How to be a minimalist about sets

Philosophical Studies 159 (1):69-87 (2012)
Abstract
According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view.
Keywords Iterative conception  Minimalism  Metaphysical dependence
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References found in this work BETA
George Boolos (1989). Iteration Again. Philosophical Topics 17 (2):5-21.
George Boolos (1998). Must We Believe in Set Theory? In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press. 120-132.
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.

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