PDF Philosophy of Mathematics: Structure and Ontology

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Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill.

The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic logicism , that the essence of mathematics is the rule-governed manipulation of characters formalism , and a revisionist philosophy that focuses on the mental activity of mathematics intuitionism. Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline. Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy.

This would be a platoni This would be a platonism concerning mathematical objects, which are the places within such structures. Alternatively, one can take an eliminative, in re approach, and understand talk of structures as shorthand for talk of systems of objects or, invoking modality, talk of possible systems of objects.


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Shapiro argues that although the realist, ante rem approach is the most perspicuous, in a sense, the various accounts are equivalent. Along the way, the ontological and epistemological aspects of the structuralist philosophies are assessed. One key aspect is to show how each philosophy deals with reference to mathematical objects.


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The view is tentatively extended to objects generally: to science and ordinary discourse. Keywords: ante rem , mathematics , modality , ontology , philosophy of mathematics , Platonism , realism , reference , reification , structuralism , universal. Forgot password?

Philosophy of Mathematics: Structure and Ontology

Don't have an account? Over the last two decades structural realism has been given progressively more elaborated formulations.

Steven French has been at the forefront of the development of the most conceptually sophisticated and historically sensitive version of the view. In his book, The Structure of the World French , French shows how structural realism, the view according to which structure is all there is ontic structural realism , is able to illuminate central issues in the philosophy of science: underdetermination, scientific representation, dispositions, natural modality, and laws of nature.

The discussion consistently sheds novel light on the problems under consideration while developing insightful and provocative views.

Notre Dame Journal of Formal Logic

Structural realism, mathematics, and ontology. N2 - Over the last two decades structural realism has been given progressively more elaborated formulations.