FIELD'S NOMINALISTIC PHILOSOPHY OF MATHEMATICS

FIELD'S NOMINALISTIC PHILOSOPHY OF MATHEMATICS objects which are not accessible according to our currently acceptable epistemological views. But whilst it is widely believed that there is quite some scope for presenting rejoinders to this argument, e.g. by questioning the conceptions of semantics * Critical Discussion of of Hartry Field, Realism. Mathematics and Modality. Oxford: Basil Blackwe1l1989, viii + 289pp. 1. In what folIows, non-footnoted references are 10 essays reprinted in Realism. Mathematics and Modality and 10 the pagination of that volume. 2. Benacerraf (1973). 216 and epistemology which generate the problem, it could also be argued that we should first press further into the motivational account, to question the propriety and desirability of epistemological homogeneity. And this is the approach Field takes in his argument for mathematical nominalism; for Field tries to reconcile acceptance of Benacceraf's first condition with the, apparently incompatible, second condition of epistemological homogeneity by drawing the sting from that condition. He accepts that we have no epistemic access to the states of affairs which provide the truth conditions, but then argues that no access is required because mathematical statements should be construed as fictions. Hence although Field seriously questions the general import of the epistemological homogeneity thesis, he has http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Grazer Philosophische Studien Brill

FIELD'S NOMINALISTIC PHILOSOPHY OF MATHEMATICS

FIELD'S NOMINALISTIC PHILOSOPHY OF MATHEMATICS


objects which are not accessible according to our currently acceptable epistemological views. But whilst it is widely believed that there is quite some scope for presenting rejoinders to this argument, e.g. by questioning the conceptions of semantics * Critical Discussion of of Hartry Field, Realism. Mathematics and Modality. Oxford: Basil Blackwe1l1989, viii + 289pp. 1. In what folIows, non-footnoted references are 10 essays reprinted in Realism. Mathematics and Modality and 10 the pagination of that volume. 2. Benacerraf (1973). 216 and epistemology which generate the problem, it could also be argued that we should first press further into the motivational account, to question the propriety and desirability of epistemological homogeneity. And this is the approach Field takes in his argument for mathematical nominalism; for Field tries to reconcile acceptance of Benacceraf's first condition with the, apparently incompatible, second condition of epistemological homogeneity by drawing the sting from that condition. He accepts that we have no epistemic access to the states of affairs which provide the truth conditions, but then argues that no access is required because mathematical statements should be construed as fictions. Hence although Field seriously questions the general import of the epistemological homogeneity thesis, he has sympathies with the underlying assumption of that view - an antipathy to any non-realist conception of truth. Wishing to retain a generally realist (and physicalist) epistemology, he investigates the other horn of Benacerraf's dilemma by questioning the concept of mathematical knowledge itself, concluding that the price of epistemological homogeneity is the abandonment of the claim that we have knowledge of mathematical truths. One of the main objections to this conclusion is that to regard mathematical statements as wholly fictionalised discourse leaves it totally unclear how mathematics can fruitfully and intimately connect...
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Publisher
BRILL
Copyright
© Copyright 1991 by Koninklijke Brill NV, Leiden, The Netherlands
ISSN
0165-9227
eISSN
1875-6735
D.O.I.
10.1163/18756735-90000467
Publisher site
See Article on Publisher Site

Abstract

objects which are not accessible according to our currently acceptable epistemological views. But whilst it is widely believed that there is quite some scope for presenting rejoinders to this argument, e.g. by questioning the conceptions of semantics * Critical Discussion of of Hartry Field, Realism. Mathematics and Modality. Oxford: Basil Blackwe1l1989, viii + 289pp. 1. In what folIows, non-footnoted references are 10 essays reprinted in Realism. Mathematics and Modality and 10 the pagination of that volume. 2. Benacerraf (1973). 216 and epistemology which generate the problem, it could also be argued that we should first press further into the motivational account, to question the propriety and desirability of epistemological homogeneity. And this is the approach Field takes in his argument for mathematical nominalism; for Field tries to reconcile acceptance of Benacceraf's first condition with the, apparently incompatible, second condition of epistemological homogeneity by drawing the sting from that condition. He accepts that we have no epistemic access to the states of affairs which provide the truth conditions, but then argues that no access is required because mathematical statements should be construed as fictions. Hence although Field seriously questions the general import of the epistemological homogeneity thesis, he has

Journal

Grazer Philosophische StudienBrill

Published: Aug 13, 1991

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