Structure and Object

Dissertation, The Ohio State University (1994)

Authors
Jill Dieterle
Eastern Michigan University
Abstract
The notion of objecthood plays a central role in many classic philosophical disputes; arguments about universals, possible worlds, propositions, sense impressions, and the ontology of mathematics all depend--in one way or another--upon the concept of an object. But often these disputes are unclear, because the concept of an object is left unexplicated. I believe that various non-equivalent notions of objecthood are involved in these disputes, thereby rendering progress unlikely. My goal in this dissertation is to clarify the concept of objecthood; against that backdrop, I try to illuminate several disputes in the philosophy of mathematics. ;I begin with the structuralist conception of mathematical objecthood. Structuralists claim that numbers are objects in the sense that they are places or positions in structures; and structures themselves are construed as types. What it is for something to be the number two, for example, is for it to be the appropriate place in the natural number structure. On this view, what qualifies as an object relative to one theory might qualify as a Fregean function relative to another. I argue that this specification of objecthood can be extended to objecthood generally. The claim is that the reason we regard certain fragments of language as referring to objects is that those fragments of language refer to places in a structure, where a structure is characterized by a coherent theory. The thesis can be summarized as follows: ; A coherent theory T characterizes a structure, and if T has explanatory power, then any expression that functions as a singular term in true sentences relative to T refers to an object. ;Briefly, a theory is a fragment of discourse with a high degree of conceptual homogeneity. I attempt to give a quasi-syntactic characterization of singular termhood, and show how this can be relativized in such a way that we can say that an expression functions as a singular term in certain contexts and not in others
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Space, Number and Structure: A Tale of Two Debates.Stewart Shapiro - 1996 - Philosophia Mathematica 4 (2):148-173.
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