Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude
Thesis (M.A.)--Memorial University of Newfoundland, 2003. Philosophy Includes bibliographical references (leaves 116-118) This essay deals with the concept of continuity, as it has been developed both in philosophy and in mathematics during the 19th and 20th Centuries. In particular, the problem of...
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ftmemorialunivdc:oai:collections.mun.ca:theses4/94567 2023-05-15T17:23:33+02:00 Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude Gardner, Stephen Ambrose Memorial University of Newfoundland. Dept. of Philosophy 2002 vi, 118 leaves Image/jpeg; Application/pdf http://collections.mun.ca/cdm/ref/collection/theses4/id/94567 Eng eng Electronic Theses and Dissertations (14.22 MB) -- http://collections.mun.ca/PDFs/theses/Gardner_Stephen.pdf a3315382 http://collections.mun.ca/cdm/ref/collection/theses4/id/94567 The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries Kant Immanuel 1724-1804--Views on continuity Russell Bertrand 1872-1970--Views on continuity Continuity Text Electronic thesis or dissertation 2002 ftmemorialunivdc 2015-08-06T19:22:11Z Thesis (M.A.)--Memorial University of Newfoundland, 2003. Philosophy Includes bibliographical references (leaves 116-118) This essay deals with the concept of continuity, as it has been developed both in philosophy and in mathematics during the 19th and 20th Centuries. In particular, the problem of focus is the relation which the continuum has to number. The debate on whether the continuum can be given as a class of atomic individuals is the principle item of consideration in this work. The negation of this claim is argued for. -- The two sides of this debate are presented in terms of the philosophical characterizations of extensive magnitude found in the writings of Bertrand Russell (representing the claim that such a reduction is possible) and of Immanuel Kant (representing the negation of this claim). In particular, the epistemological distinction between the two figures is connected with their relative positions on this debate, discussed mainly in connexion with the issue of synthetic a priori judgments. -- The principal claim argued for in this paper is that the classical analysis of the geometric continuum, and hence Russell's logical reduction of space and time, tacitly presupposes an original undifferentiated continuum among its initial principles. This point is intended to lend support to the more general view of the continuum holding the undifferentiated whole to be utterly prior over its parts. In addition to Kant, one should attach to this view the names of Peirce and Brouwer. In particular, I shall attempt to establish an understanding of the 'spatial point' as an entity which can be individuated only as the result of a synthetic act. Finally, an examination of the relation of intuitionist choice sequences with the classical set of real numbers is presented, concluding with the conjecture that no law-like system can exhaust all possible positions on the line. Thesis Newfoundland studies University of Newfoundland Memorial University of Newfoundland: Digital Archives Initiative (DAI) Bertrand ENVELOPE(-67.077,-67.077,-68.514,-68.514) |
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Memorial University of Newfoundland: Digital Archives Initiative (DAI) |
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ftmemorialunivdc |
language |
English |
topic |
Kant Immanuel 1724-1804--Views on continuity Russell Bertrand 1872-1970--Views on continuity Continuity |
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Kant Immanuel 1724-1804--Views on continuity Russell Bertrand 1872-1970--Views on continuity Continuity Gardner, Stephen Ambrose Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
topic_facet |
Kant Immanuel 1724-1804--Views on continuity Russell Bertrand 1872-1970--Views on continuity Continuity |
description |
Thesis (M.A.)--Memorial University of Newfoundland, 2003. Philosophy Includes bibliographical references (leaves 116-118) This essay deals with the concept of continuity, as it has been developed both in philosophy and in mathematics during the 19th and 20th Centuries. In particular, the problem of focus is the relation which the continuum has to number. The debate on whether the continuum can be given as a class of atomic individuals is the principle item of consideration in this work. The negation of this claim is argued for. -- The two sides of this debate are presented in terms of the philosophical characterizations of extensive magnitude found in the writings of Bertrand Russell (representing the claim that such a reduction is possible) and of Immanuel Kant (representing the negation of this claim). In particular, the epistemological distinction between the two figures is connected with their relative positions on this debate, discussed mainly in connexion with the issue of synthetic a priori judgments. -- The principal claim argued for in this paper is that the classical analysis of the geometric continuum, and hence Russell's logical reduction of space and time, tacitly presupposes an original undifferentiated continuum among its initial principles. This point is intended to lend support to the more general view of the continuum holding the undifferentiated whole to be utterly prior over its parts. In addition to Kant, one should attach to this view the names of Peirce and Brouwer. In particular, I shall attempt to establish an understanding of the 'spatial point' as an entity which can be individuated only as the result of a synthetic act. Finally, an examination of the relation of intuitionist choice sequences with the classical set of real numbers is presented, concluding with the conjecture that no law-like system can exhaust all possible positions on the line. |
author2 |
Memorial University of Newfoundland. Dept. of Philosophy |
format |
Thesis |
author |
Gardner, Stephen Ambrose |
author_facet |
Gardner, Stephen Ambrose |
author_sort |
Gardner, Stephen Ambrose |
title |
Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
title_short |
Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
title_full |
Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
title_fullStr |
Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
title_full_unstemmed |
Synthetic activity and the continuum : a criticism of Russell's account of extensive magnitude |
title_sort |
synthetic activity and the continuum : a criticism of russell's account of extensive magnitude |
publishDate |
2002 |
url |
http://collections.mun.ca/cdm/ref/collection/theses4/id/94567 |
long_lat |
ENVELOPE(-67.077,-67.077,-68.514,-68.514) |
geographic |
Bertrand |
geographic_facet |
Bertrand |
genre |
Newfoundland studies University of Newfoundland |
genre_facet |
Newfoundland studies University of Newfoundland |
op_source |
Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries |
op_relation |
Electronic Theses and Dissertations (14.22 MB) -- http://collections.mun.ca/PDFs/theses/Gardner_Stephen.pdf a3315382 http://collections.mun.ca/cdm/ref/collection/theses4/id/94567 |
op_rights |
The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. |
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1766113285308940288 |