Mathematical Thought and its ObjectsCambridge University Press, 24 de dez. de 2007 Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite. |
Conteúdo
2 Eliminative Structuralism and Nominalism | 40 |
3 Modality and Structuralism | 80 |
4 A Problem About Sets | 117 |
5 Intuition | 138 |
6 Numbers as Objects | 186 |
7 Intuitive Arithmetic and Its Limits | 235 |
8 Mathematical Induction | 264 |
9 Reason | 316 |
Bibliography | 343 |
| 365 | |
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Termos e frases comuns
abstract objects application argument arise assume axiom of replacement axiom of separation axioms basic Bernays Boolos bracket term cardinal Chapter claim concept of number concept of set consider construction context Dedekind defined discussion domain elementary elements eliminative example existence expressions fact Feferman finitary finite sets first-order arithmetic first-order logic formal Frege functions functors G¨odel given hereditarily finite sets Hilbert idea identity implies impredicative individuals interpretation intuitive knowledge intuitively evident involved isomorphic iteration Kant Kant’s kind language mathe mathematical objects Mathematics in Philosophy matter Meinong modal modal logic natural numbers nominalist notion ontological particular perception plural possible predicate primitive recursion primitive recursive arithmetic principle problem proof proposition provable quantifiers quasi-concrete question reason reference relation role second-order logic seems semantic sense sentence sequences set theory set-theoretic simply infinite system singular terms statement string stroke structuralist view structure talk theorem thesis tion tokens true truth variables
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