Search results for "Mathematical structuralism"

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Object, Structure, and Form

2012

The main task of this paper is to develop the non-Platonist view of mathematics as a science of structures I have called, borrowing the label from Putnam, `realism with the human face'. According to this view, if by `object' we mean what exists independently of whether we are thinking about it or not, mathematics is a science of patterns (structures), where patterns are neither objects nor properties of objects, but aspects (or aspects of aspects, etc.) of concrete objects which dawn on us when we represent objects (or aspects of... within a given system (of representation). Mathematical patterns, therefore, are real, because they ultimately depend on concrete objects, but are neither objec…

Patterns Mathematical structuralism Abstract objects Forms of representation Systems of representation RealismSettore M-FIL/02 - Logica E Filosofia Della Scienza
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True V or not True V, That is the Question

2016

In this paper we intend to argue that: (1) the question `True V or not True V' is central to both the philosophical and mathematical investigations of the foundations of mathematics; (2) when posed within a framework in which set theory is seen as a science of objects, the question `True V or not True V' generates a dilemma each horn of which turns out to be unacceptable; (3) a plausible way out of the dilemma mentioned at (2) is provided by an approach to set theory according to which this is considered to be a science of structures.

French hornPhilosophy05 social sciences06 humanities and the artsSettore M-FIL/02 - Logica E Filosofia Della Scienza050905 science studies0603 philosophy ethics and religionDilemma060302 philosophySet theory0509 other social sciencesMathematical economicsFoundations of mathematicsMathematical structuralism universe of sets foundations of mathematics
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