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Frege’s Theorem: AN INTRODUCTION

Manuscrito 26 (2):471-503 (2003)

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  1. Empiricism, Probability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Journal of Applied Logic 12 (3):319–348.
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...)
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  • Induction and comparison.Paul Pietrowski - 2007 - University of Maryland Working Papers in Linguistics 15:154-188.
    Frege proved an important result, concerning the relation of arithmetic to second-order logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘Carl is taller than Al’ in terms of abstracta like heights and numbers. Abstract paraphrase can be useful—as when we say that Carl’s height exceeds Al’s—without reflecting semantic structure. Related points apply to causal relations, and even (...)
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  • What is a second order theory committed to?Charles Sayward - 1983 - Erkenntnis 20 (1):79 - 91.
    The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.
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