Sunday, January 09, 2005

Analyticity

A statement is said to be 'analytic' if it is true simply in virtue of its meaning alone - 'true by definition', we might say. Synthetic statements, by contrast, depend upon empirical facts for their truth values. Quine, in his 'Two Dogmas of Empiricism' (in From a Logical Point of View), disputes that this is a genuine distinction. He begins by identifying two classes of analytic statements:

1) Logical truths, e.g. "No unmarried man is married". These statements are true by virtue of their logical form (we could replace each appearance of 'married' with a generic 'X' and the sentence would still clearly be true).

This class is unproblematic, as we have a clear method to decide whether a statement counts as a logical truth. If a (compound) statement always comes out true, no matter what truth-values we assign to the atomic statements of the language, then it is a logical truth. (Consider "P or not-P": it is true no matter whether we assign P as 'true' or 'false'.)

2) The other, more interesting, class contains statements that can be turned into logical truths by substituting synonyms. For example, "No bachelor is married" can be turned into the logical truth above by replacing 'bachelor' with its synonym, 'unmarried man'.

So we can explain analyticity in terms of synonymy. The question Quine then raises is: can we provide an adequate account of synonymy?

An obvious strategy would be to appeal to 'definition' (as I did myself in the very first sentence of this post). But this doesn't help, because most definitions (e.g. in dictionaries) just report pre-existing synonymies, rather than stipulatively creating new ones.

Quine goes on: (pp.24-25)
Just what it means to affirm synonymy, just what the interconnections may be which are necessary and sufficient in order that two linguistic forms be properly described as synonymous, is far from clear; but, whatever these interconnections may be, ordinarily they are grounded in usage. Definitions reporting selected instances of synonymy come then as reports upon usage.

Another natural answer here would be to define X and Y as synonyms iff they can interchanged in appropriate contexts without altering the truth value (i.e. if they're interchangeable salva veritate). But what contexts must we include here? Mere extensional interchangeability is clearly insufficient - for 'featherless biped' and 'human being' are extensionally identical (true of all the same actual objects), but clearly differ in meaning. So genuine synonyms must also be intensionally identical. That is, they must satisfy something like: "Necessarily, all and only X's are Y's" (where 'necessarily' is so narrowly construed as to apply only to analytic statements). But this is just to say that "All and only X's are Y's" is analytic. So we've come full circle! We can explain either analyticity or synonymy in terms of the other, but then this other one is left unsupported.

But do they really need support? One might think these concepts are intuitive enough that we could dispense with the formal explications. But further consideration casts doubt on this. Quine points out that he has no idea whether the statement "Everything green is extended" is analytic. (The statement is certainly true, but is it true partly in virtue of how the universe is, or merely because of what the words mean?)

Further, as Everitt & Fisher point out in Modern Epistemology, scientific advances have caused us to revise statements that were once seen as being obviously analytic. For example: "Two bodies which are both falling downward cannot be moving in opposite directions" (contra spherical Earth), "For any two events A and B, either A is before B or it is not" (contra special relativity), and "If a woman gives birth to a child, she is its mother" (contra IVF).

As Everitt & Fisher explain:
What these three examples show is the way in which unforeseen scientific advances can radically change our acceptance of propositions which initially seemed immune to empirical findings. In each case, our willingness to regard the "a priori truth" differently is based on the fact that the new empirical information undermines some very general assumptions which lay behind the a priori truth. [...] Sometimes the new information shows that the old "truth" was true if taken in one way but not if taken in another, where the very idea that there are two ways in which that truth might be understood becomes intelligible only in the light of the new empirical information. (p.112, original emphasis)

Nevertheless, I'm not convinced that any of this conclusively refutes the viability of the analytic/synthetic distinction. Because it does seem plausible to me that meanings change over time, and that the three examples above really are analytic on the appropriate interpretations of 'down', 'mother', etc. (Though E&F insist that there are "no good grounds" for understanding this as a change of meaning rather than only a change of empirical beliefs, presumably the reverse is also true.) And Quine's own example simply shows that there are some borderline cases which we're not sure about. I guess that's enough for us to conclude that the distinction isn't clear-cut, at least. But I'm not sure we should want to dismiss the distinction altogether.

Having said that, I do agree with Quine (p.43) that nothing is (in principle) unrevisible:
[I]t becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements, which hold come what may. Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery [of our 'web of beliefs'] can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?

But given my above remarks I guess my response would be to reject the claim that analytic statements hold "come what may". For if meanings change, then what is true simply in virtue of those meanings may also change. So I think I might like to uphold a slightly muted version of the analytic/synthetic distinction, whereby even analytic statements are open to revision, since scientific advances may lead us to revise the concepts upon which those analytic statements depend. Does that sound at all plausible?

P.S. Doing things with words has also posted an essay on this topic.

7 comments:

  1. My understanding of an analytic statement in philosophy is the same as given at wikipedia.org - something true according to the meaning of its words. This is more than the mere tautologies you seem to be presenting in the first paragraph.

    The difference between a synthetic and an analytic fact come from, for example, truth tables. Synthetic statements are true according only according to their validation, but analytic ones are true according to their meaning. Perhaps you might consider synthetic statements to be true by convention, whereas analytic ones are not subject to convention.

    For example, "My name is Tennessee" is true by convention - it happens to be so, but it is not the only name I could have had. Had my name really been Michael, the statement would have been false.

    However, "The sun is hot" is true by necessity - if the sun were not hot, it would not be a sun. The concept sun can mean nothing other than a hot body. (This is where Aquinas tried and failed to hang his hat). The words still _mean_ things, and refer to things, but do not rely on particular situations or happenstances for their truth.

    Synonyms, then, are words with the same meaning used in place of others.

    -T 

    Posted by Tennessee Leeuwenburg

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  2. T, isn't your definition captured in my introductory paragraph? I (and Quine) agree this includes more than merely logical truths (the first class described above) - that's why we also identified a second class, which you seem not to have noticed.

    Further, truth tables alone cannot identify analytic statements generally. They can only identify the first class, i.e. logical truths (by the method I described in the post). For the second class of analytic statements depend upon meaning ("all bachelors are unmarried" would not be true if "bachelor" or "married" meant something different), whereas truth-tables are purely syntactic, and contain no semantic information.

    Suppose Bx means "x is a bachelor", and Ux means "x is unmarried". A truth table would have a line where Bx were true but Ux false, since these are two logically distinct atomic statements. So (x)(Bx -> Ux) is not a logical truth. Yet it certainly is analytic when we interpret it semantically.

    I think "the sun is hot" is a bad example of analyticity, indeed I'm not convinced it is a necessary truth at all. Better to use examples involving obvious synonmy, as with the stock example I've used throughout, i.e. "all bachelors are unmarried men".

    "Synonyms, then, are words with the same meaning used in place of others."

    Sure, but that doesn't tell us anything new. It simply shifts the problem to: what is "same meaning", and how are we to identify it? Your phrase "used in place of others" is reminiscent of the interchangeablility suggestion discussed in the post, but I explained there why this doesn't work... 

    Posted by Richard

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  3. Hi Richard,

    Thanks for looking at my blog...I will post more philosophy...but if you scroll down on my blog you'll notice I have a specific section called "Philosophy Circle" and every few weeks or so I post a new philosophical question. Anyways...last semester we studied the two dogmas of empiricism (by Quine) and I guess the one thing thats always boggled my mine is that apparently the first dogma depends on the second one (reductionism)...and vice versa. Would you be able to clarify that for me? I'm just not seeing how the two depend on each other completely...or if they do at all? 

    Posted by Annie

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  4. I'm not too sure, and I don't have Quine's essay with me at the moment, so I might have to get back to you on that one... 

    Posted by Richard

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  5. Quine writes (p.41):

    "the one dogma clearly supports the other in this way: as long as it is taken to be significant in general to speak of the confirmation and infirmation of a statement, it seems significant to speak also of a limiting kind of statement which is vacuously confirmed, ipso facto, come what may; and such a statement is analytic."

    I don't find it nearly as clear as Quine apparently did, but oh well. I think the basic idea is that if you assume a verification theory of meaning, then the dogma of reductionism about statements leads one to posit the sort of 'vacuously confirmed' (i.e. analytic) statements mentioned in the quote.

    I'm not entirely sure how that's supposed to work, however. After all, if meaning is determined by method of verification, and a class of statements are all confirmed by the same method (viz., vacuously, by doing nothing at all), wouldn't that mean that all analytic statements have the same meaning? I'm confused... 

    Posted by Richard

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  6. Keith Brian Johnson7:50 am, October 12, 2005

    Well, first, I have no homepage, so I'll leave my e-mail address instead (at the end). Now, on to analyticity and Quine.

    It has been quite a while since I read "The Two Dogmas of Empiricism," but I remember quite distinctly that it seemed to me at the time that, unlikely as it was, Quine was just making a blunder. I assume I was wrong about that! But I remember that I thought this: Before one can assess a sentence as analytic or as synthetic, one must first stipulate the meaning of the sentence. One can hardly say that meanings of words change over time or are used differently by different people and that therefore there can be no analytic sentences, unless what one has in mind is exactly that it is not sentences that are analytic but rather propositions--the *meanings* of those sentences. That would make sense to me. In order to evaluate analyticity-status, one must have a clear sense of what a sentence means. The meaning of the sentence must be *stipulated* before it can be evaluated as analytic or synthetic.

    Whether or not terms are synonymous with other terms is again a matter of stipulation. Words and sentences don't have meanings all on their own; their meanings are always meanings *to* people. Whatever those meanings are, those meanings give us the propositions to be evaluated. An avowed feminist might say that "A bachelor is an unmarried man" is *not* analytic, because an unmarried woman is a bachelor, too. If we stipulate her meanings of words, then the sentence is not analytic. But it's really not the sentence that we'd be agreeing wasn't analytic, but rather a particular stipulated meaning of it (or, better, a particular set of stipulated meanings and of stipulated relations among them). When we normally claim that "A bachelor is an unmarried man" is analytic, and think it clear that it is, we agree simply because the intersubjective meanings of the particular terms used are easily agreed upon without explicitly saying so--we easily agree to stipulate that "bachelor" is synonymous with "unmarried man"--but the avowed feminist might disagree. Meaning and synonymity are matters of stipulation, and someone else might not agree so easily to make the same stipulations we do. Given the same stipulations, however, I see no reason why analyticity needs to be written off. Or am I simply getting things badly wrong?

    Keith Brian Johnson
    joyfuloctopus@yahoo.com

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  7. Hi Keith, that does sound pretty plausible, but of course I'm no expert on this stuff...

    ReplyDelete

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