Galileo:Scholastic natural philosophers :: Carnap:Quine

I'm pretty sure the following has been said before, but I don't know where: Frege (and Russell, et alii) did for the study of language what Galileo (et alii) did for the study of material nature. Galileo 'mathematized' new portions of the physical world -- previous students of nature thought that (most of) nature was too messy, imprecise, or chancey to be susceptible mathematical treatment: how could the unchanging, eternal realm of mathematics model the changing and temporal material world? Analogously, Frege and other founders of modern logic turned language into a mathematical object, by treating (e.g.) subject-predicate assertions in terms of functions and their arguments.

I bring this up because I've been looking at one of Quine's arguments against Carnapian analyticity in the 1940s. This argument appears in the long 1943 letter from Quine to Carnap in Creath's Dear Carnap, Dear Van, and in print in a 1947 article in the Journal of Symbolic Logic ("The Problem of Interpreting Modal Logic"):
The class of analytic statements is broader than that of logical truths, for it contains in addition such statements as 'No bachelor is married.' This example might be assimilated to the logical truths by considering it a definitional abbreviation of 'No unmarried man is unmarried,' which is indeed a logical truth; but I should prefer not to rest analyticity thus on an unrealistic fiction of there being standard definitions of extra-logical expressions in terms of a standard set of extra-logical primitives. What is rather in point, I think, is a relation of synonymy, or sameness of meaning, which holds between expressions of real language, though there be no standard hierarchy of definitions. (p.44, italics Quine's, boldface mine)
Quine puts the point somewhat differently in different places, but the basic idea is always that the 'rational reconstruction' of language, however it is carried out, is an 'unrealistic fiction.'

Now, I can ask the question: is Quine's charge that a 'hierarchy of definitions' is an 'unrealistic fiction' any different from Galileo's scholastic critics' charge that Galileo is somehow 'falsifying' nature by rendering it thoroughly mathematically? The answer to this question will turn on what Good Things the Galilean mathematizing strategy is able to achieve (explanatory power, new predictions, etc.), and whether these Good Things (or analogues of them) also appear in the case of a Carnapian language. It would also be useful to know of other scientific cases where the analogue of the Scholastic triumphed over the analogue of Galileo, i.e., someone tries to mathematize certain phenomena, but this mathematization is rejected for good reasons by workers in the field.


Kenny said...

It seems to me that while Galileo and Frege showed that mathematical descriptions of some part of reality are possible, they didn't show that mathematical definitions are. As far as I can tell, no one wants to treat "water is H2O" as an analytic statement, while we do want to treat "bachelors are unmarried males" as analytic. Both of these can be seen as analyses of some natural language concept, which can be described in some formal and rigorous terms. However, Carnap needs there to be a special role for the latter type of analysis. It seems to me that it would be analogous to Newton saying "force just is acceleration" rather than saying that they are correlated or proportional. When I was reading "Truth by Convention" a few weeks ago, I was struck by how Quine then seemed to also endorse the idea of letting analyses of a term serve as definitions of them, though he didn't bring up the "water is H2O" case.

Anonymous said...

I think that Russell makes the explicit comparison between Galileo's new method in physics and the "logical atomist" new method in philosophy, in "Our Knowledge of the External World".