[hist-analytic] RBJ's Proposal on analyticity
Baynesr at comcast.net
Baynesr at comcast.net
Sun Mar 8 17:15:44 EDT 2009
Prof. Aune remarks:
'As for the former, Kripke never said, “an identity between rigid designators must be necessary.” '
If two designators designate the same thing in all possible worlds, then the truth of the sentence asserting that they are identical entails their identity in all possible worlds. That is: if to be necessary is to be true in all possible worlds, then, if the identity statement is true, then it is true in all possible worlds. This would follow even if we rejected the principle of substitutivity and, therefore, Barcan's theorem. Necessity is a property of sentences, sentences such as the one I've described. His theory of rigid designation is not necessary for the claim that there are a posteriori identities. However, it is sufficient , if what I said is true; that is, that an identity statement that is true, wherein the names flanking the identity sign are rigid, is a necessary truth. As I said, before, there is a hidden strength to his theory that cannot be reached by simple substitution of modal predicates in the "principle of identity" (or "substitution"). That strength is having in his possession an an argument for the necessary diversity of diverse objects in this world!
Prof. Aune remarks:
"The positivists held that analyticity and necessity are co-extensional because they were convinced that necessities could be known only by means of conceptual analysis."
This is true, and I think it reveals a severe weakness in the positivist position, inspired as it was by an odd theory of meaning and verifiability. Of course, if you claim that the only necessities are by way of conceptual analysis , then, most assuredly, you will conclude that all necessary truths are analytic . But this is terribly question begging. It is question begging because we have not been given a good argument that all necessary truths are known by conceptual analysis. Kant's claims was simple and accurate: if you cannot arrive at all necessary truths by conceptual analysis, then if there are necessary truths besides these, they will be synthetic. This seems perfectly acceptable. Now a final word on Kripke's discovery of the a posteriori character of some necessities.
I want everyone to notice one thing, especially: ALL of Kripke's examples can ONLY be examples where the necessary truth at issue is an IDENTITY statement. I find these, philosophically, of little interest in respect to the problem of the synthetic a priori. Why? Here's why: I believe '=' is a logical operator (or at least it is in my way of doing things). Insofar as it is a logical operator, truths containing it essentially are not facts in the world, although it may describe a fact abou t the world. It is a "logical truth", and as such does not correspond to a fact in the world: there are no logical facts in the world. It may be a discovery about the world that in it one finds that since 'a = b' that there is only one thing where we thought there were two; but it is not a fact about the world that '=' is a descriptive relation between object(s). This is one reason people stumble over the question of how TWO things can be identical. THEY aren't! There is no such fact. I offer a challenge.
My challenge is this: supply me with a necessary truth that does not contain a logical operator. By the way, you can define this thing out in set theory using membership and entailment. But this only raises further questions, such as what IS a logical operator? If I am right about Quine, that is a PRAGMATIC decision. Recall the paradox of analysis. This wouldn't be an issue if "facts" of identity were relational facts. If I were to be shown a necessary truth free from the trappings of the mumbo jumbo on identity then I might "covert." I know nothing in science that rules out synthetic a priori truths; but, then, in science we have no distinctions that depend on the distinctions between sentences, judgments, propositions etc. So much the worse for science.
----- Original Message -----
From: "Bruce Aune" <aune1 at verizon.net>
To: hist-analytic at simplelists.com
Sent: Sunday, March 8, 2009 1:58:52 PM GMT -05:00 US/Canada Eastern
Subject: RBJ's Proposal on analyticity
The positivists held that analyticity and necessity are co-extensional because they were convinced that necessities could be known only by means of conceptual analysis. Rationalist and Kantian alternatives seemed unscientific and therefore unacceptable. I don’t think any informed, reasonable philosopher con responsibly contend that the coextensiveness of analyticity and necessity is “obvious.” In view of the plethora of arguments to the contrary, I think it can be defended only by a pain-staking argument, the sort I attempted in my recent book.
I am aware of no fallacies in Kripke’s arguments for the truth of a posteriori necessities (as we may call them) or even for the truth of contingent a priori truths. As for the former, Kripke never said, “an identity between rigid designators must be necessary.” What he did say was that a statement containing rigid designators would, if true, be necessary. For him, necessity is not a relation between designators (at least generally) but a relation between things: it is a relation holding between each thing and itself. But his views on the necessity of true identities did not depend on the notion of rigid designation, and it was inadvisable for me to have mentioned this notion in my email, since it always stimulates useless discussion. The formula “(x)(y)(x = y à N(x = y)” is a theorem of quantified standard first-order modal logic, and its proof in no way depends on a doctrine of rigid quantification.* (You can verify this by looking at any standard text on modal logic, e.g. the one by Hughes and Cresswell.) The relevance of the modal theorem to your thesis can be illustrated by standard examples. One is this: If water = H2O, then it is necessary that water = H2O. The assertion “water = H2O” is not (most people will agree) true by virtue of meaning, and neither is “N(water = H2O).” The truth-value of the first can be decided only by empirical investigation, and the second can be inferred from the first by means of the modal theorem. If the previous example troubles you, here is another: “The inventor of bifocals is Benjamin Franklin,” where “the inventor of bifocals” is used to pick out a certain man--the man who, as it happened, invented bifocals.”
* As I see it, Kripke introduced the notion of a rigid designator to disarm the sort of counter-examples people raised when he spoke informally of the necessity of true identities. Those erroneous counter-examples invariably involve fallacies of equivocation, when a term denoting one thing in the antecedent of a conditional, denotes something else in the consequent.
As for contingent (non-necessary) but a priori truths that can reasonably be considered analytic, consider the “The standard meter is one meter long.” At one time (when there was a standard meter) this could be known a priori, by a priori inference from a meaning stipulation, but it is not necessary, since the standard meter, if heated sufficiently, would become appreciably longer than one meter. Please don’t bother to argue with me about these cases, which I am presenting quickly and informally. If you continue to hold your present view, you better be ready to argue with others, though, because they are generally accepted as all sound.
You say,” The only relevant part of the meaning of a sentence for determination of either analyticity or necessity is the truth conditions. We know that a statement is analytic when those conditions tell us that the under all conditions the sentence is true.” I can almost agree with this, but I think “truth conditions for an arbitrary sentence” is far more problematic than you suppose. What are the truth-conditions for “Bachelors are unmarried”? If it is given by the biconditional, “’Bachelors are unmarried’ is true iff bachelors are unmarried,” what entitles us to say that the proposition expressed by “Bachelors are unmarried” is “logically necessary,” as you say? As I argue in my book, partial specifications of meaning (of the kind Carnap called “A postulates”) are, I think, vital for showing the analytic character of many sentences. And it is by reference to such postulates and other semantical rules that we can infer the a priori necessity of many analytic truths. Not all analytic truths express necessities.
As I said before, one of the classic questions of epistemology is whether there are synthetic a priori truths. To move from the vague idea of true by virtue of meaning to analytically true simply begs the question against a host of traditional arguments, which have to be considered critically and fairly. You can’t ignore them.
Your counterexample to the no color-overlap principle overlooked a crucial feature of that principle. This is that a thing or region of a thing can have no more than one determinate color . If a blue object is azure, its determinate blueness is not different from its azureness: it is the same thing. There is no problem with a thing having two generic colors, or a generic color and a determinate one belonging to that color-genus.
I stand by all the claims I made in my memo: I think your approach to analyticity is not promising as it stands. My ideas about the subject are developed at length in my chapters and 3, and I can only suggest that you have a look at them. That is really all I have to say at this point.
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