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The Cumulative Case for Platonism about Universals

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003494/00001

Material Information

Title: The Cumulative Case for Platonism about Universals Attribute-Identification in Mathematics
Physical Description: Book
Language: English
Creator: Clarke-Doane, Justin
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2005
Publication Date: 2005

Subjects

Subjects / Keywords: Philosophy of Mathematics
Universals
Metaphysics
Logic
Platonism
Collections
Sets
Set-Theory
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis I develop and defend a Platonistic, attribute-theoretic, account of natural number arithmetic as part of a cumulative case for Platonism about universals. In Chapter 1, I argue that three incontrovertible facts about natural number arithmetic commit us to arithmetic Realism, or the view that numbers exist as abstract objects. In Chapter 2, I introduce three more such facts and argue that the best explanation of the six taken together is that numbers are attributes whose most salient instances are collections. I then defend this conclusion against Paul Benacerraf's influential argument from multiple reductions, arguing that the conditions which he claims are adequate for an account of the numbers are far too lenient. In Chapter 3, I sketch a semantical account of number-talk as a special case of attribute-talk. And in Chapter 4, I consider the ontological status of collections, arguing that they are things with parts, not in their most evident manifestations, at least, sets. I conclude with the suggestion that, contrary to popular belief, sets may not figure into our best ontological account of reality at all.
Statement of Responsibility: by Justin Clarke-Doane
Thesis: Thesis (B.A.) -- New College of Florida, 2005
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Edidin, Aron

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2005 C59
System ID: NCFE003494:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003494/00001

Material Information

Title: The Cumulative Case for Platonism about Universals Attribute-Identification in Mathematics
Physical Description: Book
Language: English
Creator: Clarke-Doane, Justin
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2005
Publication Date: 2005

Subjects

Subjects / Keywords: Philosophy of Mathematics
Universals
Metaphysics
Logic
Platonism
Collections
Sets
Set-Theory
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis I develop and defend a Platonistic, attribute-theoretic, account of natural number arithmetic as part of a cumulative case for Platonism about universals. In Chapter 1, I argue that three incontrovertible facts about natural number arithmetic commit us to arithmetic Realism, or the view that numbers exist as abstract objects. In Chapter 2, I introduce three more such facts and argue that the best explanation of the six taken together is that numbers are attributes whose most salient instances are collections. I then defend this conclusion against Paul Benacerraf's influential argument from multiple reductions, arguing that the conditions which he claims are adequate for an account of the numbers are far too lenient. In Chapter 3, I sketch a semantical account of number-talk as a special case of attribute-talk. And in Chapter 4, I consider the ontological status of collections, arguing that they are things with parts, not in their most evident manifestations, at least, sets. I conclude with the suggestion that, contrary to popular belief, sets may not figure into our best ontological account of reality at all.
Statement of Responsibility: by Justin Clarke-Doane
Thesis: Thesis (B.A.) -- New College of Florida, 2005
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Edidin, Aron

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2005 C59
System ID: NCFE003494:00001

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