Munich Center for Mathematical Philosophy (MCMP)

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Talk (Work in Progress): Eckehart Köhler (MCMP/Institute Vienna Circle)

Location: Ludwigstr. 31, ground floor, Room 021.

27.06.2019 12:00  – 14:00 


How Much Realism is Possible for Carnap's Conventionalism?


The most prominent aspect of Carnap's Conventionalism is his notorious Principle of Tolerance (very likely influenced by the éminence grise of the Vienna Circle, Friedrich Nietzsche). Consequently Conventionalism was immediately classified as anti-Realist, seemingly a recipe for Anarchism in Logic and Mathematics. But wait! Carnap did require consistency, after all. In fact, he went farther and added "pragmatic criteria" as well to guide the selection of acceptable conventions. In Bryan Norton's all too little-noticed monograph on Carnap's "Metaphilosophy", it turns out that just the pragmatic criteria give us a handle to specify ontologies in a way Bryan claims is not available to Quine. (Norton claims Quine has no adequate criterion for ontological commitment, and Carnap does.) I claim that Carnap's Conventionalism therefore turns out to be equivalent to something like Penelope Maddy's "mathematical practice"; and Practice, for Maddy, was her main standard for Realism in Mathematics!

I discovered that Conventions actually imply (Paul Samuelson: "reveal") intuitions, just what both Gödel explicitly and Carnap implicitly denied. According to my explication of intuitions, based on a phrase Carnap himself used in 1965 when "outing" himself in supporting intuitions as evidence for logic. (Carnap: "intuitions discriminate between valid and invalid" principles and rules.) Intuitions are thereby (just) value judgments. [Furthermore, they are nothing other than what Herbert Simon (Carnap's student) called "heuristics" — following George Pólya. This is what both Quine and Gödel, the earlier Carnap, and even Harsanyi missed!! Following Hume, we know that value judgments are dimensionally separated from factual observations; so there we have the desired analytic/synthetic dichotomy.

Looking more closely at some positions Carnap took on Realism, of course we find anti-Realist statements (my favorite being in a letter to Thomas Kuhn praising him for The Structure of Scientific Revolutions); on the other hand we find even more famous and stronger statements favoring Realism, in particular Carnap's life-long upholding of the Analytic/Synthetic Dichotomy. I claim that Carnap nolens volens was thereby a "closet Platonist" all along. The surprising thing is that Gödel very discreetly failed to point this out when refereeing The Logical Syntax of Language. Gödel's influence was already considerable, for his Gödelization method not only provided the logical "infrastructure" for Logical Syntax, he also instigated the Tolerance Principle itself.