Citations of:
The Existence (and Nonexistence) of Abstract Objects
In Frege's Theorem. Oxford University Press (2011)
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ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by (...) 



Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most finegrained abstraction principle that is invariant in each sense. Hume’s Principle is the most finegrained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...) 

Guillermo E. Rosado Haddock, ed. Husserl and Analytic Philosophy. Berlin/Boston: Walter de Gruyter GmbH, 2016. ISBN 9783110496550 ; 9783110497373 ; 9783110494181. Pp. viii + 338. 

There are multiple formal characterizations of the natural numbers available. Despite being interderivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Some influential philosophers of mathematics have argued for a nonegalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. This paper addresses two related issues. First, we review some of (...) 