new draft on analytic truth

I've just finished a draft of a short paper (<3000 words) that asks: are there any sentences whose meaning suffices for their truth? Many post-Quineans say no; the paper argues that, for sentences expressing logical truths, the answer is yes.

The paper can be downloaded here. I would really appreciate all comments great and small. Thanks!

Against "Carnap and Logical Truth" again

In "Carnap and Logical Truth," Quine makes the following argument (expanded by Harman in his 1967 article "Quine on Meaning and Existence: I" in Review of Metaphysics):

"Consider... the logical truth 'Everything is self-identical'... We can say that it depends for its truth on traits of the language (specifically on the usage of '='), and not on the traits of its subject matter; but we can also say, alternatively, that it depends on an obvious trait, viz. self-identity, of its subject matter, viz. everything. The tendency of our present reflections is that there is no difference."
(Carnap Library of Living Philosophers volume, p.390)

I think, contra Quine, that there might be a clear difference. To say that one thing (e.g. the truth-value of a sentence) depends on another (e.g., the traits of a language, or the traits of its subject matter) usually means that changing the second can change the first; the first is sensitive to changes in the second. E.g. thermometer readings depend on ambient temperature: as the ambient temperature changes, the readings change. This is not to say that 'X depends on Y' means that every change in Y will have a corresponding change in X (that would be perfect correlation), but it does require that there must be some change in Y that results in a change in X. If X stays the same no matter what values Y takes, then X does not depend on Y.

Now think about Quine's (English) sentence 'Everything is self-identical.' If we were to vary the traits of the language in which this is written, e.g. by letting 'self-identical' mean not self-identical but red, then the sentence would be false. This shows that (as Quine happily admits elsewhere) the truth-value of a sentence does depend on the traits of the language in which it is expressed.

But now think about varying the traits of the subject-matter of this sentence, 'viz., everything,' or the world, or however you want to think about it. Assuming we hold the meanings of the words fixed, there is no possible way the world can be that would change the truth-value of this sentence. That is, there is NO change in the way the world is that would change the truth-value of this sentence. (In logic-ese, the sentence is true in all models.) Thus, if the above characterization of dependence is right, then the truth-value of 'Everything is self-identical' does not depend on the traits of its subject matter, viz. everything.

Analytic truth and the Daily Show

Many philosophers have suggested that the sentence 'I am here' is an analytic truth. The view goes back to Kaplan, and it has recently been vigorously defended by Gillian Russell in her recent book Truth in Virtue of Meaning (which I'm currently reading).

On The Daily Show with Jon Stewart recently (May 11th), there was an exchange that made me wonder whether 'I am here' really is analytically true. On the Daily Show, the correspondents are often presented as 'on location' in Washington DC or Kabul etc., but are actually in the studio standing in front of a backdrop of DC or Kabul. On this show, there was a particularly unconvincing backdrop of DC behind correspondent John Oliver. There was then the following exchange (cleaned up transcript -- the full video is available online; start at about 5:00):

Stewart: "For more on this story, we go to John Oliver, who joins us live from Washington. [Audience laughs] Washington."
Oliver: "That's right, I'm here. [Audience laughs] I'm here."

Oliver seems to be saying that he is in DC. But he's clearly not; he's in New York. So we appear to have an utterance of 'I am here' that is false (which is why the audience laughs), and thus it seems that 'I am here' cannot be analytic.

What to do? Here's one suggestion for how to save at least the truth (if not necessarily the analyticity) of 'I am here': say that 'I am here' is true both literally and in the pretense/fiction, but that what 'I' and 'here' refer to in the fiction differs from what they refer to literally. Literally, 'I' refers to John Oliver, and 'here' to the Daily Show studios in New York. In the pretense, 'I' refers to the journalist character (who happens to be named 'John Oliver'), and 'here' refers to DC. Then, 'I am here' is both true in the pretense and true literally. (The statement 'That's right' is true in the pretense but false literally.)

However, this maneuver does not get us all the way to 'I am here' being analytically true in the pretense -- more details about the meanings of indexicals in fiction would have to be spelled out to get there, and this post is long enough already. (Plus, I haven't thought the matter through.)

Does anyone have other thoughts about this instance of 'I am here'?

puzzles from the later Quine on meaning and synonymy

In the Quine volume of the Library of Living Philosophers, Quine says the following in his "Reply to Alston":

"It would be reasonable to refer to those conditions [="the conditions under which a sentence may be uttered"] collectively as the meaning of the sentence."

But "the synonymy relation gains no support from this notion of meaning. The reason is that, on this notion of meaning, no two sentences can have the same meaning; for no two sentences are wholly alike in their conditions of utterance." (1986, p.73)

That last claim strikes me as implausible; is that just me and my un-Quinean prejudices? Is there a decent argument for Quine's claim that two sentences never have the same conditions of utterance?

That's my main question. But I should mention that Quine gives his own very terse argument: "A sentence can be uttered only to the exclusion of all other sentences, and// hence only under conditions not totally shared, if we grant determinism" (73-74). But that strikes me as a (for lack of a better word) weird argument, for at least two reasons. 1. The fact that sentence A is uttered instead of sentence B at a given time and place does not mean that B could not have been uttered (note that the definition of 'meaning' is the conditions under which a sentence MAY be uttered, not IS (ACTUALLY) uttered. 2. I would've thought that any reasonable notion of 'conditions of utterance' would not require the conditions to be specified up to the level of detail of full physical theory; that is, there could be physically different instantiations of the same 'conditions of utterance'. And it strikes me as very strange to require determinism at that linguistic level (even if we want to be hardcore determinists about physics): sometimes I just keep my mouth shut, even if there's some utterance that would have been fully appropriate for those conditions.

Validity, Venn diagrams, and ex falso quodlibet

(The first 2 paragraphs here are set-up; those in the know can start at the third paragraph.) I teach a class called "Critical Thinking and Reasoning" most semesters. It covers argument recognition, reconstruction, and evaluation. At the very end of the semester, we talk about how one can show a particular argument form is valid. For propositional/ sentential logic, we use truth tables: if there is no row of the truth table where all the premises are true and the conclusion false, then the argument form is valid. For categorical logic, we use Venn diagrams. If you are not familiar with how this works, it's very straightforward and simple; here is a quick introduction for the unacquainted. The basic idea is that you diagram all the premises on a single diagram, and then check whether you have 'already' diagrammed the conclusion.

One interesting thing about presenting both of these to an intro class is their difference over ex falso quodlibet: in classical propositional logic, any argument with inconsistent premises is valid, whereas in categorical logic there are invalid arguments with inconsistent premises. This is reflected in the semantics for the two logics, truth-table or Venn diagram, respectively. That is, if you diagram 'All A are B' and 'Some A are not B', you have not already diagrammed 'All C are D' (or whatever -- I mean, or quodlibet). Whereas, in the truth table case, if one of your premises is p and another is 'not-p', it is of course impossible for there to be a row where both all the premises are true and the conclusion is false -- since there is no row in which all the premises are true.

Everything so far is completely uncontroversial. Now comes the point I've been wondering about for the last couple of days. What if we set up a validity test for a propositional language that looked more like the Venn-diagram test for categorical logic? That is, instead of thinking of validity in the usual way as absence of counterexamples (in the propositional case, no row of the truth table has all true premises and a false conclusion), we demand that the diagram of all the premises be a diagram of the conclusion. In categorical logic, each of the points in the Venn diagram represents an individual object, and the circles represent sets of objects; in a propositional Venn diagram, we let each point be a case/circumstance/state of affairs/whatever, and let the circles be sets of cases etc. The resulting propositional logic would NOT be classical, since ex falso quodlibet would not hold.

Why care about setting up such a Venn-diagram validity test for propositional logic? Here's why: when relevance logicians (and anyone else who doesn't like EFQ) accept the 'no counter-example' account of validity, they are forced to say some pretty counterintuitive things, first and foremost that there is a case (or whatever) in which both p and 'not-p' are true (and some other q false). If they don't say this, then they can't say EFQ is invalid. But if this Venn-diagram validity test for a propositional language is viable, we can reject EFQ without accepting true contradictions. All that's required is tweaking the no-counterexample notion of consequence -- a tweak that is already used in critical thinking textbooks.

Finally, this idea seems so obvious that somebody must have already explored it. Any pointers to the relevant literature?

Logical pluralism and special relativity

I spent the end of last week at UCSD. I had a great time, and I got some extremely useful feedback on a couple of things I've been working on. I'm especially grateful to my host, Chris Wüthrich.

At dinner, we had a helpful discussion about the logical pluralism project I've been working on. The basic hope is to figure out if Beall and Restall are right in saying that the notion of consequence really is "unsettled" or indeterminate. I've had a couple of past posts discussing whether 'entails' is ambiguous (as Beall and Restall sometimes suggest). The upshot of those posts was that, if 'entails' is indeterminate, its indeterminacy arises from having a (hidden) parameter. This hidden parameter is what Beall and Restall call a 'case', as in: 'An argument is valid = In every CASE where all the premises are true, the conclusion is too.' Different logics fall out of different specifications of cases.

The next question to ask is: Is there any evidence that 'entails' really does have a hidden parameter? One way to answer this is to look at an argument that (most) people think is impeccable, which concludes that some concept does harbor a hidden parameter -- and then ask whether 'entails' is like that. The case that springs to my mind is Einstein's argument that simultaneity is relative in special relativity, i.e., whether 2 events are simultaneous is relative to a 3rd parameter, an inertial trajectory.

Let's spell this out. Let e1 and e2 be events. ‘e1 and e2 are simultaneous’ cannot be true simpliciter; rather, it can only be true relative to a frame of reference. This suggests a possible analogy with logical pluralism: ‘P1... Pn entails C’ is not (or at least rarely -- B&R make two little exceptions) true simpliciter, but rather relative to a specification of cases. So ‘entails’ is analogous to ‘simultaneous with’ (or any other predicate of temporal order), and ‘case’ is like ‘frame of reference.’

The key question is then: does the evidence that Einstein appealed to in order to show that there is not one correct notion of simultaneity have an analogue in the logical case?

So what is the physicists’ justification for claiming that there is no preferred frame of reference in special relativity? The fundamental reason is that the laws of nature can be couched in such a way that they are the same in all inertial frames. For one of the frames to be physically privileged, there would have to be some essential physical difference between it and the others. And because there is no privileged or distinguished frame, there is no basis for elevating one standard of simultaneity above the others—and it is in that sense that simultaneity is relative in special relativity.

Can we draw an analogy to the logical case? To be explicit, the relativistic argument is basically this:

P1. Different frames of reference yield different notions of simultaneity.
P2. The laws of nature are the same in every frame of reference.
Thus, there is no privileged frame of reference.
Thus, simultaneity is relative, i.e. there are multiple acceptable notions of simultaneity.

And, as said above, we are taking specifactions of cases as analogous to frames, and simultaneity as analogous to validity. This yields:

P1. Different specifications of cases yield different notions of validity.
P2. _______ is/are the same in every specification of cases.
Thus, there is no privileged specification of cases.
Thus, validity is relative, i.e. there are multiple acceptable notions of validity.

The question is: what should -— what could -- go in the blank in P2? What is the same in every specification of cases? I can see two suggestions B&R might make: 1. Identity and transitivity hold in every specification of cases. But B&R reject this as far too weak. 2. The desiderata for a logical consequence relation (formality, necessity, normativity) are the same in every acceptable (or something similar) specification of cases (‘acceptable’ will rule out possible worlds, right?). But are these desiderata really like ‘the laws of nature’ in the physics case?

Of course, the evidence for one type of pluralism (e.g. about simultaneity) need not have the same form as evidence for another type of pluralism (e.g. about consequence). That is, even if one cannot create a plausible argument for pluralism about validity analogous to the Einsteinian argument for pluralism about simultaneity, that obviously says nothing about whether another, entirely different sort of argument would do the job. Does anyone out there see what it could be? At UCSD, Jonathan Cohen pushed me on this point over dinner; in particular, he pointed out that Einstein's argument is an instance of an argument from symmetry, and that the broader genus of (good) arguments from symmetry might well encompass an argument-type that would do the trick for Beall and Restall's logical pluralism. Can anyone point me to an example of such?

Validity in logics with ambiguous terms

First, I have to give a little background about free logic; the point of this post comes towards the end. In model theory for classical logic, every name (= individual constant) is interpreted by exactly one object (in the domain of quantification); colloquially: the name ‘Chicago’ picks out exactly one thing -- the spatiotemporal object Chicago. Free logic relaxes this assumption, by allowing individual constants to be associated with no objects (in the domain of quantification). The rationale here is that some names do not successfully pick out anything in the world (think about ‘Santa Claus’, ‘Pegasus’, or ‘Planet Vulcan’), and since we don’t always know which of our terms are genuinely referential and which ones fail to refer, perhaps we should not build it into our logic that every name in fact refers. (There is another motivation for free logic as well: that we should allow models whose domain of quantification has cardinality zero, since it’s not a matter of logic that at least one thing exists in the universe.)

When we allow names that can refer to nothing into our language, the usual deduction rules have to be modified. In particular, the following (classically valid) argument form is invalid (where a is an individual):

All x are F
Thus, a is F

If a is a non-denoting name, then the premise can be true and the conclusion false or truth-valueless (depending on your preferred semantics for sentences containing non-denoting names). So in short: allowing non-denoting names forces us to give up the usual ‘All’-elimination rule (a.k.a. ‘Universal Instantiation’) just above.

I have recently been thinking about languages in which we relax the classical univocality assumption for names in the ‘other direction’: that is, languages containing terms that refer to more than one thing. (I gave them the uninspired tag ‘Multiply-Referring languages.’) The point of the formal exercise is to model ambiguous or confused terms. I have already developed a family of model theories for such languages (published in JPL last year), and am currently thinking about proof systems.

Back to free logics for a moment. There are three species of semantics for free logics: negative, neutral, and positive. They are distinguished by how they treat atomic sentences containing non-referring names. Negative: all false; neutral: all truth-valueless; positive: at least one atomic sentence with a non-referring name is true. For example, consider ‘Pegasus=Pegasus’: negative semantics declares this false, neutral semantics declares it truth-valueless, and positive semantics declares it true. I take this tripartite characterization straight over into multiply-referring languages.

Now here, finally, is my point. In positive multiply-referring languages without identity, the above rule of Universal Instantiation is valid. And, as far as I can see, all the other classical rules are valid (=truth-preserving) as well. Which means, surprisingly (to me), that the classical introduction and elimination rules for FOL without identity all are also valid rules for positive multiply-referring langauges. More simply, allowing ambiguous names into an otherwise classical language without identity makes no difference to validity. (At least in the sense of truth-preservation; it does mess up ‘backwards-falsehood-preservation,’ for reasons I won't detail here.)

But things change once an identity predicate is introduced into the language. Universal instantiation becomes invalid: ‘Everything is not identical to a’ is true if a is multiply-referring, but ‘a is not identical to a’ is not true. This raises a question for me about the best way to construct the proof system here: put roughly, is the problem with universal instantiation, or with identity? Both of them have to be present to generate the invalid argument form, so which is the one that should be altered? I’ve never tried to make my own proof theory before, so I don’t know how one should proceed under such circumstances. Any thoughts?

Going back to Pittsburgh

I know posting here has been pitiful lately. Unfortunately, this isn't even going to be a real post: I just wanted to let people know that I am going to be in Pittsburgh this weekend for a conference on underdetermination at the Center for Philosophy of Science. Anybody in Pittsburgh who wants to meet up, just send me an email or leave a comment here, and we'll sort something out.

Also, for folks who can't make it, there are abstracts at the site linked above, and some of the papers are up on the phil-sci archive, on a special conference page.

It's only a theory

I imagine just about everyone who reads this blog already knows the following, but... A big group blog in philosophy of science has recently been started by Gabriele Contessa. It's called It's Only a Theory, and Gabriele has assembled an all-star cast of contributors. For reasons beyond me, he also invited me to join. So in the future, my philosophy of science posts will usually be cross-posted both here and there; however, the history and logic posts will be here only.

Darwin day disappointment

In honor of Darwin's birthday today, I checked out a couple of recent books on Darwinism from the library: Michael Ruse's Darwinism and its Discontents and Philip Kitcher's Living with Darwin. After a quick perusal, both books looked pretty good; both are pitched at a more or less at a pop science/ pop philosophy of science level.

The 'disappointment' in this post's title is that, directly under every one of the chapter titles in Ruse's book, someone had written "answersingenesis.org". (Why every single chapter title?)