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Facets of infinity : = A theory of finitistic truth.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Facets of infinity :/
Reminder of title:	A theory of finitistic truth.
Author:	Damnjanovic, Zlatan.
Description:	1 online resource (341 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 54-06, Section: A.
Contained By:	Dissertations Abstracts International54-06A.
Subject:	Philosophy. -
Online resource:	click for full text (PQDT)
ISBN:	9781392439265

Facets of infinity : = A theory of finitistic truth.
Damnjanovic, Zlatan.

Facets of infinity :A theory of finitistic truth. - 1 online resource (341 pages)

Source: Dissertations Abstracts International, Volume: 54-06, Section: A.

Thesis (Ph.D.)--Princeton University, 1992.

Includes bibliographical references

The thesis critically examines the question of the philosophical coherence of finitism, the view which seeks to interpret mathematics without postulating an actual infinity of mathematical objects. It is argued that a widely accepted characterization of finitism, most recently expounded by Tait, is inadequate, and a new characterization based on the notion of elementary abstraction is proposed. It is further argued that the notion of elementary abstraction better explains the bearing of Godel's incompleteness theorems on the issue of the coherence of finitism. By abstraction is meant a procedure by which one recognizes or establishes that some infinite process exhibits a distinctive uniformity. If the procedure does not require one to conceive of the integers in any other way than as the result of simple iterations, we call such abstraction elementary. Some six different formal models exploring a variety of different ways in which this notion can be made precise are proposed as possible formal characterizations of finitistic truth. It is proved that all these different models are equivalent with respect to finitistically meaningful sentences. This is taken as strong evidence that the notion of elementary abstraction is determinate enough to provide a basis for a coherent philosophical formulation of finitism.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9781392439265Subjects--Topical Terms:

559771
Philosophy.
Index Terms--Genre/Form:

554714
Electronic books.

Facets of infinity : = A theory of finitistic truth.
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100 1 $a Damnjanovic, Zlatan. $3 1469350
245 1 0 $a Facets of infinity : $b A theory of finitistic truth.
264 0 $c 1992
300 $a 1 online resource (341 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 54-06, Section: A.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Benacerraf, Paul.
502 $a Thesis (Ph.D.)--Princeton University, 1992.
504 $a Includes bibliographical references
520 $a The thesis critically examines the question of the philosophical coherence of finitism, the view which seeks to interpret mathematics without postulating an actual infinity of mathematical objects. It is argued that a widely accepted characterization of finitism, most recently expounded by Tait, is inadequate, and a new characterization based on the notion of elementary abstraction is proposed. It is further argued that the notion of elementary abstraction better explains the bearing of Godel's incompleteness theorems on the issue of the coherence of finitism. By abstraction is meant a procedure by which one recognizes or establishes that some infinite process exhibits a distinctive uniformity. If the procedure does not require one to conceive of the integers in any other way than as the result of simple iterations, we call such abstraction elementary. Some six different formal models exploring a variety of different ways in which this notion can be made precise are proposed as possible formal characterizations of finitistic truth. It is proved that all these different models are equivalent with respect to finitistically meaningful sentences. This is taken as strong evidence that the notion of elementary abstraction is determinate enough to provide a basis for a coherent philosophical formulation of finitism.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Philosophy. $3 559771
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
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