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Intuiting the infinite

Philosophical Studies 171 (2):327-349 (2014)

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  1. Epistemically Transformative Experience.Jane Friedman - manuscript
    A discussion of L.A. Paul's 'Transformative Experience' from an Author Meets Critics session at the 2015 Pacific APA.
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  • Philosophy of Mathematics for the Masses : Extending the scope of the philosophy of mathematics.Stefan Buijsman - 2016 - Dissertation, Stockholm University
    One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...)
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  • Do Ante Rem Mathematical Structures Instantiate Themselves?Scott Normand - 2019 - Australasian Journal of Philosophy 97 (1):167-177.
    ABSTRACTAnte rem structuralists claim that mathematical objects are places in ante rem structural universals. They also hold that the places in these structural universals instantiate themselves. This paper is an investigation of this self-instantiation thesis. I begin by pointing out that this thesis is of central importance: unless the places of a mathematical structure, such as the places of the natural number structure, themselves instantiate the structure, they cannot have any arithmetical properties. But if places do not have arithmetical properties, (...)
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