Some readers may already be familiar with the π vs. τ debate. If not, I recommend checking out Michael Hartl's τ manifesto and this fantastic short video by Vi Hart. An attempt at a balanced evaluation of π vs. τ can be found here.
For those who don't know, τ is just 2π. The defenders of τ argue (as seen in the above links) that using it instead of π makes many things much clearer and simpler/ more elegant.
Let's assume for present purposes that the τ-proponents turn out, in the end, to be right. I want to ask a further question: what would this then say about Quine's denial of the analytic-synthetic distinction? Quine's denial, virtually all agree, is the claim that all rational belief change is pragmatic, i.e. there is no principled difference between questions of evidence/justification on the one hand, and questions of efficiency and expedience on the other (= between external and internal questions, i.e. between practical questions of which language-form to adopt, and questions of whether a particular empirical claim is supported by the available evidence).
So here's my question: if Quine is right, then is our old friend C=2πr simply wrong (and C=τr right)? If not, how can a Quinean wiggle out of that consequence? And if so (i.e. C=2πr really is wrong), does the Quinean have any way of softening the sting of this apparently absurd consequence?
Showing posts with label Quine. Show all posts
Showing posts with label Quine. Show all posts
1/03/2014
10/15/2007
Yet another way to think about Quine's critique of Carnap
Several of the blog entries here have been about the Quine-Carnap debate over the status of analytic truth. Generally, I don't feel the force of Quine's arguments as they are usually presented, either because his interpretation of Carnap is unfair or inaccurate, or the arguments just aren't that persuasive. Multiple commentators on the Quine-Carnap debate have suggested that the two are 'talking past each other,' at least to some degree. So, I am constantly trying to find a way to make Quine's view make sense to me, AND simultaneously really disagree with Carnap. This seems like installment 19 or so in that endeavor.
Carnap and Quine agree that language can be studied at various levels of abstraction. Using Carnap's taxonomy, we start at the level of pragmatics, where we study how individual speakers use expressions under particular circumstances. This level contains the most detail: speakers, their circumstances, plus the meanings of the words for particular speakers under particular circumstances. At the next, more abstract level, we have semantics, which abstracts away from particular speakers and particular circumstances. And at the highest level, we have syntax, which abstracts away the meanings of words, leaving just the symbols, the way they are put together, and which strings follow from others.
In each transition from pragmatics to semantics to syntax, some information about language is omitted/ discarded. (Like the move from Euclidean geometry to neutral geometry, which drops the parallel postulate.) Now, we can conceive of Quine's indeterminacy of meaning thesis (the radical translation thought experiment) as critiquing Carnap in the following way: Carnap is importing or introducing new information at the semantic level, because the semantic facts Carnap includes in a semantically-characterized language [a "semantic system"] cannot be 'read off' even the information contained at the pragmatic level. The analogy in the geometry case shows why this is clearly an unacceptable maneuver. It would be: thinking that there exists some claim that could be proved in neutral geometry (= Euclid's first four postulates only) but couldn't be proved in Euclidean geometry.
This may not be Quine's actual worry; his concern may stem from the fact that applied semantics (or whatever branch of language study) underdetermines pure semantics (or whatever). However, Carnap is perfectly happy to accept that claim: Creath says this is why Carnap's copy of Word and Object Ch.2 (Indeterminacy of Translation) has no marginalia. [But how does the geometry analogy fare here? Would Carnap admit that applied geometry underdetermines pure geometry? My guess is yes; and that that's not so bad...
Carnap and Quine agree that language can be studied at various levels of abstraction. Using Carnap's taxonomy, we start at the level of pragmatics, where we study how individual speakers use expressions under particular circumstances. This level contains the most detail: speakers, their circumstances, plus the meanings of the words for particular speakers under particular circumstances. At the next, more abstract level, we have semantics, which abstracts away from particular speakers and particular circumstances. And at the highest level, we have syntax, which abstracts away the meanings of words, leaving just the symbols, the way they are put together, and which strings follow from others.
In each transition from pragmatics to semantics to syntax, some information about language is omitted/ discarded. (Like the move from Euclidean geometry to neutral geometry, which drops the parallel postulate.) Now, we can conceive of Quine's indeterminacy of meaning thesis (the radical translation thought experiment) as critiquing Carnap in the following way: Carnap is importing or introducing new information at the semantic level, because the semantic facts Carnap includes in a semantically-characterized language [a "semantic system"] cannot be 'read off' even the information contained at the pragmatic level. The analogy in the geometry case shows why this is clearly an unacceptable maneuver. It would be: thinking that there exists some claim that could be proved in neutral geometry (= Euclid's first four postulates only) but couldn't be proved in Euclidean geometry.
This may not be Quine's actual worry; his concern may stem from the fact that applied semantics (or whatever branch of language study) underdetermines pure semantics (or whatever). However, Carnap is perfectly happy to accept that claim: Creath says this is why Carnap's copy of Word and Object Ch.2 (Indeterminacy of Translation) has no marginalia. [But how does the geometry analogy fare here? Would Carnap admit that applied geometry underdetermines pure geometry? My guess is yes; and that that's not so bad...
5/10/2007
Help me write a book
This post falls under the category of "shameless begging." I am in the later stages of writing a book (based on my dissertation) called Carnap, Quine, and Tarski's Year Together. The plan is to send the manuscript to the publisher in about two months, i.e. very early July. Between then and now, the only thing I'm working on is the book.
I need your help with this. I would greatly appreciate any feedback, large or small, on the manuscript. It definitely needs to be looked at by a fresh set of eyes (preferably attached to a clever mind, but I'll take what I can get). The manuscript can be downloaded, as a 1MB Word file, here.
Thanks in advance to anyone who lends a hand. In my limited experience, the greater the number of people who tear apart something I've written, the better the final product is.
I need your help with this. I would greatly appreciate any feedback, large or small, on the manuscript. It definitely needs to be looked at by a fresh set of eyes (preferably attached to a clever mind, but I'll take what I can get). The manuscript can be downloaded, as a 1MB Word file, here.
Thanks in advance to anyone who lends a hand. In my limited experience, the greater the number of people who tear apart something I've written, the better the final product is.
5/18/2006
Quine on logical truth, again
In a previous post, I asked about the relationship between Quine's definition of logical truth and the now-standard (model-theoretic) one. Here's the second installment, which I decided to finally post after sitting on it for a while, since Kenny just posted a nice set of thoughts on the very closely related topic of logical consequence.
The standard definition is:
(SLT) Sentence S is a logical truth of language L = S is true in all models of L.
Quine's definition is:
(QLT) S is a logical truth = "we get only truths when we substitute sentences for [the] simple [=atomic] sentences" of S (Philosophy of Logic, 50).
(Quine counts open formulas, e.g. 'x burns', as sentences; specifically, he calls them 'open sentences.' I'll follow his usage here.)
So what does Quine think is the relationship between the standard characterization of logical truth and his own? He argues fot the following equivalence claim:
(EQ) If “our object language is… rich enough for elementary number theory ,” then “[a]ny schema that comes out true under all substitutions of sentences, in such a language, will also be satisfied by all models, and conversely” (53).
In a nutshell, Quine argues for the 'only if' direction via the Löwenheim-Skolem theorem (hence the requirement of elementary number theory within the object language), and for the ‘if’ direction by appeal to the completeness of first-order logic. I'll spell out his reasoning in a bit more detail below, but I can sum up my worry about it here: in order to overcome Tarski’s objection to Quine’s substitutional version of logical truth, Quine appeals to the Löwenheim-Skolem theorem. However, for that appeal to work, Quine has to require the object language to be rich enough to fall afoul of the incompleteness results, thereby depriving him of one direction of the purported equivalence between the model-based and sentence-substitution-based notions of logical truth.
The 'only if' direction
Quine presents an extension of the Löwenheim-Skolem Theorem due to Hilbert and Bernays:
“If a [GFA: first-order] schema is satisfied by a model at all, it becomes true under some substitution of sentences of elementary number theory for its simple schemata” (54).
A little logic chopping will get us to
If all substitutions of sentences from elementary number theory make A true, then A is satisfied in all models.
-- which is what we wanted to show. (I think this argument is OK .)
The 'if' direction
Quine takes as his starting premise the completeness result for first-order logic:
(CT) “If a schema is satisfied by every model, it can be proved” (54).
(Quine then argues that if a schema can be proved within a given proof calculus whose inference rules are “visibly sound,” i.e., “visibly such as to generate only schemata that come out true under all substitutions” (54), then such a schema will of course ‘come out true under all substitutions of sentences,’ Q.E.D.) This theorem is of course true for first-order logic; however, Quine has imposed the demand that our object language contain the resources of elementary number theory (explicitly including both plus and times, so that Presburger arithmetic—which is complete—is not in play). And once our object language is that rich, then Gödel’s first incompleteness theorem comes into play. Specifically, in any consistent proof-calculus rich enough for elementary number theory, there will be sentences [and their associated schema] that are true, i.e., satisfied by every model, yet cannot be proved -- providing a counterexample to (CT). So the dialectic, as I see it, is as follows: to answer Tarski's objection to the substitutional version of logical truth, Quine requires the language to be rich enough to capture number theory. But once Quine has made that move, the crucial premise (viz., CT) for the other direction of his equivalence claim no longer holds.
I think I must be missing something -- first, Quine is orders of magnitude smarter than I am, and second, while Quine is fallible, this does not seem like the kind of mistake he's likely to make. So perhaps someone in the blogosphere can set me straight.
And I have one more complaint. Quine claims that his "definition of logical truth agrees with the alternative definition in terms of models, as long as the object language is not too weak for the modest idioms of elementary number theory. In the contrary case we can as well blame any discrepancies on the weakness of the language as on the definition of logical truth" (55). This defense strikes me as implausible: why would we only have (or demand) a well-defined notion of logical truth once we reach number theory? Don't we want a definition to cover all cases, including the simple ones? If the model-theoretic definition captures all the intuitive cases, and Quine's only when the language is sufficiently rich, isn't that a good argument against Quine's characterization of logical truth?
------
(And for those wondering what Quine thinks is the advantage of his characterization of logical truth over the model-theoretic one, the answer is: Quine's uses much less set theory. "The evident philosophical advantage of resting with this substitutional definition, and not broaching model theory, is that we save on ontology. Sentences suffice,… instead of a universe of sets specifiable and unspecifiable. … [W]e have progressed a step whenever we find a way of cutting the ontological costs of some particular development" (55). Quine recognizes that his characterization is not completely free of set theory, given the proof of the LS theorem, so he says his "retreat" from the model-based notion of logical truth "renders the notions of validity and logical truth independent of all but a modest bit of set theory; independent of the higher flights" (56).)
The standard definition is:
(SLT) Sentence S is a logical truth of language L = S is true in all models of L.
Quine's definition is:
(QLT) S is a logical truth = "we get only truths when we substitute sentences for [the] simple [=atomic] sentences" of S (Philosophy of Logic, 50).
(Quine counts open formulas, e.g. 'x burns', as sentences; specifically, he calls them 'open sentences.' I'll follow his usage here.)
So what does Quine think is the relationship between the standard characterization of logical truth and his own? He argues fot the following equivalence claim:
(EQ) If “our object language is… rich enough for elementary number theory ,” then “[a]ny schema that comes out true under all substitutions of sentences, in such a language, will also be satisfied by all models, and conversely” (53).
In a nutshell, Quine argues for the 'only if' direction via the Löwenheim-Skolem theorem (hence the requirement of elementary number theory within the object language), and for the ‘if’ direction by appeal to the completeness of first-order logic. I'll spell out his reasoning in a bit more detail below, but I can sum up my worry about it here: in order to overcome Tarski’s objection to Quine’s substitutional version of logical truth, Quine appeals to the Löwenheim-Skolem theorem. However, for that appeal to work, Quine has to require the object language to be rich enough to fall afoul of the incompleteness results, thereby depriving him of one direction of the purported equivalence between the model-based and sentence-substitution-based notions of logical truth.
The 'only if' direction
Quine presents an extension of the Löwenheim-Skolem Theorem due to Hilbert and Bernays:
“If a [GFA: first-order] schema is satisfied by a model at all, it becomes true under some substitution of sentences of elementary number theory for its simple schemata” (54).
A little logic chopping will get us to
If all substitutions of sentences from elementary number theory make A true, then A is satisfied in all models.
-- which is what we wanted to show. (I think this argument is OK .)
The 'if' direction
Quine takes as his starting premise the completeness result for first-order logic:
(CT) “If a schema is satisfied by every model, it can be proved” (54).
(Quine then argues that if a schema can be proved within a given proof calculus whose inference rules are “visibly sound,” i.e., “visibly such as to generate only schemata that come out true under all substitutions” (54), then such a schema will of course ‘come out true under all substitutions of sentences,’ Q.E.D.) This theorem is of course true for first-order logic; however, Quine has imposed the demand that our object language contain the resources of elementary number theory (explicitly including both plus and times, so that Presburger arithmetic—which is complete—is not in play). And once our object language is that rich, then Gödel’s first incompleteness theorem comes into play. Specifically, in any consistent proof-calculus rich enough for elementary number theory, there will be sentences [and their associated schema] that are true, i.e., satisfied by every model, yet cannot be proved -- providing a counterexample to (CT). So the dialectic, as I see it, is as follows: to answer Tarski's objection to the substitutional version of logical truth, Quine requires the language to be rich enough to capture number theory. But once Quine has made that move, the crucial premise (viz., CT) for the other direction of his equivalence claim no longer holds.
I think I must be missing something -- first, Quine is orders of magnitude smarter than I am, and second, while Quine is fallible, this does not seem like the kind of mistake he's likely to make. So perhaps someone in the blogosphere can set me straight.
And I have one more complaint. Quine claims that his "definition of logical truth agrees with the alternative definition in terms of models, as long as the object language is not too weak for the modest idioms of elementary number theory. In the contrary case we can as well blame any discrepancies on the weakness of the language as on the definition of logical truth" (55). This defense strikes me as implausible: why would we only have (or demand) a well-defined notion of logical truth once we reach number theory? Don't we want a definition to cover all cases, including the simple ones? If the model-theoretic definition captures all the intuitive cases, and Quine's only when the language is sufficiently rich, isn't that a good argument against Quine's characterization of logical truth?
------
(And for those wondering what Quine thinks is the advantage of his characterization of logical truth over the model-theoretic one, the answer is: Quine's uses much less set theory. "The evident philosophical advantage of resting with this substitutional definition, and not broaching model theory, is that we save on ontology. Sentences suffice,… instead of a universe of sets specifiable and unspecifiable. … [W]e have progressed a step whenever we find a way of cutting the ontological costs of some particular development" (55). Quine recognizes that his characterization is not completely free of set theory, given the proof of the LS theorem, so he says his "retreat" from the model-based notion of logical truth "renders the notions of validity and logical truth independent of all but a modest bit of set theory; independent of the higher flights" (56).)
4/03/2006
Tarski, Quine, and logical truth
The following must have been addressed already in the literature, but I'm going to mention it anyway--perhaps a better-informed reader can point me in the direction of the relevant research. W.V.O. Quine offers the following characterization of logical truth:
Now some historical questions: did Quine think his condition was sufficient, or just necessary? (I quickly checked "Truth by Convention," and I didn't find any conclusive evidence that he considered it sufficient.) If Quine does consider this a proper definition of logical truth, how does he/ would he answer Tarski's objection? -- and/or why doesn't Quine simply adopt Tarski's definition of logical truth, viz. 'truth in all models'?
(You might think Tarski's objection shouldn't count for much, since I used a very contrived language to make the point against Quine. In Tarski's defense, however, (a) assuming that every object has a name in our language also seems somewhat artificial, and (b) Tarski proved (elsewhere) that a single language cannot contain names for all (sets of) real numbers (See "On Definable Sets of Real Numbers," reprinted in Logic, Semantics, Metamathematics).)
The logical truths are those true sentences which involve only logical words essentially. What this means is that any other words, though they may also occur in a logical truth (as witness 'Brutus,' 'kill,' and 'Caesar' in 'Brutus killed or did not kill Caesar'), can be varied at will without engendering falsity. ("Carnap and Logical Truth," §2)All I wanted to mention here is that Alfred Tarski had already shown, in 1936's "On the Concept of Logical Consequence," that Quine's characterization is a necessary condition for a sentence to be a logical truth, but not a sufficient one. For example, if one is using an impoverished language that (i) only has proper names for things over five feet tall, and (ii) only has predicates applying only to things over five feet tall, then the sentence 'George W. Bush is over five feet tall' will be a logical truth -- because no matter what name from this impoverished language we substitute for 'George W. Bush' or what predicate we substitute for 'over 5 feet tall' in this sentence, the resulting sentence will be true.
Now some historical questions: did Quine think his condition was sufficient, or just necessary? (I quickly checked "Truth by Convention," and I didn't find any conclusive evidence that he considered it sufficient.) If Quine does consider this a proper definition of logical truth, how does he/ would he answer Tarski's objection? -- and/or why doesn't Quine simply adopt Tarski's definition of logical truth, viz. 'truth in all models'?
(You might think Tarski's objection shouldn't count for much, since I used a very contrived language to make the point against Quine. In Tarski's defense, however, (a) assuming that every object has a name in our language also seems somewhat artificial, and (b) Tarski proved (elsewhere) that a single language cannot contain names for all (sets of) real numbers (See "On Definable Sets of Real Numbers," reprinted in Logic, Semantics, Metamathematics).)
7/29/2005
Is 'p is a priori' itself a priori?
My most recent posts have been far too long by blogging standards, so I am determined here to be brief. Most philosophers (though not all, e.g., anyone who holds the Quine-Putnam indispensibility thesis) believe the following sentences are true:
(1) "'2+3=5' is true a priori"
(2) "'The earth is round' is true a posteriori"
The question is: are (1) and (2) true a priori or a posteriori? Put metaphorically, does experience teach us that logical theorems are known independently of experience? I am not sure there are any non-question-begging arguments to be given one way or the other; if there is one, I would love to hear it.
That's all I wanted to say. If you are curious about what motivated me to think about this question, keep reading. There are two motivating sources:
First, my dissertation, which deals with the academic year Carnap, Tarski, and Quine spent together at Harvard in 1940-41. In a private conversation Carnap had with Quine, one way they formulate the difference between themselves is as follows.
Carnap: 'p is analytic in language L' is itself an analytic statement.
Quine: 'p is analytic in L' is a synthetic statement, to be settled by a behavioristic investigation into the linguistic habits of L-speakers.
Granted, 'analytic' is not identical to 'a priori' -- but for Carnap, they were extensionally equivalent, and the question above is very close to this issue.
Second, for the last 10 years, van Fraassen has been suggesting that we think of empiricism not as a theory or assertion but as a stance. (See "Against Naturalized Epistemology" (1995) in On Quine and 2002's The Empirical Stance.) The primary argument he offers is that empiricism, if conceived as an assertion, is self-defeating: "All knowledge about the world is a posteriori" (or any other slogan intended to capture the empiricist's thesis) will be difficult to construe as having experience as its source. And, van Fraassen says, if the empiricist thesis cannot be justified on the basis of experience alone, then it fails to live up to its own standards, and is therefore self-defeating. But van Fraassen is assuming that "such-and-such is a posteriori" must itself be an a posteriori claim. And that is taking for granted an answer to my question above.
(1) "'2+3=5' is true a priori"
(2) "'The earth is round' is true a posteriori"
The question is: are (1) and (2) true a priori or a posteriori? Put metaphorically, does experience teach us that logical theorems are known independently of experience? I am not sure there are any non-question-begging arguments to be given one way or the other; if there is one, I would love to hear it.
That's all I wanted to say. If you are curious about what motivated me to think about this question, keep reading. There are two motivating sources:
First, my dissertation, which deals with the academic year Carnap, Tarski, and Quine spent together at Harvard in 1940-41. In a private conversation Carnap had with Quine, one way they formulate the difference between themselves is as follows.
Carnap: 'p is analytic in language L' is itself an analytic statement.
Quine: 'p is analytic in L' is a synthetic statement, to be settled by a behavioristic investigation into the linguistic habits of L-speakers.
Granted, 'analytic' is not identical to 'a priori' -- but for Carnap, they were extensionally equivalent, and the question above is very close to this issue.
Second, for the last 10 years, van Fraassen has been suggesting that we think of empiricism not as a theory or assertion but as a stance. (See "Against Naturalized Epistemology" (1995) in On Quine and 2002's The Empirical Stance.) The primary argument he offers is that empiricism, if conceived as an assertion, is self-defeating: "All knowledge about the world is a posteriori" (or any other slogan intended to capture the empiricist's thesis) will be difficult to construe as having experience as its source. And, van Fraassen says, if the empiricist thesis cannot be justified on the basis of experience alone, then it fails to live up to its own standards, and is therefore self-defeating. But van Fraassen is assuming that "such-and-such is a posteriori" must itself be an a posteriori claim. And that is taking for granted an answer to my question above.
7/13/2005
This week's complaint about "Two Dogmas"
I am willing to admit that Quine's "Two Dogmas of Empiricism" has many virtues, and if I ever write anything one-tenth as intelligent or one-hundredth as widely read, I will count my philosophical career an unequivocal success. However, I find it a very frustrating piece when it is considered as a critique of Carnap's views on language circa 1950. A number of people who have considered "Two Dogmas" in this light have also felt that it does not directly rebut Carnap's views, but instead offers (to put it in Kuhnian terms) a different paradigm for understanding language (recently, see P. O'Grady's 1999 article in PPR). Interestingly, the first person to suggest this interpretation of "Two Dogmas" was apparently Carnap himself (see Howard Stein's "Was Carnap Entirely Wrong, After All?", Synthese 1992). This post is about my most recent round of frustrations in attempting to read "Two Dogmas" as a straightforward argument against Carnap.
My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives
Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.
Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.
My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
Once we seek to explain 'S-is-analytic-for-L' for variable 'L'..., the explanation 'true according to the semantical rules for L' is unavailing; for the relative term 'semantical rule of' is as much in need of clarification, at least, as 'analytic for.' (34)So Quine is telling us that there is no decent explanation or clarification of the term 'semantical rule of,' if we generalize away from particular languages.
It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
a semantical system [is] ... a system of rules, formulated in a metalanguage and referring to an object language, of such a kind that the rules determine a truth-condition for every sentence of the object language, i.e., a sufficient and necessary condition for its truth. In this way the sentences [of the object language -GFA] are interpreted, i.e., made understandable. (22)What are some of Carnap's examples of semantic rules? (Where English is both the object and metalanguage):
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives
Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.
Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.
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