Monday, August 31, 2009

An argument against naturalism

This is another variant of Leon Porter's 1983 argument against semantic naturalism. Suppose:

  1. Unless the reliability of our doxastic faculties can be explained scientifically, naturalism is false.
  2. As a matter at least of nomic necessity, every grammatically correct sentence in the language of science (i.e., the language that a completed and correct science would use) expresses a proposition which is either true or false.
  3. Only claims that can be made in the language of science can be given a scientific explanation.
  4. If a language can express the claim that our doxastic faculties are reliable, then the language has a predicate T equivalent to (minimally: "of nomic necessity coextensive with") a truth predicate for utterances, and a predicate U equivalent to the predicate "is an utterance".
  5. Some habitable locations in spacetime can be specified in the language of science solely in terms of relations to inorganic phenomena.
  6. If x is any habitable location in spacetime that can be specified in the language of science solely in terms of relations to inorganic phenomena, and A and B are predicates in the language of science, then there is a nomically possible world at which there is a description D of x in the language of science, and an utterance at x of a sentence equivalent to "No item satisfying both A and B is located at any place satisfying D", with there being no other utterances at x.
Let's read some things off this. For a reductio, suppose naturalism is true. Then, from 1, 3 and 4 we learn that the language of science has "is true" and "is an utterance" predicates. From 5 and 6, we learn that an utterance of a scientific sentence equivalent to "No item that is both an utterance and true is located at any place satisfying D" nomically could be located at a place satisfying D, with no other utterances being located there. But such a sentence would be false if true and true if false, thereby contradicting 2. Hence naturalism is false.

I think the controversial claims are (1)-(3). Claim (1) is not a conceptual truth. But if the reliability of our doxastic faculties cannot in fact be explained scientifically, then naturalism fails to explains something that theism can explain easily and simply. Hence we have good reason to prefer theism to naturalism then. What makes naturalism in regard to us at all plausible is the possibility of evolutionarily explaining central features of us. But our doxastic reliability is one of those features.

Claim (2) is, perhaps, best seen this way. The language of all our modern scientific theories is such as to make (2) be true if these theories are true. It is extremely plausible that the same will be true of the language of completed science. If we think that the language of completed science will be mathematical, (2) is very plausible.

While (3) is plausible, one might worry a little about the conjunction of (1) and (2). One's worry might take this. Perhaps the explanation of our doxastic reliability is done in two steps. The first step is to philosophically establish a bridge between some scientific claim and the claim that our doxastic faculties are reliable, in such a way that one can argue philosophically that if the scientific claim is true, then our doxastic faculties are in fact reliable. I think this is only plausible, however, if the scientific claim includes predicates equivalent to "is true" and "is an utterance". (One might think that only the truth of beliefs, not of utterances, needs to be talked about scientifically. But I think this is mistaken in light of the way that language is in fact involved in our doxastic functioning.)

Sunday, August 30, 2009


There is a special pleasure in making something oneself, something that works. For someone with my avaricious tendencies, a part of that pleasure is the pleasure of getting something for next to nothing. However, that is not everything, because a significant component in the pleasure is also there when one makes something for someone else. Moreover, some of the pleasure (though to me, a pleasure mixed with pain) would be present when one makes something even when one had to purchase tools and supplies that are more expensive than a commercial version of the item one is making.

There is also a special pleasure in using something one had made oneself. For instance, this summer I made myself a small blue 68mm refractor (for the pleasing price of about $17—$12 for a chipped lens, the chip being easily blacked out, $5 for miscellaneous hardware, and the rest being scrap like old cardboard tubes), which I normally use as a finder scope on my 13" Coulter (which I did not make), but which I also took along while visiting family, and put on my father's photo tripod. Even though the views through the small telescope weren't particularly impressive (though the dark skies of the B.C. Gulf Island where I was mainly using it helped!), there was a special pleasure in seeing distant galaxies through something I had made myself, a pleasure that would have been greater had I ground the objective lens myself and had I made the eyepieces myself.

The best explanation I know of these special pleasures of making and using something one had oneself made is that in both cases one is taking relish in a particular way in which we are in the image of God who is both creator and the self-sufficient one. (Another argument for the existence of God?)

Currently I am working on an 7.4" effective aperture Newtonian travel scope made from a cracked 8" mirror (some of it is duct-taped off) that I acquired for very little. So far I made the primary and secondary cells.

Of course the non-moral perfections involved—production and independence—are ones that are rather dangerous to us humans, especially independence which in fallen humans can be in tension with community and dependence on God, but of course as found in the blessed Trinity is in no tension with anything. There is the danger of vanity or even pride. (In the telescope-making, it helps to know that other people have done much better, and that my design has benefited from other people's experience and much advice from friends. Plus borrowing other people's tools--thanks, Trent!--makes it more of a communal project.)

Friday, August 28, 2009

Liar and Curry

Consider this sentence:

  1. No true sentence (i.e., sentence that is true) satisfies F.
Observe that for some F's, this is quite unproblematic, and even true. For instance, no true sentence is written on the surface of Io, no true sentence is self-contradictory, no true sentence is such that it is both original and was uttered in the Honorable Member's speech. Now, if (1) is the one and only sentence that satisfies F, then (1) is a liar sentence. So some instances of (1) are paradoxical, and some are not.

In general, as in the Io case, it seems that:

  1. When F does not have semantic vocabulary and no sentence satisfies F, then (1) is unproblematically true.

If we accept (2), we get an interesting result. Suppose that F is the predicate "is identical to (1) and not-p", where "p" is any non-semantic statement. Then, (1) says that no true sentence is identical to (1) and is such that not-p. This is equivalent to the claim that if (1) is true, then p. In other words, in this case, (1) is equivalent to a Curry sentence just like:

  1. If (3) is true, then p.
Now suppose that p is in fact true. Then no sentence satisfies F, and by (2), it follows that (1) is unproblematically true. Therefore, it seems that (3) is also unproblematically true. But if (3) is unproblematically true, then we have established something quite interesting: Curry sentences with true non-semantic consequents are true.

No Curry sentence can be false. For if it's false, then it's true, because any material conditional with false antecedent is true. But whenever a Curry sentence is true, its consequent is true as well, by modus ponens (the antecedent is true because the Curry sentence is true!). So a Curry sentence is true when its consequent is true (assuming the consequent lacks semantic vocabulary) and is nonsense when its consequent is false.

Or so this argument shows. My own intuition is that (3) is nonsense even when p is true. But then I need to get out of the above arguments...

Tuesday, August 25, 2009

Sensory and religious experiences

One might think that the following marks a significant difference between religious and sensory experiences:

  1. If x in context C has a veridical sensory experience of K, then typically another person in C with properly functioning sensory apparatus would also experience K.
Here, "context" does not include the fact of x's experiencing K, since then the conditional would be trivial. But, of course, (1) is not true in the case of religious experiences.

But (1) is false. Here is an easy counterexample. There are some things that are "on the edge" of normal human visual capabilities. For instance, seeing a paramecium or the Pinwheel Galaxy (in a dark enough sky) naked-eye is like that. If the organism were somewhat smaller or the galaxy somewhat fainter, people with normal vision would no longer be able to see it. But people with exceptional or well-trained vision (with "vision" understood broadly as including the brain post-processing of noisy data) still could. Thus there will be cases where a person has a veridical sensory experience of a tiny organism or a faint galaxy, but it is false that typically another person with properly functioning sensory apparatus would also see it. Only a person with exceptionally well functioning sensory apparatus would see it. Moreover, even such a person might not be able to see it under all conditions, but only under conditions of being optimally concentrated and rested.

Perhaps we can save (1) by replacing "properly functioning" with "properly functioning on this occasion at least as well as x's faculties in C were". Call this "(1*)". But now it is harder to tell that the analogue to (1*) is false in religious experience cases. For how would we compare how well different people's religious experience faculties are functioning on different occasions. So while it may be that the analogue to (1*) is false in religious experience cases, it is hard to give a non-theological argument for this. (One can give a theological argument by noting that God is surely free in choosing to whom he should reveal himself.)

Moreover, it seems that it can be a matter of chance what one sees and when. Last night, I was looking at NGC 6852 through my Coulter 13.1". Very faint, i.e., low contrast, even through an Oxygen III filter (it wouldn't have been so faint in a darker sky, but my backyard has a lot of light pollution). First, I just saw the blackness of the sky. Then eventually my eyes (or brain!) picked out a very, very faintly brighter patch of the darkness. Then that disappeared. It reappeared again. Eventually I managed to "hold it in view" for a longer time. A fuzzy elliptical patch of extremely faint light. It seems that I was dealing with a pretty random process of perception here: sometimes my brain was managing to pick the nebula out of the visual system noise and sometimes it wasn't. There may have been some oscillation in the atmosphere, but it probably wasn't relevant (it's relevant to seeing detail, but not so much to seeing a faint object).

Now, it is possible to put all this detail into the context C. But then one is in effect building into the context that the situation was such that one would manage to experience K. And that trivializes (1*) and makes it impossible to point out a difference with religious experience.

One might try to save (1) in a different way. Not by saying that the particular experiences—say, of that faint nebula—would be had by someone else, but by saying that anybody with properly functioning faculties at some point have some experience of this sort (say, a visual experience). But now it is not clear that religious experiences fail to pass muster. After all, a lot of people have religious-type experiences, say while seeing a sunset or a really elegant proof of the Pythagorean Theorem. And while some don't, it is far from obvious that this isn't just evidence that their sensus divinitatis is malfunctioning.

However, I think there is theological reason to think that this needn't just be a malfunction (e.g., think of the phenomenon of the dark night of the soul). So there is theological reason to think that religious experience is disanalogous in this way from sensory experience.

Monday, August 24, 2009

Death and the Second Coming

If I recall rightly, Aquinas had the somewhat strange idea that those people alive at the Second Coming would still die, though only for a moment (using "moment" non-technically). This is an odd position, and one might think it results from an overreading of Scriptural claims that all people die. But consider this argument:

  1. (Consummated) Christian marriage only ends with death.
  2. After the Last Judgment, there are no marriages.
  3. All people will be alive after the Second Coming.
  4. Therefore, all Christian married couples who are alive just before the time of the Second Coming will experience the death of at least one of the spouses by the time the Last Judgment is complete.
Now it seems like it would be really odd if God chose exactly one member of each married couple to die at the Second Coming. It would also be surprising if there were no Christian married couples alive just before the Second Coming (I suppose everyone might have become a monk or nun, but it seems improbable). So it is plausible that:
  1. If (4), then all people on earth who are alive just before the Second Coming will die by the time the Last Judgment is complete.
  2. Hence, all people on earth who are alive just before the Second Coming will die by the time the Last Judgment is complete.

One might challenge (1) as follows. Christian marriage ends with death or with the transformation of the body at the time of the general resurrection. We do not know what that transformation involves, but perhaps it is radical enough to make marriage no longer fitting.

Sunday, August 23, 2009

Three dimensions of evaluation of bad actions

To steal pears without intending to sell or eat them is not only immoral, but hard to understand. To kill a rich and annoying uncle is easier to understand, but morally worse. And of course serial killers commit crimes that are both hard to understand and morally bad. The two dimensions, thus, appear to diverge.

Notice an interesting asymmetry between the morally good and the immoral. A morally good action may excite wonder, but it is not that hard to understand. It is only the immoral and the neutral action that can be really hard to understand.

A third dimension, which I indicated in an earlier post, is the degree to which the deed is reflective of a bad character. This dimension is to some degree independent of the preceding two. It is equally understandable why someone might kill for money or to defend a friend's honor in a duel, but the former reflects a more vicious character. Tormenting an invertebrate is less bad than killing to defend a friend's honor, but more reflective of a vicious character.

The dimensions are not entirely independent, however.

Saturday, August 22, 2009

A variant of the genetic fallacy

Consider the following argument form:

  1. p is believed because of argument A.
  2. If A is a good argument, then q.
  3. Not q.
  4. Therefore, not p.
This is a kind of cross of the genetic fallacy with a denial of the antecedent (in the conditional: If A is a good argument, then p). For example:
  1. The Immaculate Conception (the doctrine that Mary was saved by grace alone in the first moment of her existence) is believed because of the argument that Jesus would be subject to original sin if Mary was.
  2. But if Mary's original sin would have infected Jesus, then the original sin of Mary's parents would have infected Mary, and so on, and hence all of Mary's ancestors would need to be without original sin.
  3. But not all of Mary's ancestors are without original sin.
  4. Therefore, the Immaculate Conception is false.

Notice, however, that there is an argument form in the vicinity of (1)-(4) that is better. Namely, we replace (4) with:

  1. Therefore, the belief that p is not justified.

However, if we do that, we need to read (1) as saying "p is only believed because of argument A". But people are not very good at figuring out the reasons why they themselves believe something, and are much worse at figuring out why others believe something (that explains why so much political discussion is heated—for it is often difficult for people to figure out why someone might take a political position that disagrees with theirs, unless that person is stupid or vicious). So if the implied epistemic agent in (1) and (9) is someone other than the person offering the argument (1)-(3),(9), the argument is likely to be unsound in step (1). I think that when the argument form is found in the wild, it is common for (1) to fail.

Furthermore, it is important to keep constant the epistemic agent constant between (1) and (9).

I think the Marian case likely screws up on all of these counts. First of all, in (5) the epistemic agent is likely some ordinary believer or at best an incautious rookie apologist. In the analogue of (9), the epistemic agent is the Church. Second, even in the case of the ordinary believer or the rookie apologist, (5) ceases to be true if we read "is believed" as "is only believed", because in fact the ordinary believer and the apologist believe in the Immaculate Conception not just on the basis of their flawed argument, but primarily on the basis of the Church's authority.

Moreover, arguments of the form (1)-(3),(9) are often annoying to the interlocutors. I remember a job interview where a candidate tried to convince me that I only rejected his or her view because of thinking about a topic under the influence of a certain other position. This bit of mind-reading not only was incorrect (I can be accused of many things, but not of that particular influence; I rejected the candidate's view cause the conjunction of its claims obviously entailed some absurd proposition that we were both committed to the denial of), but I found it annoying and a bit offensive, and the other members of the interview committee did not like it either. That was a somewhat different version of the genetic fallacy, but the genetic fallacy is generally annoying.

There are places for arguments of the form (1)-(3),(9). But when one gives such arguments, danger is all about.

Friday, August 21, 2009

Circularity and regress

I am not entirely convinced of the arguments below. But they are fun.

Say that p is explanatorily prior to q provided that p contributes to some explanation of q. I shall assume that explanatory priority only holds between true propositions. Let us suppose that:

  1. No contingent proposition is explanatorily prior to itself.
Thus, anybody who thinks that explanatory priority among contingent propositions could be circular—for instance, p prior to q, q prior to r, and r prior to p—is committed to denying the transitivity of explanatory priority.

Now, let us posit two plausible formal principles for explanatory priority:

  1. If p is prior to q, and r is prior to s, then p&q is prior to q&s.
  2. If p and q are conjunctions, and differ only in the order of the conjuncts, and p is prior to r, then q is prior to r.
For a reductio, suppose a circle of size three (the argument works in general): p is prior to q, q is prior to r and r is prior to p, where all three are contingent and true. Using (1) twice, we conclude that p&q&r is prior to q&r&p. Using (3), we conclude that q&r&p is prior to q&r&p, which contradicts (1), since the conjunction of contingent truths is a contingent truth.

Now suppose that a backwards infinite regress of contingently true propositions is possible:

  1. ... p−3 prior to p−2, p−1 prior to p0.
Then a doubly infinite regress is surely also possible:
  1. ..., p−3 prior to p−2, p−1 prior to p0, p0 prior to p1, p1 prior to p2, p2 prior to p3, ....
(Here is a quick way to go from (4) to (5): let pn be the proposition that 1+1=3 or pn−1 for n>0. Then, pn−1 is explanatorily prior to pn.) Suppose that all the propositions in the regress are distinct (otherwise, there is a circularity, which has already been ruled out). Suppose that the infinitary analog of (2) holds:
  1. If A and B are two sets of propositions, with a one-to-one correspondence c between the members of A and those of B, such that c(a) is prior to a for every member a of A, and if p is the conjunction of all the members of A, and q is the conjunction of all the members of B, then q is prior to p.
Now, let A be the set of all the pn for n an integer (positive, negative or zero). Let B=A. Let c(pn)=pn−1. The antecedents in (6) are satisfied. Hence, the conjunction of all the members of B is prior to the conjunction of all the members of A. But A=B. Thus, we have a violation of (1), once again.

The weakness of this argument is that (6) seems less plausible than the finite version (2).

An argument against (2) (and hence also against (6)) is that (2) implies that p can be prior to q even though p and q have a conjunct in common. (Suppose p is prior to q and q is prior to r; then p&q is prior to q&r.) And that might be implausible.

Thursday, August 20, 2009


Imagine a language like English but that has no disjunction—it still, however, has conjunction and negation. There is a sense in which speakers of that language are not missing out on any aspect of reality. It may or may not be true that the English "p or q" expresses the same proposition as "it's not both the case that not p and that not q", but there seems to be an intuitive sense in which whatever reality is pointed out by "p or q", it is also pointed out by that disjunction-free circumlocution. Hold on to that sense of "not missing out".

Now, take a language like English but devoid of indicative and subjunctive conditionals. However, the language has disjunction, negation and conditional probabilities ("it is (very, somewhat, not at all, etc.) likely that ... given ..."). Are the speakers of that language missing out on any aspect of reality? Is there any irreducibly conditional aspect of reality?

Let me grant for the sake of argument that the English indicative "q if p" is not logically equivalent to "q or not p". But are there aspects of reality that can only be captured by indicative conditionals, with disjunction and negation not being adequate to the task? I do not know of any. That is a weak argument for their non-existence, I know. However, I tend to be fairly self-conscious about my use of conditionals, and I talk about a large variety of subjects, so there is some evidence here. Certainly, it does not appear that science requires an indicative conditional. "Either the reaction occurred or the chemicals were not mixed" seems to do just as well as "The reaction occurred if the chemicals were mixed."

There may be conditional obligations. But a conditional obligation either uses a sui generis conditional that is neither the indicative nor the subjunctive, or else can be expressed disjunctively: "Either I should do what I promised or I cannot reasonably do what I promised."

If Molinism is true, the subjunctive conditional is irreducible, and expresses features of reality that cannot be otherwise expressed. But I think Molinism is false.

It is tempting to think dispositions cannot be expressed in any way other than by subjunctive conditionals. But it's really hard to express dispositions even by means of subjunctive conditionals, given finkish problems.

Wednesday, August 19, 2009

Tuesday, August 18, 2009

The liar paradox and desire

The standard desire version of the liar paradox is to consider a person whose only desire is to have no satisfied desires. But that's a weird enough desire that one might wonder if it's possible to have it. Here is a version of the liar paradox using desires that are more imaginable.

Malefa has only one desire: That none of Bonnie's desires be satisfied. Bonnie has only one desire: That all of Malefa's desires be satisfied. Whose desire is satisfied? If Malefa's is, then Bonnie's isn't, and Malefa's isn't. If Malefa's isn't, then Bonnie's is, and Malefa's is, too.

What assumptions does this paradox depend on?

  1. It is possible that Malefa and Bonnie both have the above desires.
  2. The following disquotational schema for desire satisfaction is correct: A desire that p is satisfied iff I(p) (where I(p) is p rewritten with the subjunctive mood replaced by the indicative; thus, I("he eat ice cream") is "he eats ice cream"; to be more precise in the schema, I need to put in quotation marks of the right sort, but I'm not going to bother);
  3. Classical logic.

In regard to (1), one might worry that it's not possible to have only one desire. But that's easily handled by modifying the cases. Maybe Malefa's strongest (or most intense or latest acquired) desire is that Bonnie's strongest (or most intense or latest acquired) desire not be satisfied, and Bonnie's strongest (or ...) desire is that Malefa's strongest (or ...) desire be satisfied.

Moreover, there is nothing absurd about having desires that someone else's desires be or not be satisfied.

One could do what I did in my Monday post and argue that whether Malefa actually manages to have the indicated desires depends on what Bonnie desires (or vice versa or both). Somehow, I find this less plausible in the case of desire—I guess I feel a pull of a certain internalism about desire.

A different move would be based on the Gorgias. In the Gorgias, Socrates argues at length that the tyrant, though he is able to put enemies to death and all that, gets less and less of what he wants the more powerful he is. The reason for that is that he does not really desire to put enemies to death and all that—what he really wants is happiness. There are a couple of ways of taking Socrates' point. One way is to say that there are no instrumental desires. If the tyrant had a desire to have enemies put to death, that would be merely instrumental. Another way (I think Heda Segvic took this view) is to make desire have a normative dimension, such that to desire is to desire appropriately, so that the tyrant does not desire the deaths of his enemies.

Both of these two readings undercut the view that everything that can be put in a (subjunctified) "that clause" can be an object of desire. Moreover, they in particular make questionable the possibility of one person desiring that another's desires not be satisfied: that desire seems too much akin to the tyrant's desire that so-and-so die.

The paradox gives support for the thesis of the Gorgias. But there is something uncomfortable in using a paradox to give support to a substantive philosophical position.

Moreover, one might think that the solution in the case of the desire-satisfaction form of the paradox should be the same as in the case of the truth form. I am not completely sure. (Here is a consideration to back up my uncertainty: the complements of desires are subjunctified that-clauses, while the complements of beliefs and assertions are indicative that-clauses. This observation weakens—ever so slightly—the standard view that the object of a desire is a proposition. But the object of belief and assertion is a proposition. (I say this without committing to a realism about propositions.))

Monday, August 17, 2009

An argument for semantic externalism

I am not actually convinced by this argument. But let's go.

  1. If it is possible that whether an utterance expresses a proposition depends on what happens at the same time in distant places in the universe, then semantic externalism is true.
  2. It is possible that whether an utterance expresses a proposition depends on what happens at the same time in distant places in the universe.
  3. Therefore, semantic externalism is true.
I am not going to defend (1). It's fairly plausible, though I think it's actually a weak point. I want to defend (2). Suppose Fred and Janine are in distant places in the universe, and speak simultaneously. Fred says:
  1. The sentence Janine is now uttering is true.
Janine says:
  1. The sentence Fred is now uttering is not true.
It cannot be that both of Janine's and Fred's utterances succeed in expressing a proposition. For if they do, then if what Janine says is true, it is not true, and if what Janine says is not true, it is true, which is a contradiction. But in a world where Fred instead says:
  1. 2+2=5.
and Janine still says (5), what Janine utters does express a proposition—indeed, a true one. And in a world where Fred still says (4) but Janine says (6), Fred's utterance expresses a false proposition. So it must be that whether Janine's utterance expresses a proposition depends on what Fred says far away, or that whether Fred's utterance expresses a proposition depends on what Janine says far away. Either option is sufficient to yield (1).

Sunday, August 16, 2009

An optimistic B-theoretic way to think of finite lives

Thinking of the ever-decreasing amount of (earthly) life left can be depressing. That's the A-theoretic way. But there is a B-theoretic way: one can think of the span of one's life as a puzzle or painting that one needs to fill in in good ways. At any time t during one's life, one is only obligated to fill in the remaining parts of the puzzle or painting, the parts that are causally dependent on the here-and-now.

There is, in a sense, less stress the less of the puzzle or painting remains, since there is less of a future to make decisions for. Of course, one might have screwed up in the past, and now one has less time to compensate. But, apart from cases of genuine moral dilemmas, one is not obliged to do more than the best one can now do, and God's forgiveness is always available. The A-theorist can say many of the same things, but to me, these things fit better with the B-theory.

Take an extreme case. Suppose one is down to one minute left. Well, then, the problem is merely how best to live that minute. In a way, that is momentous, since it is a culminating minute. But, then again, it's only a minute, and unless one has a likelihood of deep wisdom, or sins that one hasn't repented of, the problem is not so great: the problem is merely how to live one minute.

At the same time, thinking of life in this way, as a puzzle or a painting to fill in, makes each moment crucial. For while a painter can always paint over a portion, we paint our lives in a way that does not allow for that. This is a way in which eternalist theories of time may lead to a cherishing of each moment, of living it out as best one can, since that moment always stands. A presentist can say similar things, but they seem less compelling then, I think.

The above is not an unattractive picture of life. Notice that there are two views here: one of life as a puzzle and the other as a painting. I think there is a way in which both views are right. Life is like a painting, but we are not the primary painter. The primary painter is God. For us, it is more like a puzzle, in that we should be trying to paint it in not according to our conception of what life is artistic, but according to God's. Moreover, we need not navel-gaze and puzzle-solve all that much, but all we need to do is love, and then God will take care of the painting (think of the life of a St Francis—here, there is a painting, but St Francis surely didn't care nearly as much about the painting, i.e., about his life, as about God, neighbor and the rest of creation). So there is a way in which the analogy isn't so good at all.

Saturday, August 15, 2009

Ungrammatical sentences

I think there is something important to be learned in the philosophy of language from the fact that grammatically wrong sentences often succeed in clearly expressing propositions. (Maybe something along the lines of the claim that speaker meaning is the only meaning there is.)

Friday, August 14, 2009

Back in five minutes

You are visiting an office, and read: "I'll be back in five minutes." What have you been informed? Not that the person will return five minutes from now. Nor that the person will return five minutes from having written the note, since such notes can be re-used (this nicely shows that one can make an extended utterance simply by tacking up a sign—one is uttering, without writing, speaking or gesturing). Rather, you've been informed that the person returns five minutes from when the sign was made public.

You, obviously, understand the sign, and know what it says. What the sign says is, of course, the proposition which it expresses. So what does the sign say to you? It tells you, informs you, that the person returns five minutes from then, where of course the demonstrative "then" points to the time at which the sign was published. But that the person returns five minutes from then is a B-proposition. Hence, what the sign tells you is a B-proposition.

But unless we want to special-case posted signs, by exactly the same token when a person leaving an office tells you "I'll be back in five minutes", she is apprising you of a B-proposition, namely that she returns five minutes from then. It is simpler to handle the sign case and utterance case uniformly, so let's do that.

So now we see that paradigmatic A-sentences express B-propositions. But the A-theorist thinks that A-sentences express something other than B-propositions. Hence the A-theorist is wrong.

Objection: What you learn from the sign is the A-proposition that the person will be back five minutes from then.

Response: That is incorrect. Suppose that the sign was published at 1:30 pm, and you're reading the sign at 1:40 pm. The sign is informing you that the person is back five minutes from then, i.e., from 1:30 pm. But it is ungrammatical to say that you are informed that she will be back at t, when in fact t is in the past. (This is an interesting case of the phenomenon that whether a sentence is grammatically correct depends on non-linguistic facts. Another case would be the use of non-generic gendered pronouns.) Grammatically, what you would need to say is that she was back five minutes from then. But you can't say that if you don't know that the sign was published more than five minutes ago. So if you want to stick to tensed language, what you need to say is that she (in the generic sense of "she") was, is or will be back five minutes from then. That is, indeed, an A-sentence, but an eternal one. If all A-sentences express eternal A-propositions, then the the non-eternality in the A-theory is lost, and one might as well be a B-theorist.

Thursday, August 13, 2009

Bill Gates poster

I'm proctoring comprehensive exams (wish them luck, folks), and a poster grabbed my attention: here it is, as sold by the American Library Association. Look carefully at the "R E A D" at the top, and the "Open/Learn/Close/Never Quit" menu on the left. What font is this?

Yes, it's very clearly a version of Chicago--the standard classic Macintosh menu font, with that distinctive thick diagonal in the "N" and that "v" curving on the right. It's a Mac menu!

The blurb on the ALA page says: "Microsoft mogul knows that reading opens windows to the world." Or, perhaps, the real message is: "Bill Gates likes reading as much as he likes Macs." Ooops. I wonder if it's an accident. I kind of imagine a catty Mac user at the design agency having a bit of fun. The copyright date on the poster is 1997. Chicago was used by default for Mac menus through MacOS 7.6, and OS 8 was released mid-1997, so at the time the poster was made, that would have been quite recognizable. And graphical designers (typically) don't pick fonts at random.

In case anybody is curious, I use Windows and Linux most of the time, though I also have a working Powerbook 190 with MacOS 7.6.

Some opinions, with little argument


  1. The first full sentence in this post is not true.
  2. The second is true.
  3. The third does not express a proposition.
  4. The fourth is true or false.
  5. The fifth expresses a proposition.

I am quite sure that: The token (1) does not express a proposition that is true. Therefore, the first full sentence (here I am stipulatively taking "sentence" in the usual grammatical sense, rather than in a more beefy sense that I actually prefer) in this post is not true. Note that there is no contradiction between the two preceding sentences. In fact, I think the token (1) does not express a proposition

I am pretty sure that the token (2) does not express a proposition that is true. Therefore, the second full sentence in this post is not true. It does not follow from this that the token (2) expresses a proposition that is false. I suspect the token (2) does not express a proposition.

I am strongly inclined to think that the tokens (3)-(5) likewise fail to express propositions.

Now, if only I had good arguments for my judgments about (2)-(5), I'd be happy.

Tuesday, August 11, 2009

Sita Sings the Blues

Over the last three nights or so, I watched Sita Sings the Blues (available for free on youtube, and downloadable as an almost free DVD). I enjoyed it immensely. It was both moving and funny, and visually striking. Almost tone-deaf as I am, I found the musical elements too long, but they were nice, too, especially with Closed Captions turned on. (Pet peeve: Films--especially foreign-language ones--where the subtitles don't give song lyrics. Not so here!) It's tempting to assign it to my Love and Sex class in the marriage and commitment section.

The non-actuality of sceptical scenarios

(Cross-posted to prosblogion.)

Sceptical scenarios are usually taken to raise "A how do we know that not p?" question. But let's ignore that question. Of course, we are not brains in vats, there is no evil demon deceiving us about everything, most of our perceptual states have causes, and the world is more than five minutes old. The question how we know, or at least are justified in believing in, these facts is for the epistemologists to scratch their heads over, but we metaphysicians and natural theologians can take them for granted just as dentists and archaeologists do.

Nonetheless, there are genuinely metaphysical questions in the vicinity. Given a sceptical scenario p, we can ask: "Why is it not the case that p?" Why do we have bodies rather than just being brains, why are there no evil demons deceiving us about everything, why do at least most of our perceptual states have causes, and why did the world come into existence in inchoate form with a big bang, rather than fully-formed the way it was five minutes ago?

We can also ask the more general question: Why are all sceptical scenarios non-actual?

A theist has a fairly easy answer to the general question (essentially Descartes' answer): God is unlikely to permit persons to be generally deceived in ways that they cannot reasonably get out of no matter how hard they try. And this answer also works for the specific questions. An anti-realist has a way of getting out of the question by arguing that no distinction can be sensibly made between p and not-p.

The realist non-theist's best bet is to try to answer the specific questions one-by-one, because the prospects for a single answer to them all are poor. Thus, maybe, there are no evil demons because materialism is true. Our perceptual states have causes because a Causal Principle holds, either necessarily or contingently, and perhaps restricted in some way (I don't know that there is any good way to restrict it in a way that gives causes to most of our perceptual states but does not ground a cosmological argument, but that's a different debate). It's harder to explain why there are so few brains in a vat. Maybe one can talk about how brain-in-a-vat scenarios are unlikely to arise apart from certain kinds of agency (people vatting other people), and how these kinds of agency are not so likely to be exercised on a vast scale (or maybe that civilizations are likely to die out before they achieve the technology to turn people into brains in a vat), so that, most likely, most people are not brains in a vat.

The five minute hypothesis presents its special difficulties. Because the entropy of the universe five minutes ago is higher than the initial entropy of the universe, there is an intuitive argument that if the universe came into existence by chance, it is more likely to have come into existence much as it was five minutes ago than much as it was at the Big Bang. That's a tough one. Evolutionary theorists of mind can argue, however, that consciousness requires an evolutionary history, and hence it is impossible for minded beings to arise in accord with the five minute hypothesis. That probably won't help much with the fifty million or at least one billion year hypotheses. Or one might find some good physical reason why universes need to start in a lower entropy state than the that obtained five minutes ago. But it's a hard problem.

Can something like this be said for every sceptical scenario? Maybe, and maybe not. But notice that for a lot of these scenarios, what we will have said is something probabilistic. And unless the probabilities of non-actuality that these considerations yield for the individual scenarios are extremely high, that still leaves the question why no sceptical scenario (to do this argument in earnest, we'd need to explain this notion somewhat!) is actual. And whatever the probabilities are, the theist has a unified explanation of the apparent coincidence that for no sceptical scenario p, is it the case that p is true.

Monday, August 10, 2009

Imposing duties

A complete stranger can impose duties on us, independently of any consent on our part. While you're having a conversation with a friend, Jane walks up to the two of you and makes a nasty bigoted remark. You may well now have the duty to express your disapproval (through a cold look, or through pointedly ignoring her). She goes on from the remark and commits murder. You now have the duty to try to contribute to her punishment.

It is tempting to say that these duties are consequent on some implicit agreement between you and society. But that, I think, is mistaken. For the duty to disapprove of Jane's remark and to contribute to her punishment are not just duties you owe society: they are duties of justice to Jane. While a failure to express the called-for disapproval of the remark does do harm to the victims of the remark, the duty would exist even if the remark had no victims (suppose Jane makes a remark about a group that she thinks is real, but which is not, and where the remark is nasty that it would be unjustified even if the group were real). Likewise, there would be a duty to punish Jane for murder even if the murder did not in fact harm anyone, and if Jane could not be expected to commit any further crimes. (How could a murder fail to harm? Well, suppose that Patrick has just shot an arrow at George. George is standing at the top of the cliff. Jane doesn't know about Patrick, and pushes George over the precipice. She thus extends George's life, because he would die sooner of the arrow than of the cliff. But she is a murderer. We can tweak the case to make George's death be less painful, too, as a result.)

Similarly, a complete stranger can gain a claim in justice to our gratitude by offering us unsolicited help (I am assuming a case where the offer is not irksome).

Sunday, August 9, 2009

Just-so stories and pet theodicies

It is common for critics of evolutionary theories to accuse the proponents of such theories of giving just-so stories—stories about the evolutionary path to F with the property that if they are true, then some feature F of an organism has an evolutionary explanation, but where there is little independent evidence (independent of the claim that evolution is the correct explanation for biological features in general) for the truth of the story. It is common to criticize this by noting that a moderately clever person could give just-so stories for almost about any imaginable feature and its lack.

I take the accusation that evolutionary theorists sometimes give just-so stories to be correct, but not damning. What is important is to be clear on what the just-so story accomplishes: It shows that for all we know the development of F is compatible with evolutionary theory. It is also important to be clear on what the story does not accomplish: It does not provide significant independent evidence for the truth of evolutionary theory. The just-so story is, thus, a defensive move by evolutionary theorists, and as such is perfectly respectable, but one must be clear that it is not an offensive move.

Similarly, theists when challenged why God would have permitted some particular evil E are apt to answer with a "pet theodicy"—a story about the benefits of E with the property that if it is true, then God had good reason to permit E, but where there is little independent evidence (independent of theism, that is) for the truth of the story. These stories are relevantly very much like just-so stories. Typically what triggers the just-so story is the question of why evolution would lead to an organism with some feature that appears to be bad for the organism (cf. this discussion of blushing), while what triggers the pet theodicy is the question of why God would allow the occurrence of something bad (perhaps in a different sense of "bad"—but I am highlighting the structural similarity) that does not appear to lead to the good.

Therefore, an anti-evolutionary theist who thinks that it is damning for evolutionary theorists to give just-so stories must eschew such pet theodicies, and an evolutionary atheist who thinks that the practice of giving pet theodicies is intellectually corrupt (e.g., because a moderately clever person can give a pet theodicy for just about any imaginable evil) must refrain from just-so stories. But both would be wrong. For as defensive moves, just-so stories and pet theodicies are perfectly reasonable. What gives them bad press is the perception, just or not, that their proponents are using the stories to provide significant independent positive evidence for their theories. As long as it is clear that this is not what is being done, there does not appear to be anything problematic going on.[note 1]

Saturday, August 8, 2009

Benefiting from evil

A topic on which there has been some, but not enough, written is that of complicity after the fact. A standard case is the question whether it is permissible to use the small amount of usable Nazi concentration camp medical "research" data (apparently some of the typhus and hypothermia data is useful). Is there any reason to avoid benefiting from the evils of others? I've made a distinction between two sorts of benefits: those benefits that the original evildoer intended, and other benefits. For instance, the Nazi camp doctors may have intended to benefit medical science. If so, then by using their data, one is "playing along" with their plan—one is, in some sense, complicit. It does not follow that the action is wrong, but it does follow that one has a reason (perhaps not conclusive) to refrain from it. On the other hand, the police officer who gets promoted for catching a criminal benefits from crime in a way that the criminal did not intend. This kind of benefiting from an evildoer's action is not a case of complicity, and there is no prima facie reason to refrain from it.

It has hit me that an exactly parallel issue comes up for benefiting from one's own past evil activity. If one has lied on one's resume and as a result got a job, then one's continuing to have the job is a way of benefiting from one's own past ill deed, and, moreover, the benefit is one that was intended by oneself when one lied. It seems to me that one can and should say very similar things about benefiting from one's own past evil deeds as about benefiting from others' evil deeds. In other words, when the benefit is not an intended one, and especially if it was not even hoped for or expected, one is not playing along, and one need have no qualms. For instance, when one benefits from one's past sins by becoming more humble through reflection on one's past weakness, that is not something one has any reason against. On the other hand, one does have prima facie reason not to continue in the job when one got it illicitly. Nonetheless, ultima facie, one might have reason to remain in the job—for instance, if one's employer could not replace one without significant loss to the employer (for instance, because one's employer has put significant effort into training one), one may have sufficient reason to continue in the job.

I think that the parallel between complicity in one's own past sins and in the past sins of others is illuminating and worth plumbing further.

Friday, August 7, 2009


Soames (in Understanding Truth) argues that the Tarskian truth predicate fails to help capture the meaning of the language in the way that the ordinary-language truth predicate may. Nevermind the details of the argument (which looks sound to me). I wonder, however, whether the Tarskian truth predicate might not continue to help capture the meaning of the language when one adds the information that it is a truth predicate. If so, then Tarski has produced a reduction of truth facts to a naturalistic truth predicate and a non-naturalistic higher order is-a-truth-predicate predicate.

I don't know if what I've said is true. But whether it is true or not, it highlights an interesting pattern one might have in a philosophical analysis. We start with a "problematic" (because semantic, non-natural, normative, vel caetera.) natural language predicate P. We find a reduction of P to an "unproblematic" predicate Q that is extensionally correct. But then to use Q to capture the facts that were captured with P, it turns out we also need the higher order fact that Q is a P-predicate which we cannot reduce (unless we want to embark on a regress). The reduction from P to Q might, nonetheless, be informative.

Here is an example of how this might work. Take the natural language binary predicate good for. Consider some non-normative reduction of this, such as the claim that x is good for y means that y desires x (nobody defends this anymore, but it'll be nicely illustrative). Let's assume this is extensionally correct (everybody working on well-being knows the counterexamples), and let's assume that "desires" is not normative (the Socrates of the Gorgias might disagree). Nonetheless, something is left out by the reduction. For while it is a trivial truth that it is an instance of benevolence to promote someone's good, it is a non-trivial truth that it is an instance of benevolence to promote someone's desire-satisfaction. So we lose information about situations by moving from is good for to is desired by. But, assuming extensional correctness, we can put this information back when we add the higher order fact that is desired by is the good-predicate.

Actually, the above is simplistic. For what is good for something or someone is dependent on the relevant kind of that something or someone. It is good for a basketball player to be very tall and thin, but may not be good for a swimmer—even if one and the same person is a basketball player and a swimmer. However, the above pattern does allow for a generalization. We have a higher-order binary predicate: ... is a (the?) good predicate for kind .... And then we have first-order "good-predicates" for different kinds. The first-order "good-predicates" might be non-normative and naturalistic. But they fail to capture the relevant information. For instance, the good predicate for the kind basketball player will "typically imply" tallness (i.e., it will entail a disjunction of tallness and some other qualities, such as even more exceptional jumping skills, which other qualities are rare). But this reductive good predicate fails to capture all the information in the ordinary predicate good for basketball players, because it fails to capture the fact that the qualities it implies, or typically implies, are good for basketball players, as opposed to swimmers, say! In fact, it might even turn out that the predicate makes no reference to basketball, simply giving a conjunction of general skills. (And that it makes reference to basketball would anyway not be enough to capture the fact that it is a predicate that it is good for a basketball player to have. After all, the predicate might also make mention of other sports, such as swimming. For it might be good for a basketball player as such to occasionally engage in other sports to develop certain skills and muscles.) So in addition to that reductive predicate, we need the higher order fact that it is a (or, the) good predicate for the kind basketball player.

I suspect that this point can be made with respect to a lot of reductive analyses. The philosophy of mind would be an interesting place to try to apply this.

Thursday, August 6, 2009

More on the meaning of life

Both of the following claims are plausible to me but appear to be in tension:

  1. A full finite "Aristotelian" life of seriously attempting to practice the intellectual and ethical virtues could be satisfactory.
  2. I rightly find a finite purely natural life unsatisfactory (our hearts are rightly restless until they find rest in God).
When thinking about this, one can put the focus on the finite length of life or on the lack of a supernatural component in the Aristotelian life.

But now observe that (1) and (2) are not logically contradictory. To see that, notice that there are several logically possible stories to be told on which both (1) and (2) are true. The first story is that of grace and fallenness: I am fallen, and without the supernatural component of grace in my life, I couldn't actually lead a life of seriously attempting to practice the virtues—I would, instead, slide into vice unless I happened to die early (in which case the life wouldn't be "full"), and eventually I would abandon the serious attempts to practice the virtues. If that story is true, then (2) is true, because any finite purely natural life would be a life without grace (by definition of "natural") and hence could not be a full "Aristotelian" life.

A second, complementary way to reconcile (1) and (2) is this. I have received the grace of longing for the joy of supernatural union with God. The grace of Christ both makes me long for that joy and directs me to it. As a result of that grace, my heart is restless unless it rests in God. (I don't know if Augustine would allow that the truth of his dictum is dependent on grace.) Given the grace to have the intensively infinite beatitude of union with God, any purely natural life would indeed be objectively unsatisfactory. But, nonetheless, an Aristotelian life could be fully satisfactory—not to me as I am, but to a hypothetical human being who is both unfallen (and hence can live the Aristotelian life) and has not received the grace of that longing.

A generalization of the second way to reconcile (1) and (2) is this. We read (1) in this way: There are possible beings in many ways like us who would be rightly satisfied by a finite Aristotelian life. But these possible beings are not us. Here, "are not us" can be read in two ways. First, as we did in the second way: they are not us who are graced with a longing for God. Second, we could have a completely different reading: they are not human. On this reading, the finite Aristotelian life is not a life for human beings, but for perhaps hypothetical non-humans who do not have the infinite beatitude of union with God as their telos. This gives us a third way to reconcile (1) and (2).

However, a natural human life is indeed sufficient to fulfill the human being's natural needs. It takes grace to long for more than the natural needs. So human beings should, in fact, be able to be satisfied with a natural life, absent grace, at least if they are unfallen. This makes the third way to reconcile (1) and (2) problematic. However we can focus not on the naturalness of the Aristotelian life in (1), but on its finitude. It may be that living forever is actually natural to us. (That we needed the fruit of the tree of life is compatible with this, because there is nothing absurd about needing external goods to live out our nature.) If so, then the beings that would rightly be satisfied with a finite Aristotelian life (note that Aristotle himself was open to the possibility of an afterlife) are not humans.

These three answers appear compatible with one another, and all appear plausible, so the full story is that an infinite Aristotelian life would be satisfactory to us, if we were unfallen and ungraced, but fallen as we all are, and by and large graced as we are (I think grace is offered to all at some point, but for some that point may not yet have come), we rightly find the thought of such a life insufficient. And a finite Aristotelian life would be satisfactory only to humanoids who are not human. The story also explains why some people might find an infinite Aristotelian life satisfactory—for they have not received grace—and why some might feel satisfied by the thought of a finite Aristotelian life—for their aspirations are lowered by the fall.

Tuesday, August 4, 2009

The meaning of life and the afterlife

Consider this intuition:

  1. If this earthly life is all there is, our lives are insufficiently meaningful.
I think this is an intuition a lot of ordinary people have. But now let's turn this fact—the fact that people have the intuition in (1)—into a puzzle. It doesn't seem at all easy to find an argument for (1). After all, it seems like our earthly lives are meaningful on their own: they provide opportunities for the practice of the intellectual and moral virtues, and such practice seems to be "sufficiently" meaningful. (Sufficiently for what? I guess sufficiently for us to say that our lives "have real meaning". This is vague.) Maybe there is some easy-to-fall-for unsound argument (compare the case of the common intuition that there is a problem between omniscience and free will; there, it is easy to attribute that intuition to the existence of a modally fallacious argument together with the mistaken idea that backwards causation is impossible, which mistaken idea may rest on some fallacious arguments as well), but I don't actually know of one. Rather, the intuition about (1) seems quite direct.

Maybe there is a non-cognitive explanation, tied to the selective advantages of our believing (1). As a general methodological principle, however, I want to avoid such non-cognitive evolutionary explanations of beliefs absent particular evidence, because that path leads to scepticism, besides being strewn with unevidenced just-so tales.

Let me suggest one cognitive explanation: People intuit (1) because they have a more basic perception that:

  1. The main meaning of our earthly lives comes from or is largely shaped by the meaning that these lives have in the light of our lives after death.
Now, there is an argument from (2) to one interpretation of (1). If (2) holds, the main kind of meaning that our lives have is in fact dependent on an afterlife. Thus, there is a true counterfactual that says that:
  1. If there were no afterlife, then our lives would be insufficiently meaningful, where "insufficiently" is measured relative to the kind of meaning that they in fact have.
And then people report the counterfactual fact in (3) as (1).

Now let me add one further twist. After all, there are people who don't believe in an afterlife but who still find (1) very plausible—and their belief in (1) then makes them feel terrible. (Cf. Mickey in the middle portion of Woody Allen's Hannah and Her Sisters.) They cannot justify (1) by means of (3). Nonetheless, (1) appears well-entrenched.

Here I want to use a really clever idea that Dan Johnson gives in a recent issue of Faith and Philosophy to examine our justification for the possibility premise in the ontological argument. Johnson thinks that the premise that possibly God exists is a premise that we derive from the claim that God exists, and the latter claim is one we have prior knowledge of by means of the sensus divinitatis. An atheist may then lose the justified belief that God exists, while keeping the derived belief that possibly God exists, with this derived being still justified by its past justification. The S5 ontological argument can then be used to leverage this derived belief into a full-blown belief that God exists. This is circular—and yet perfectly justified, as long as the atheist did not have good reason to cease believing in God. Johnson makes a similar move with regard to the cosmological argument, but I am less willing to go there with him.

Anyway, applying Johnson's idea to the case at hand is a cinch. We have a prior intuition that (2). From this, we derive (3) and then (1), right sense of "sufficiently". Even if we lose a belief in an afterlife, we can hold on to (1), which is a kind of shadow of the deep intuition that (2). We can even give an argument from (1) to (2), which is in a sense circular, but not viciously so:

  1. Given the fact that a finite life of intellectual and moral virtue could be meaningful, (1) only has a reasonable interpretation on which it is true if (3) and (2) are true.
  2. The intuition in (1) does have a reasonable interpretation on which it is true.
  3. Therefore, (2) is true.
I think we do, in fact, have a very resilient (but perhaps not indestructible) pull towards (5).

Sunday, August 2, 2009

An anti-sceptical argument schema

  1. Concept C is not further analyzable.
  2. If C is an actually-had (by a human being) concept that is not further analyzable, then C is possibly satisfied.
  3. If C is an actually-had concept that is not further analyzable, then, probably, C is actually satisfied.
  4. Someone actually has the concept C.
  5. Therefore, both possibly and probably there is something that has C.
Plausible cases: causation, materiality, possibility, goodness, consciousness, numinousness, etc.

Saturday, August 1, 2009

A modal liar

Let's have some fun, which may not lead anywhere. While the meaning of a sequence of characters is a contingent matter, the meaning in Contemporary English of a sequence of characters is not a contingent matter, because "Contemporary English" rigidly refers to a particular dialect of English. I shall suppose abstracta, like Contemporary English, to be necessary beings. I will now use a modified diagonalization procedure which neatly simplifies things. I shall use 'the Goedel number of s' as an abbreviation for some complex expression that I shan't bother to give, but I shall assume that Goedel numbers are all positive. (I will use single quotes to introduce abbreviatory marks; abbreviations are to be substituted for both in unquoted contexts and in double-quoted contexts. Thus, if 'x' is an abbreviation for "the dog", then each time I write "the x runs" and x, that should be taken as short for "the the dog runs" and the dog.) I shall use 'the modified Goedel number of s' as an abbreviation for "the Goedel number of the sequence of characters formed from s by replacing the first contiguous sequence of arabic digits with 0 if this Goedel number is equal to the number expressed by that sequence and zero otherwise or if there are no arabic digits in that sequence". Now, let 'n' abbreviate the arabic expression of the Goedel number of:

The sequence of characters whose modified Goedel number is 0 expresses in Contemporary English an impossible proposition.
Now, I will use 'S' be an abbreviation for the above sequence of characters (including the period) but with "0" replaced by "n". Observe that n is the modified Goedel number of "S". I could, if I so wanted, expand out "modified Goedel number", and calculate n according to some Goedel numbering scheme, and use no abbreviations, but I am too lazy.

Now, let us reason. If S, then the proposition expressed by "S" is impossible, and so it is impossible that S, and hence it isn't the case that S.[note 1] Since the inference "If p, then not p; therefore not p" is valid, it follows that it is not the case that S. But then the sequence of characters whose modified Goedel number is n does not express an impossible proposition in Contemporary English. Suppose that that sequence does express a proposition—after all, it seems that every sequence obtained from the block-quoted sequence displayed above by replacing "0" with a different arabic sequence expresses a proposition. So, the sequence expresses a possible proposition in Contemporary English.

Thus, there is a possible world where S. Let w be such a world. Then, at w, S. So, at w, the proposition expressed in Contemporary English by the sequence with modified Goedel number n is impossible. But "S" expresses in Contemporary English the very same proposition at every world, since "S" has no indexical elements and "Contemporary English" refers rigidly, and S is the only possible sequence with modified Goedel number n. Thus, at w, the proposition expressed by "S" is impossible. But if it is impossible at w, then at w, it is not the case that S. Hence, at w, it is and is not the case that S, which is a contradiction, given that w is a possible world.

This argument shows that we can run a liar argument using modal properties of propositions instead of truth, as long as we accept the following disquotation schema:

  1. The proposition expressed by "..." is impossible iff it is impossible that ....
Of course, the liar argument makes a whole bunch of other assumptions, including:
  1. What proposition an indexical-free sentence type expresses in Contemporary English is not a contingent matter.
  2. It makes sense to talk of a sentence type having a meaning.
  3. The rule of inference "If p, then not p; hence, not-p" is correct.
  4. From impossibility one can infer non-actuality.
I myself deny (2).

Actually, it should be no surprise that one can generate liar paradoxes using an impossibility predicate that satisfies (1), since one can directly use an impossibility predicate that satisfies (1) to define a predicate coextensive with truth in w, where w rigidly designates a world:

  1. p is true in w if and only if the conjunction of p with the proposition that w is actual is not impossible.
And of course we don't need truth, but just truth in @ (where "@" is a name of the actual world), to generate the liar paradox:
  1. Sentence (7) expresses a proposition that is not true in @.

It seems, then, that the liar paradox is not so much a phenomenon of truth, as of disquotation, and other predicates that have disquotation schemas generate liar paradoxes as well. It would be interesting to come up with a general characterization of the sorts of disquotation schemas that generate liar paradoxes. For instance the schema:

  1. x believes the proposition expressed by "..." iff x believes that ...
does not appear to generate a paradox.