called antipastism "Shrinking Block".

Tough double effect cases

I think the distinction between the foreseen and the intended is central to a lot of our moral thinking, and that some form of the Principle of Double Effect is correct.

Here is a pair of cases that I find particularly difficult, however.  This post owes things to a discussion I've been having with Daniel Hill.

Case 1: Matilda knows that a house contains two people, one an innocent and the other a terrorist.  Matilda is flying over the house and can drop a bomb on it, and if she does so, both people will die.  However, the terrorist will then be unable to detonate a bomb that would kill hundreds.  Matilda has no other way of preventing the detonation of the bomb.  Is it permissible for her to drop the bomb?

Case 2: This time Matilda is on the ground, and has a gun.  The two residents of the house are in front of her.  One of them is the innocent and the other is the terrorist.  She can't tell which is which.  The only way to prevent the detonation of the bomb is by killing the terrorist.  (Why is wounding not good enough?  Maybe from her position, she can only aim for the head, and so she'll either kill or miss.)  Is it permissible for her to shoot both?

The first case seems to be just like the standard double effect case of tactical bombing where if you drop the bomb on the enemy HQ, innocent visitors to the HQ (e.g., spouses of officers), will also die.  It is hard to distinguish Case 2 from Case 1, since it doesn't seem like it should morally matter whether one drops one bomb or takes two shots.  But the action in Case 2 seems wrong if you have strong deontological intuitions.  It sure seems like you're intentionally killing two people, where you know that one of them (but you do not know which--and that may change things) is an innocent.

So the challenge for the defender of double effect reasoning is to either show in a morally compelling way how Case 2 differs from Case 1, or show that the intuitions that the shooting in Case 2 is wrong are mistaken.

I will try for the first, but I don't know how morally compelling my story will be.  I think it will only be compelling to those who find double effect reasoning compelling.  Still I hope the story will have some plausibility.  Let the two people in the house be Susan and Tricia.  Matilda's intention in Case 1 is that the terrorist in the house die.  By what means?  By means of the place where the terrorist is being seared by an explosion.  Matilda need have no intention in Case 1 regarding the non-terrorist, or regarding Susan qua Susan or Tricia qua Tricia.  Her intention is explicitly about the terrorist as such.

Now consider Case 2.  Suppose Matilda has Susan in her gunsights and squeezes the trigger.  What are Matilda's reasons for so doing?  The most plausible account seems to be something like this: "Susan may be a terrorist, and if so, then many lives will be saved by her death, so I will shoot her."  In other words, the plan of action seems to be: "Shoot Susan dead, so that if she is the terrorist, the terrorist is dead."  If that's the plan of action, then Matilda is (literally) aiming to kill Susan.  And by the same token, Matilda is aiming to kill Tricia. Therefore, Matilda is intending the death of two persons, one of whom she knows to be an innocent.  She knows, thus, that in her overall action plan there is an innocent whose death she is aiming at.  And that is wrong.

Elsewhere, I have speculated that there are some actions that are only permissible with certain intentions.  For instance, perhaps it is only permissible to assert with the intention of avoiding the assertion of a falsehood and perhaps sexual relations are only permissible with the intention of uniting maritally.  It now seems quite plausible to me that intentional killing is like that.  To kill someone intentionally and permissibly it is not enough that one believe that the person is an aggressor (or is probably an aggressor?) that one is duly authorized to kill, or however exactly the exceptions on the prohibition of killing should be put.  The soldier or police officer needs to kill because the person is an aggressor that one is duly authorized to kill.  The Allied soldier who justly kills a German soldier must do so because the German soldier is an aggressor.  If the Allied soldier, instead, solely kills Helmut because Helmut is German or because Helmut has a long nose or because target practice is fun, the Allied soldier is morally corrupt.  (What if the Allied soldier kills Helmut both because Helmut is an aggressor and because Helmut is German?  I think more detail will be needed about the deliberative structure here, and I want to bracket this case.)

Now, let us suppose that in fact Susan is the terrorist.  Then Matilda in intentionally killing Susan is not killing Susan because Susan is a terrorist.  Rather, Matilda is killing Susan because Susan might be a terrorist.  And that is not good enough.  The intention to kill someone because she is a terrorist is compatible with love of that person, since doing justice to someone is compatible with love, and sometimes required by love.  But that is not Matilda's intention.

This has an interesting implication for military ethics.  It is often said to be necessary for soldiers to dehumanize their enemy in order to kill, to see them as enemies rather than as people, and this is often seen as a criticism of the military enterprise.  But if I am right, it is morally required that the soldier kill Helmut under a description that includes something like "enemy aggressor" rather than simply under the description "Helmut" or "that man over there, who no doubt has a family who are awaiting his return."  Perhaps in the ideal the humanity of the enemy, and the fact that he has a family who are awaiting his return, does enter into how the action is done--with compassion, sadness and only as necessary for due defense of the innocent.  But Helmut's aggressor status needs to be in the soldier's intentions.

But let us go back to Case 2.  One might cleverly object that it need not in fact be Matilda's intention that Susan die (Daniel Hill queried me about such an idea).  It could perhaps be Matilda's intention that Susan die if she is a terrorist.  Now, it is certainly possible to have such intentions.  If one has, or thinks one has, a magic bullet that kills only terrorists, one could shoot Susan intending that she die if she is a terrorist.  In that case, one's means to the conditional end that Susan die if she is a terrorist is shooting a bullet that discriminates between terrorists and non-terrorists.  But in the actual Case 2, one brings it about that Susan dies if she is a terrorist by bringing it about that Susan dies: the conditional end is brought about, in this case, by the unconditional means.  So one still intends that Susan die, as a means to the conditional end that Susan die if she is a terrorist.

But what if Matilda is a clever double effect casuist, and says: "My intention is that a bullet should go through such and such a location in space, and that if there be the head of a terrorist in that location, that terrorist should die"?   However, I think this is an incorrect statement of Susan's intentions.  Intentions aren't inner speeches.  They embody our actual reasons for acting.  Matilda's reason for sending the bullet to that location in space is that she can see Susan's head there.  Her plan for making sure that the terrorist in that location should die seems to be that Susan should die, and hence if the terrorist is there, the terrorist should die.  Susan's death still seems to be a means to the death of the terrorist in that location, if there be one there.  And likewise for Tricia's death.  I am not completely happy about this story, but it has some plausibility.

In Case 1, however, the aim is less personal, and that does actually matter: the only death aimed at is the death of "the terrorist", under that definite description.  Certainly, we would expect Matilda to be much more traumatized by Case 2 than by Case 1 (and if she weren't, we would think there is something wrong with her), and we should take such trauma to be defeasible evidence for a morally relevant difference between the two cases.

[Typo fixed.]

Christ's sacrifice and presentism

After it took place, Christ's sacrifice had never ceased to be a part of reality. But Christ's sacrifice did not continue to be always a part of the present. (Christ's sacrifice is present during the Mass, but there have been times, since Christ's crucifixion and resurrection, during which no Mass was being celebrated.) Hence, the present and reality are not coextensive.

Whether this contradicts presentism depends on what one makes of the imprecise predicates "is a part of reality" and "is a part of the present".

Deep Thoughts XXXIII

Everything is possible except the impossible.

A reliabilist moral argument for the truth of some religious belief

Let P be the process of genetically or mimetically producing belief in non-empirical claims in order to enhance social cooperation.  Let moral realism be the claim that we know some non-trivial moral truths.  Consider this argument:

1. (Premise) Evolutionary process P is the relevant process that produced both our religious and our moral beliefs.
2. (Premise) If all religious beliefs are false, P is unreliable (since roughly half of the basic types of beliefs produced by P are then false).
3. So, if all religious beliefs are false, then the relevant process that produced our moral beliefs is unreliable. (By 1 and 2)
4. (Premise) Beliefs produced by an unreliable relevant process are not knowledge. (This is a consequence of reliabilism.)
5. So, if all religious beliefs are false, we lack moral knowledge. (By 3 and 4 plus the analytic truth that knowledge requires belief.)
6. (Premise) If moral realism is true, we have moral knowledge. 
7. So, if all religious beliefs are false, moral realism is false. (By 5 and 6)
8. So, if moral realism is true, some religious beliefs are true. (By 7)

And moral realism is true.

Now, I am not sure whether 1 is true.  But I think the main alternative to 1 is that God produced some of our religious or some of our moral beliefs or both.  And if that alternative is true, then some religious beliefs are true, namely those that say that God exists.  So my uncertainty about 1 does not harm the argument.  I am also not sure about the reliabilist premise 4, and that's more serious.


I think the naturalist reliabilist who wants to deny 8 will accept that P produced our religious and moral beliefs, but say that P is not the epistemologically relevant process.  The relevant process is, perhaps, the sub-type of P which is the genetic or mimetic production of beliefs in moral claims in order to enhance social cooperation.  I think this identification of the relevant sub-type is objectionably ad hoc.

Would it have been crazy to think everything is made of water?

According to Aristotle, Thales held that the whole physical world is made out of water.  I don't know if Aristotle was an accurate interpreter of Thales, but let's suppose he was.  The claim that the whole physical world is made out of water seems really wacky.

But I think it was quite defensible before we got the successes of modern chemistry.  And I want to sketch one line of thought why.  I am not claiming that this line of thought was in fact Thales'.  But it could have been: it won't rely on any science inaccessible to Thales.  The line of thought has three steps.

Step 1. All liquids are the same substance.

Here is a line of thought towards this.  Granted, obviously samples of liquids differ widely in shape, color, opacity, taste, wholesomeness, viscosity, miscibility, temperature and inebriativeness.  But such variability does not challenge the claim that all liquids are in fact forms of the same substance.  After all, apples differ widely in size, color, taste, wholesomeness and hardness, but they are all fundamentally apples.  Moreover, samples of liquids apparently of the same sort can differ in most if not all of the above properties.  The most obvious are shape and temperature: simply by varying the environment, the shape and temperature of a sample of a liquid can change.  More interestingly, the opacity, taste and inebriativeness of grape juice changes over time.  The viscosity and at least apparent miscibility of honey changes over time.  The taste and wholesomeness of milk change significantly very quickly.  It is a very reasonable hypothesis, then, that mere differences in these observable qualities do not correspond to a fundamental difference in kind, that the grape juice and the wine, or the milk and the yogurt, are one and the same liquid, despite significant differences in causal powers.  But the differences between water and, say, milk or oil seem to be precisely differences in respect of qualities that do not make for different kind of thing.

The alternate hypothesis of explanation of the differences in properties between liquids, and that is that they have different ingredients rather than different properties.  But there was good reason to doubt this alternate explanation.  The significant changes happening in juice, milk and honey apparently do not require the introduction of any additional ingredients, nor the removal of any ingredients.

Step 2. All liquids are water.

If all the liquids are forms of the same kind of substance, we may want to figure out what the basic, generic or fundamental form of that substance is.  And here water seems a very plausible choice.  It is colorless, transparent, tasteless, devoid of medicinal effects except relief of thirst (which it shares with many other common liquids), non-viscous, quite miscible and non-inebriative.  It is reasonable to suppose, for instance, that when water acquires the properties of whiteness, milky taste and a bit of viscosity, it becomes milk.  One might wonder: how does one get water to acquire these properties?  Well, a reasonable thing to say is that female goats make rainwater acquire milky properties.  Certainly, when you stop the access to water, the goats stop making milk (and die).

Water, on this hypothesis, is the fundamental liquid, having the minimal set of properties needed for being a liquid, and when it acquires different properties, we call it by different names.

Step 3. Everything physical is water.

Step 3a. Everything solid is water.

Water can turn into a solid without anything being added to or substracted from it.  One might think that "cold" is being added to it, but supposing cold as a substance may be questionable (though, less so to the Greeks than to us), and besides if cold had to be added to water in order to turn it into ice, it would follow that the formation of ice should reduce the amount of cold in the air.  But the freezing of water does not appear to warm the surrounding air.

Furthermore, metallurgy shows that certain kinds of rocks can be turned into liquid, and then solidified into metals.  Some varieties of mud, which appears to be a particularly viscous liquid, can be solidified into brick or ceramic.  Sand can be melted into a clear liquid, and then solidified into glass.  Since Step 2 hypothesized that all liquids are water, it becomes very plausible to generalize to the hypothesis that all solids are water, too, albeit with the property of solidity.

Step 3b. All gases are water.

When water is heated, it turns into steam, which looks like a cloudy form of air, and hence one can suppose that air is a kind of steam.  Smoke comes from solid objects when these are on fire.  Since solid objects are water by Step 3a, smoke is also water.  It is reasonable to hypothesize that all gases are water.

Step 3c. Fire is water.

This is perhaps the toughest step, intuitively.  Fire and water seem to be opposites.  But one might hypothesize that when water is added to fire, the fiery qualities of the fire simply become diluted by the water. Steam is hot and burns, though it does not glow.  Fire, thus, could be reasonably thought of as a particularly vivid kind of steam.

We can generalize from Steps 2-3c to conclude that everything physical is water.

Final remarks.  On this highly speculative interpretation, Thales' thesis stands in sharp contrast to ingredient-based theories of the natural world, such as we have in modern Mendeleevian and ancient four-element chemistries.  We do not need to posit differences in ingredients to explain differences between things.  We generally don't posit differences in ingredients to explain differences in shape.  So why should we posit them to explain differences in, say, color or taste?

Of course, if a particular ingredient-based theory comes to have significant predictive and explanatory power, Thales' thesis needs to be abandoned.  I do not think the four-elements theory that some other ancients preferred was all that superior in predictive or explanatory power.

Mendeleevian chemistry, on the other hand, was far superior in predictive and explanatory power over either Thalesian or four-elements chemistry.

Fetal and our potentiality

Consider this standard story:

Whatever value fetuses have derives from their potentiality (and here various distinctions matter) to grow into humans that actually have various valuable features, features that are not simply potentialities. Typical human adults actually have the valuable features that ground their moral status, while fetuses only potentially have these features. The question of the moral status of the fetus, then, is the question of how far their potentiality makes it possible to extend to them the moral status that typical human adults have (and, likewise, to extend the moral status of typical human adults to atypical ones).

I have argued in earlier posts that the kind of potentiality fetuses have does call for the extension of moral status. But I now wonder if this whole line of thought doesn't presuppose a mistaken view, namely that the moral status of typical human adults is grounded in the actual possession of valuable non-potentiality features. Specifically, I worry that this line of thought has too optimistic a view of the human race.

The feature of human beings that matters most centrally seems to be the moral life. But in practice our moral life just isn't all that good. We are full of self-deceit, akrasia and dollops of malice, in different combinations. Is it really the case that typical human beings are morally good in such a way that their actual moral goodness gives them the kind of moral status we are thinking about?

And in any case, even if, say, 70% of adult human beings do have such moral goodness, what about those of us who are in the other 30%? They, too, have moral status. No matter how many crimes one has committed previously, no matter how wicked one is, one has the moral and legal right to a fair trial, to a punishment that does not exceed the gravity of the offense.

What I said about the moral life also goes for the intellectual life: the typical human's intellectual life just isn't much to be proud of. Just think of all the fallacious forms of reasoning we engage in. Plus, I do not know how central the intellectual life is to moral status. Suppose there was a race of super-intelligent mathematicians who had no drive but to prove interesting theorems and no moral life to speak of. Would they have the kind of moral status humans have? I don't know. (It could be that they would have to have the rudiments of a moral life, in that they would have to be attuned at least to the values of truth and beauty to practice mathematics well. So it could be that the thought experiment is impossible.)

Now, it may well be that the above thoughts are too pessimistic. The George MacDonad quote here seems quite significant. But I still think this is worth thinking about, and I think there is something to the idea that the moral status of typical adult humans comes not so much from actual valuable properties, but from their innate potentiality for the good moral life. It is what we should (eventually?) be, not what we are, that is central to our dignity on this suggestion.

Telescope making instructable

My instructable for making a small (6") Dobsonian telescope got posted on the front page of Instructables. Yay! I built the scope with one of my colleagues at Baylor--we've got quite a nice little group of amateur astronomers in the Philosophy Department. (I also entered this project in their space-related contest.)

Fetal potentiality

Jarrett Cooper raised an important and interesting question about the potentiality of fetuses to become adults in a comment, and I thought I'd make a post with a response. The center of the question is:

There are those who dislike the use of the potential verbiage that is used for pro-life arguments. Namely, to ground the moral worth of fetuses in that they have the potential (albeit undeveloped) to become beings with consciousnesses, intellect, language, etc. They argue that the word "potential" has a very broad scope and therefore defending the use of potential with regards to fetuses becomes arbitrary.
What I gather is that their concern is there are many things have potential to be such and such. After all, it is said that we are star dust, but yet we don't view exploding stars nor the mere star dust remnants themselves as human beings. This is because even if we are just star dust, there's a whole bunch of processes that have to occur to get a human being.

I think we can identify two relevant distinctions between how an F (say, a fetus, a bit of star dust, or some clay) becomes a G, and corresponding to these two distinctions there are relevant distinctions as to F's potentiality to become a G.

The first distinction is implicit in the rest of Mr. Cooper's comment and may be on a continuum. This is the distinction between F's changing itself into a G and F's being changed into a G.

For instance, an acorn changes or transforms into an oak tree, but an oak tree is changed or transformed into a canoe. In both cases there is both internal and external causal agency. The acorn needs water, soil and sunlight to become an oak tree. The oak tree needs cutting and joining to become a boat. Note, however, that the second of these two sentences, while having an interpretation on which it is true, sounds odd. For while the acorn seems to be primary agent when it becomes the oak tree, the boat-builder is the primary agent when the oak tree becomes a boat. The water, soil and sunlight have a supportive role in the transformation, and the acorn, driven by its DNA, has a primary active role. In the case of the boat, however, the boat-builder does not merely have a supportive role in the process. Either she is the primary agent, or else she and the oak tree are jointly primary agents.

Corresponding to this distinction there is a distinction between an F's potentiality to change itself into a G, and an F's potentiality to be changed into a G. Neither the human ovum nor star dust have the potentiality to change themselves themselves into an adult. In the case of the human ovum, that is because a genetically equal or almost equal input from the sperm is required (almost, since DNA may not be the sum total of the genetic code; cytological context matters, for instance). And a fortiori star dust can't change itself into an adult human.

There is a second distinction, perhaps more principled. There are three ways in which we can say that an F changes into a G. First, we have accidental change, where the entity that is initially identical with an F is eventually identical with a G. Thus, the child becomes the adult: the same individual that was the change is later the adult. Second, we have substantial change, where the entity that is an F perishes an a G comes into existence. For instance, this happens when a book burns into smoke and ashes. There is no one entity that once was a book and later is smoke and ashes (though there may be particles that once constituted a book and later constitute smoke and ashes). Third, we have what we might call constitutional change, where the F comes to constitute a G. In this case, the "be" in "F comes to be a G" is the "to be" of constitution rather than of identity. For instance, sticks become a house. But it is never literally true that the sticks are identical with a house. To be more precise, we should say that the sticks come to constitute the house.

It is never true to say that the entity that was identical with star dust is now identical with a human. What we can say, depending on difficult metaphysical questions, is at most that the star dust comes to constitute a human (or, better, a human's body) or that the particles that constituted star dust now constitute the human. Likewise, the ovum is not identical with the adult human. It changes substantially into a human adult: the ovum perishes, by merging with the sperm, and a human comes into existence from its death, like smoke and ashes come into existence from a book.

On the other hand, a fetus's change into an adult is an accidental change: the same entity that was identical with a fetus comes to be identical with an adult.

A potential to change oneself accidentally into an adult human is a much more morally significant potential than a potential to be changed substantially or constitutively into an adult human.

It may sound strange to say that a potential for an accidental change would give rise to a more important status than a potential for a substantial change. But the reason for that is that the fact that the fetus's change into an adults is an accidental change means that there is only an accidental difference between the fetus and an adult.