Journal ArticleDOI
A platonist epistemology
TLDR
It is shown that spatio-temporal creatures like ourselves can attain knowledge about mathematical objects by simply explaining how they can do this and to accept Benacerraf's challenge and meet it head on by constructing an epistemology of abstract mathematical objects.Abstract:
A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist.read more
Citations
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Journal ArticleDOI
The intellectual given
TL;DR: In this article, the notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states.
Book ChapterDOI
What Is the Benacerraf Problem
TL;DR: In this article, Benacerraf presented an epistemological problem for mathematical realism, which was later used in the first edition of "Mathematical truth" and "mathematical realism".
Journal ArticleDOI
Fictionalism, Theft, and the Story of Mathematics
TL;DR: This paper developed a mathematical fictionalism and defended it against three objections or worries, viz., (i) an objection based on the fact that there are obvious disanalogies between mathematics and fiction; (ii) a worry about whether fictionalism is consistent with whether certain mathematical sentences are objectively correct whereas others are incorrect; and (iii) a recent objection due to John Burgess concerning “hermeneuticism and “revolutionism”.
Journal Article
Debunking Perceptual Beliefs about Ordinary Objects
TL;DR: Korman as mentioned in this paper showed that there is a range of beliefs that are invulnerable to debunking arguments, namely, our perceptual beliefs about which macroscopic physical objects there are, right before our eyes.
References
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Book
On the Plurality of Worlds
TL;DR: In this article, the Thesis of Pluraliry of Worlds is used to describe a Philosopher's Paradise, and the Ersatzist Program is used as an alternative.
Journal ArticleDOI
On the Plurality of Worlds
James E. Tomberlin,David Lewis +1 more
TL;DR: On the Plurality of Worlds as discussed by the authors is one of the most influential philosophers of our age, and it is the magnum opus of On the Plurality of Worlds.
Journal ArticleDOI
What is mathematical truth
TL;DR: In this paper, the authors argue that mathematics should be interpreted realistically, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as "set" and "function".
Book ChapterDOI
What is Cantor's continuum problem?
TL;DR: In this paper, what is the continuoustime problem of the Cantor's Continuum Problem and how to solve it is discussed. But it is not a continuous problem, it is continuous.
Book
Realism, Mathematics, and Modality
TL;DR: In this paper, the context principle of Frege's context principle can we dispense with space-time? realism, mathematics and modality, and anti-realism about mathematics is mathematical knowledge just logical knowledge? on conservativeness and incompleteness Platonism for cheap?