Philosophia Mathematica (III) 15 (2007), 357–365. doi:10.1093/philmat/nkm027 Advance Access publication June 23, 2007 Full-Blooded Reference † Gabriel Rabin ∗ In ‘Just what is full-blooded platonism?’ Greg Restall outlines several objections to Mark Balaguer’s theory of full-blooded platonism. I reply to these objections by explicating the semantic framework for the reference of mathematical terms that full-blooded platonism requires. Expanding upon these replies, I then explain how the full-blooded platonist, in light of the explicated semantic framework, should treat mathematical terms and statements in order to avoid certain pitfalls. 1. Objection Mark Balaguer’s Platonism and Anti-Platonism in Mathematics presents a realist view about mathematical objects called ‘full-blooded platonism’ (hence: FBP). Balaguer’s thesis is simple: any consistent mathematical theory truly describes some part of the mathematical realm. We can also express this thesis by the catchier slogan ‘any mathematical object that could exist does’. For the most part, Balaguer refrains from presenting a full formalization of FBP, although he does present a few formulas designed to characterize his view. Greg Restall, in his paper ‘Just what is full-blooded platonism?’, presents several objections to Balaguer’s attempt at formalization, claiming that Balaguer’s formulas, and possible revisions thereof, are either too weak or too strong. My goals in this paper are two-fold. First, I wish to reply to one of Restall’s objections. In order to do so I must explain a semantic framework for dealing with referential phenomena to which the full- blooded platonist is committed. My second goal will be to explain this framework and discuss the wider implications of the referential phenomena the framework is designed to handle. I will argue that Restall’s first objection is mistaken because he fails to account for an important fact about the interaction between FBP and the reference of mathematical terms. I will deal directly with only one † I want to thank Mark Balaguer, Phillip Bricker, and Greg Restall for helpful comments on earlier drafts of this paper. ∗ Department of Philosophy, 405 Hilgard Avenue, University of California Los Angeles, Los Angeles, California 90095-1451, U.S.A. grabin@humnet.ucla.edu Philosophia Mathematica (III) Vol. 15 No. 3  The Author [2007]. Published by Oxford University Press. All rights reserved. For Permission, please e-mail: journals.permissions@oxfordjournals.org at University of California, Los Angeles on October 25, 2010 philmat.oxfordjournals.org Downloaded from