(1) the “analytic” versus “synthetic” distinctionWith regard to analyticity, it is also possible to distinguish three types of analytic sentence, as follows:
This is a distinction involving the semantic form of propositions. A sentence is analytic if and only if it is true solely by virtue of the meanings of terms used (Elugardo 1997: 13). Every sentence that is not analytic is synthetic;
(2) the notion of “necessity” versus “contingency”
This relates to the nature of truth and can be understood in (i) a metaphysical/ontological sense or (ii) a conceptual/verbal sense (or de dicto). A logically necessary truth in sense (ii) is not metaphysically necessary, but true only by virtue of the definitions of terms used;
(3) the a priori versus a posteriori distinction
This involves how a proposition is epistemologically known to be true or false. An a priori truth is known without appeal to experience, and an a posteriori truth is known by appeal to experience or empirical evidence.
(1) an explicit analyticity, such as “Bachelors are bachelors.” These can also be called “identity propositions” or “truths of logic”;Types (1) and (2) describe what is called “Frege analyticity” (Boghossian 1997) in the following senses:
(2) an implicit analyticity, where the sentence is true by definition, e.g., “Bachelors are male.” Here we have a predicative proposition in which the predicate asserts something of a subject already containing that idea implicitly; and
(3) another type of analyticity where propositions are true in virtue of the meanings of the words used, but not true by definition: “Nothing is both red and green all over” or “whatever is coloured is extended.”
“A sentence is analytic if and only if either (i) it is a logical truth, or (ii) it can be converted into a logical truth by substitution of synonymous expressions, salve veritate, and formally valid inferences.” (Elugardo 1997: 15).All “Frege analytic” truths are known a priori.
But type (3) above describes a kind of analyticity that is wider in sense than (1) or (2), and the epistemological status of (3) was once held to be synthetic a priori (Elugardo 1997: 15). Today many would say it is analytic a priori, but a type that Boghossian (2008: 203) calls “Carnap analyticity” (after the logical positivist Rudolf Carnap).
In 1951, Quine (1951) attacked the analytic–synthetic distinction. Elugardo (1997: 15) argues that Quine admitted the existence of “Frege analytic” truths in sense (1), but thought that even these logical truths are open to revision. But Quine also argued that Frege analyticity in sense (2) is untenable. Quine’s rejection of this type of analytic statement is derived from his unwillingness to accept any definition of “synonymy” that is circular (in that it relies in turn on the concept of “analyticity” for its definition), and because of his verbal behaviourism.
But Quine’s attack on Frege analyticity is controversial. Many modern analytic philosophers think Quine did not succeed in his arguments, and that analyticity does indeed exist (Grice and Strawson 1956; Putnam 1962 and 1975; Quinton 1967; Glock 1996 and 2003; Nimtz 2003). Nor it is surprising that modern Rationalists support the existence of Frege analyticity (Katz 1967; Chomsky 1988).
Quine also argued against the logical positivist view that verification of a single synthetic proposition is possible by empirical evidence and without the need for verifying other sentences. For Quine, every synthetic proposition relies on and presupposes a number of other sentences, a view which lead to Quine’s confirmation holism and the Quine-Duhem thesis.
Thus knowledge is an interconnected “web of belief,” and those beliefs at the core are only the most difficult to give up, while those at the periphery are easy to give up. Nevertheless, all beliefs are capable in principle of being given up and none immune to revision (Elugardo 1997: 14). Philosophers have continued to debate this view too.
Such were the main controversies in analytic philosophy on epistemology until the 1970s. Until the 1970s, most analytic philosophers thought that all necessary truths are a priori and all contingent truths are a posteriori. Then Saul Kripke argued that the three concepts above are distinct, and that there are actually “necessary a posteriori” truths, such as, for example, the statement that “water is truly H2O.”
Kripke introduced a revolution in analytic metaphysics and epistemology, and he also argued that scientifically true identities are necessary a posteriori truths (Elugardo 1997: 12).
Kripke also contended that there is such a thing as “contingent a priori” truth, but the existence of this type of truth is still disputed.
“The Return of Metaphysics into Analytic Philosophy,” August 29, 2013.
“Epistemology and Kinds of Knowledge,” July 25, 2013.
“Schwartz’s A Brief History of Analytic Philosophy: from Russell to Rawls: Chapter 3,” August 25, 2013.
“Quine and the Analytic–Synthetic Distinction,” August 24, 2013.
“Schwartz’s A Brief History of Analytic Philosophy: from Russell to Rawls: Chapter 2,” August 23, 2013.
“Schwartz’s A Brief History of Analytic Philosophy: From Russell to Rawls: Chapter 1,” August 22, 2013.
Boghossian, Paul. 1996. “Analyticity Reconsidered,” Nous 30: 360–391.
Boghossian, Paul. 1997. “Analyticity,” in B. Hale and C. Wright (eds.), A Companion to the Philosophy of Language. Basil Blackwell, Oxford. 331–368.
Boghossian, Paul. 2008. “Analyticity Reconsidered,” in Paul A. Boghossian, Content and Justification: Philosophical Papers. Clarendon Press, Oxford. 195–224.
Chomsky, Noam. 1988. Language and Problems of Knowledge: The Managua Lectures. MIT Press, Cambridge, Mass. and London.
Elugardo, R. 1997. “Analytic/Synthetic, Necessary/Contingent, and a priori/a posteriori: Distinction,” in Peter V. Lamarque (ed.), Concise Encyclopedia of Philosophy of Language. Pergamon, New York. 10–19.
Frege, Gottlob. 1986. The Foundations of Arithmetic (2nd rev. edn.). Basil Blackwell, Oxford.
Glock, Hans-Johann. 1996. “Necessity and Normativity,” in Hans Sluga and David G. Stern (eds.). The Cambridge Companion to Wittgenstein. Cambridge University Press, Cambridge and New York. 198–225.
Glock, Hans-Johann. 2003. Quine and Davidson on Language, Thought and Reality. Cambridge University Press, Cambridge.
Grice, H. P. and P. F. Strawson. 1956. “In Defence of a Dogma,” Philosophical Review 65: 141–158.
Horwich, Paul. 1992. “Chomsky versus Quine on the Analytic-Synthetic Distinction,” Proceedings of the Aristotelian Society n.s. 92: 95–108.
Katz, Jerrold J. 1967. “Some Remarks on Quine on Analyticity,” Journal of Philosophy 64: 36–52.
Katz, Jerrold J. 2010. “Analyticity,” in Jonathan Dancy, Ernest Sosa and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Blackwell, Malden, MA and Oxford. 224–230.
Nimtz, C. 2003. “Analytic Truths – Still Harmless After All These Years?,” in H. J. Glock, K. Gluer, and G. Keil (eds.), Fifty Years of Quine’s ‘Two Dogmas’. Rodopi, Amsterdam and New York. 91–118.
Pap, Arthur. 1958. Semantics and Necessary Truth: An Inquiry into the Foundations of Analytic Philosophy. Yale University Press, New Haven.
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Quinton, Anthony. 1963–1964. “The ‘a priori’ and the Analytic,” Proceedings of the Aristotelian Society n.s. 64: 31–54.
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I guess part of the concern is that a lot of these lines are blurred. Putnam seemed to characterize it as the difference between a "dichotomy" and a "distinction". Quine's critique of analytic/synthetic (along with Putnam's critique of fact/value) showed it wasn't a dichotomy but there still may be subtle differences. (I think Putnam said he got Quine to concede this.)ReplyDelete
The issue is more confusing with things like mathematics. With the failure of logicism, where does mathematics fit? It's not exactly analytic.
It's certainly not in sense (1).
Arguing for it in sense (2) would be difficult but perhaps possible.
Regarding sense (3), I never know what to make of those statements. Regarding the examples, I share Mike Huben's sentiment from this post. Do we mean "color" as a psychological phenomenon or as a metaphysical? If the former, then would it be extended? If the latter, then coming up with how to to even define color is pretty vague. I mean, if I shine a "red" light (what's a "red" light?) on a "white" object (what's a "white" object?) is it "white" or "red"?
The other issue is that even mathematics (or at least parts of it) have been regarded as, at least, quasi-empirical inquiries. Even Godel suggested this with regard to the continuum hypothesis, a view Martin Davis has dubbed "Empirical Platonism".
I almost get the impression we have a tool set, a proverbial hammer so to speak, but we're not working with nails. Perhaps we need different tools.
"The issue is more confusing with things like mathematics. With the failure of logicism, where does mathematics fit?"ReplyDelete
But in what sense did logicism fail?
According to Stephen P. Schwartz ( A Brief History of Analytic Philosophy: From Russell to Rawls. Wiley-Blackwell, Chichester, UK, 2012. p. 19), the consensus today is still that most of classical mathematics can be derived from pure logic and set theory. To that extent, it would appear to be analytic a priori in sense (3) above.
When applied to the world, applied mathematics would appear to be synthetic a posteriori -- just like geometry we must distinguish pure mathematics from applied mathematics.
Godel's 2nd incompleteness implies you can't prove the system is consistent. If you can prove the system is consistent then I'm not sure how you can claim it's analytic. [OK, technically you can prove it's consistent via transfinite induction but I believe that raises just as many questions as it answers.]Delete
But here's a question for you. What do you count as a definition? Because, I'm willing to call a lot of things definitions but I have hard time believing that certain axioms are definitions.
For example, would you consider each axiom of ZF (Or ZFC) to be a definition? IMO, most of them aren't merely definition but also posit the existence of said entities defined. For a non Platonic interpretation, it's as if it's constructing the existence of sets.
So I would be willing to agree with the statement that "most of classical mathematics" can be derived from set theory but I'm not convinced that set theory is analytic. In some cases you can even deny some of the axioms and get a different consistent theory. (Axiom of choice is independent IIRC; I wouldn't be surprised if others were as well).
And last point, since you brought up sense (3) here, can you give me a statement that is true and is analytic in sense (3)?
I have reservations about the examples you used. For example, what does it mean to say that an object "is red"? To be clear, I'm asking how you would formalize a proof of that statement from a set of definitions. I'm not saying it can't be done I'm not sure that it can either. You're welcome to give another example of course.
For example, I would claim it's not possible to derive what physics textbooks typically claim is Netwon's 2nd Law (F=ma) from what Newton actually said the 2nd Law to be (F=dp/dt) by mere definitions alone. You would need to assume something else (like Newton's first law) to derive the result and I'm not seeing how the additional assumption could be satisfied that would make it a definition. (If you're wondering what, when you apply the product rule, you get a term with dm/dt so you have to assume that it's 0 or assume something that would imply that it's 0.)
Allow me to take a step back for a moment because I think I should have clarified a bit (or you can clarify a bit).Delete
If I understand you, you're claiming that a type (3) analytic statement is, say, a theorem from an argument with premises which are, themselves, analytic. Is this correct?
So ultimately a type (3) analytic statement should purely follow from classical logic + definitions and nothing more.
Part of what I think is that formal systems aren't purely logical (what's logic?) nor purely definitional. They postulate things. In geometry we postulate lines and circles (well, Euclid told us we can draw them, language which is quite distinct from Hilbert's more Platonic language). In set theory we postulate sets.
I'm suggesting that I have no logical obligation to postulate these. In fact, I can postulate other statements which are contrary to these and make alternative perfectly consistent formal system.
On what grounds ought we privilege one such system over the other?
Without offering an answer to that, I will say that they aren't purely logical grounds. And as such I have to conclude such systems are not analytic. Perhaps they are "a priori" (if we take, say Phillip Pinkerton's suggestion that the statements follow from the definitions and rules of the game.).