(Zwarenstein, 2024)
Benacerraf’s Dilemma (BD), as formulated by Paul Benacerraf in “Mathematical Truth,” is about the apparent impossibility of reconciling a “standard” (i.e., classical Platonic) semantics of mathematics with a “reasonable” (i.e., causal, spatiotemporal) epistemology of cognizing true statements. In “Mathematical Truth Regained” Robert Hanna offers a new solution to BD. He calls this new solution “a positive Kantian phenomenological solution” for three reasons: (1) It accepts Benacerraf’s preliminary philosophical assumptions about the nature of semantics and knowledge, as well as all the basic steps of BD, and then shows how we can, consistently with those very assumptions and premises, still reject the skeptical conclusion of BD and also adequately explain mathematical knowledge. (2) The standard semantics of mathematically necessary truth that Hanna offers is based on Kant’s philosophy of arithmetic, as interpreted by Charles Parsons and by Hanna. (3) The reasonable epistemology of mathematical knowledge that Hanna offers is based on the phenomenology of logical and mathematical self-evidence developed by early Husserl in Logical Investigations and by early Wittgenstein in Tractatus Logico-Philosophicus.
REFERENCE
(Zwarenstein, 2024). Zwarenstein, C. “Numbers Game: Is Math the Language of Nature or Just a Human Construct?” Salon. 27 July. Available online at URL = <https://www.salon.com/2024/07/27/numbers-game-is-math-the-language-of-nature-or-just-a-human-construct/>.
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