6/18/2009

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.

7 Comments:

At 18/6/09, Blogger Daniel Lindquist said...

This seems to assume that "Everything is self-identical" is a necessary truth. But Quine wouldn't have any reason to grant this; it's just that the models (or worlds) where "Everything is self-identical" is false are really non-useful for us, or something like that. (For one thing, they have to use logical rules which are pretty screwbally from the perspective of classical logic.) If one goes along with Quine in being skeptical of the distinction between necessary and contingent truths, then his argument here seems to stand fast against your objection. And of course necessity was one of the things Quine was skeptical of, along with analyticity. (Otherwise put: He was skeptical about contingency and synthetic truth both.)

 
At 19/6/09, Blogger Greg Frost-Arnold said...

Hi Daniel --

Thanks for the comment. It's good to see you're still reading the blog. A couple of immediate reactions:

1. If the logical laws have to be pretty screwy to make 'Everything is self-identical' come out true, then you are NOT holding the language constant. I am imagining a case in which we hold the language constant, and then imagine what would be true if the world (='everything') had been different.

2. I think you are right that Quine might think this doesn't meet his scientific standards that forbid modal locutions. But all I need is the idea that there are ways the world could have been,
(uh-oh: maybe there's a Quinean response to this argument that shows it proves too much. If one agrees with Quine that "there is no higher or more austere form of necessity than natural necessity," and natural necessity is cashed out as Humean regularities, then analogous reasoning to that in the post would show that any physical law is not dependent on the world, but only on language. Maybe that was your point, Daniel, to begin with?)

(Finally, a terminological note: usually models are not true or false; sentences are true or false in a model, i.e. (roughly) models make sentences true or false.)

 
At 19/6/09, Blogger Daniel Lindquist said...

1. I may have given up too much in my first comment: you might be able to hang on to classical logic, but just have this be a world where everything is true (and so also false) -- a trivial world. This is pretty obviously not how things really are, but that's just to say that "Everything is self-identical" is really true, and not false. (Obviously so.) This would give you a (very drastically different) case which would make "Everything is self-identical" (at least) false, while keeping the logic (and the meaning of the sentence) the same. I'm less certain of the following strategy: change what "everything" can range over, so it ranges over some non-self-identical "entities" along with all of the self-identical entities, and so "Everything is self-identical" becomes false. (I can at least imagine someone who finds this persuasive: there are not really any entities without identity, but that is just how the world happens to be; things might've been much more awkward than they really are. In either case, "Everything" just ranges over whatever there happens to be, self-identical or not.)

At least, I think this should satisfy a Quinean. I'm also not sure how strongly Quine needs to make his case here; the conclusion he wants isn't that "Everything is self-identical" is really an obvious fact about how the world is (as opposed to being true because of its meaning); that would just make it synthetic. He wants to convince us that it doesn't matter whether we call it "analytic" or "synthetic" -- we can draw the A/S line wherever, it doesn't matter, since in so doing we aren't tracking any real distinction between two groups of our sentences. There's no fact of the matter about whether any particular sentence is analytic or synthetic, since we can just as well draw the line so that it is or it isn't. (But we do draw the line, in another sense: there are always, in scientific investigation, sentences we are not willing to revise and sentences which we are willing to revise; the ones we hold constant guide us in how to handle revising the ones we're open to revising. We can, if such revisions prove unhappy, change which sentences we hold constant, but this is not the same as just changing something which we already held as open to revision. I take this to be a Quinean gloss on Sellars's dictum that "in science anything is open to revision, though not everything at once". The rejection of the A/S distinction (and its cousins necessity/contingency, apriority/aposteriority, etc. -- the family of interdefinables Quine discusses in part one of "Two Dogmas") is then the denial of the claim that there are sentences which *must* be held constant, or sentences which *must* be held open to revision. Nothing forces us to place any particular sentence on either side of the divide, and so there is nothing in nature which divides our sentences between the analytic and the synthetic. We divide them as we deem best, at the moment, as pragmatist persons of science.)

(I also suspect that my earlier line of argument sits uneasily alongside Quine's "change the logic, change the topic" argument against non-classical logics, but then I don't think that part of his thinking coheres very well with his rejection of the analytic/synthetic distinction anyway. Nor do I find it persuasive in its own right.)

2. I think that "ways the world could have been" are probably too much for a Quinean to be happy to grant; they smell like possible worlds to me. And yeah, Quine does allow for physical necessity (=what is or is not consistent with the laws of physics); if "there not being a way the world could be that would make P false" makes P analytic (=true just because of our language), and if one wants physical necessity to be the only necessity one credits, then it does look like you get the weird conclusion you mention: laws of physics are analytically true or false. So it looks like you need a different notion of necessity to handle things like you'd wanted to (which was the point I wanted to make).

 
At 19/6/09, Blogger Daniel Lindquist said...

I hit a character limit; I didn't actually know blogger comments had those. 4,096 characters was too many. Here's the bit that got cut off (it is a side-note anyway):

Re: Terminological note: I don't see where I slipped and said that a model was true or false? By "models where 'Everything is self-identical' is false" I meant the models in which it is false. I suppose "where" rather than "in which" isn't standard, but I'm pretty sure I've seen it before.

Also, "family of interdefinables" above was too strong; necessity/apriority/analyticity/synonymy/etc. doe't have to be interdefinable, they just have to be a package deal. Quine's conclusion in part one of "Two Dogmas" is that if you can make sense of one of the bits he doesn't like, you can use that as leverage to rehabilitate them all; this doesn't have to go by defining them all in terms of one member of the group.

 
At 19/6/09, Blogger Greg Frost-Arnold said...

Hi Daniel --

Re: terminological note. Ack, the perils of commenting first thing in the morning... you're of course right that you didn't call a world true or false. Sorry.

I agree with most of what you said; just two quick notes: there's no (classical/ Tarskian) model in which a contradiction is true. (That is, there's no such thing, so far as I know, as what you called the 'trivial model'.)

Also, you could not have entities in the domain of discourse that are not self-identical without changing the interpretation of '=' (i.e. you would have to change the language).

p.s. - looking at your webpage, it looks like we have a couple of things in common: I was raised in Dallas, and some of my family still lives there, and I went to the U of C for my undergraduate degree (though the faculty were pretty different then).

 
At 11/10/09, Anonymous Anonymous said...

HI, Howie Mandel here,
"traits" of a language? What do you mean by traits?
You could define traits to mean whatever supports your point.
I could just say that I have a
definition that does allow the truth value to change if the world changes in some way. I could redefine "everything" and
"self-identical" toward the same end.

OR,I could say that the sentence "everything is self identical" is itself part of the world, and so the truth value does depend on the
traits of its subject matter---the world---since the sentence is part of the world.

 
At 11/10/09, Blogger Greg Frost-Arnold said...

Hi Howie --

1. "Traits" is Quine's word. I don't know exactly what he means by it, but it at least includes the meanings of words.

2. I would like to see the definition you have in mind, in which the language stays fixed, and yet the truth-value of 'Everything is self-identical' differs depending on the way the world is (assuming that that sentence meaning what it normally does).

3. Even if you regard the sentence 'Everything is self-identical' as part of the world, I don't see how the truth-value of that sentence depends on the way the world is.

 

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