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Albert A Mullin - One of the best experts on this subject based on the ideXlab platform.

Paul Hoffman - One of the best experts on this subject based on the ideXlab platform.

Robert Hanna - One of the best experts on this subject based on the ideXlab platform.

  • Mathematical Truth regained
    2010
    Co-Authors: Robert Hanna
    Abstract:

    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 this paper I spell out a new solution to BD. I call 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 I offer is based on Kant’s philosophy of arithmetic, as interpreted by Charles Parsons and by me. (3) The reasonable epistemology of Mathematical knowledge that I offer 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.

Melvyn B. Nathanson - One of the best experts on this subject based on the ideXlab platform.

Mark Balaguer - One of the best experts on this subject based on the ideXlab platform.

  • a theory of Mathematical correctness and Mathematical Truth
    Pacific Philosophical Quarterly, 2001
    Co-Authors: Mark Balaguer
    Abstract:

    A theory of objective Mathematical correctness is developed. The theory is consistent with both Mathematical realism and Mathematical anti-realism, and versions of realism and anti-realism are developed that dovetail with the theory of correctness. It is argued that these are the best versions of realism and anti-realism and that the theory of correctness behind them is true. Along the way, it is shown that, contrary to the traditional wisdom, the question of whether undecidable sentences like the continuum hypothesis have objectively determinate Truth values is independent of the question of whether Mathematical realism is true.