Search

8 - Inference Rules
from Part II
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 94-101
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter presents a formal system for reasoning about logical possibility, whose axioms (I claim) seem clearly true, and whose inference methods seem clearly truth preserving.

17 - Logicism and Structuralism
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 183-188
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter situates both the nominalist and neo-Carnapian approaches to mathematics introduced in Chapter 10 with particular reference to Logicism and Structuralism.

Appendix D - Archimedean and Rich Instantiation
from Appendices
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 229-231
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

6 - Purified Potentialist Set Theory: An Informal Sketch
from Part II
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 81-86
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter advocates a particular Putnamian Potentialist understanding of set theory, specifying how set theoretic sentences are to be formalized using the conditional logical possibility operator.

Acknowledgments
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp vii-viii
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

4 - Overview of My Proposal
from Part I
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 42-56
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter introduces the key notion of (conditional) logical possibility, and argues that using it to formulate a version of Putnamian potentialism solve the problems noted in Chapter 3.

1 - Introduction
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 1-10
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter introduces the book’s key aims: showing how a logical possibility operator helps formulate potentialist set theory, intuitively justify the ZFC axioms, clarify applied mathematics and more.

12 - Modal If-Thenist Paraphrase Strategy
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 126-134
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter presents (and notes certain advantages of) a basic modal if-thenist strategy for nominalistically paraphrasing Platonism theories in response to indispensability arguments.

10 - Platonism or Nominalism?
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 111-115
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter notes how the potentialist set theory advocated in previous chapters can be naturally extended to a larger philosophy of mathematics, either in a nominalist or a neo-carnapian fashion.

2 - Actualist Set Theory
from Part I
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 13-30
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter discusses problems for actualist concerning the intended height of the hierarchy of sets and intuitively justifying the axiom of Replacement.

14 - Physical Magnitude Statements and Sparsity
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 146-154
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter suggests classic indispensability worries about nominalizing scientific theories can be answered by adding some cheap tricks to the modal if-thenist paraphrase strategy of Chapter 12.

19 - Conclusion
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 202-204
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter concludes the book and highlights certain questions for future study.

9 - Defense of ZFC
from Part II
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 102-108
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter sketches the justification for (potentialist translations of) the ZFC axioms for set theory, from axioms of Chapter 13, including a somewhat distinctive justification for Replacement.

Appendices
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 205-231
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Part I
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 11-78
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Appendix A - Logico-Structural Potentialism
from Appendices
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 205-209
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Bibliography
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 232-237
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

11 - Indispensability
from Part III
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 116-125
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter contrasts some different Indispensability arguments (Quinean, Explanatory, Reference and Grounding) against mathematical nominalism and tries to clarify what it takes to answer them.

3 - Putnamian Potentialism: Putnam and Hellman
from Part I
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 31-41
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

This chapter reviews existing forms of potentialist set theory in the Puntamian school. It discusses proposals by Putnam and Hellman, and notes certain problems for these.

Part II
Sharon Berry
Book:

A Logical Foundation for Potentialist Set Theory

Published online:

10 February 2022

Print publication:

17 February 2022, pp 79-108
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Search Results

Refine search

Refine search

Actions for selected content:

42 results

8 - Inference Rules

Summary

17 - Logicism and Structuralism

Summary

Appendix D - Archimedean and Rich Instantiation

6 - Purified Potentialist Set Theory: An Informal Sketch

Summary

Acknowledgments

4 - Overview of My Proposal

Summary

1 - Introduction

Summary

12 - Modal If-Thenist Paraphrase Strategy

Summary

10 - Platonism or Nominalism?

Summary

2 - Actualist Set Theory

Summary

14 - Physical Magnitude Statements and Sparsity

Summary

19 - Conclusion

Summary

9 - Defense of ZFC

Summary

Appendices

Part I

Appendix A - Logico-Structural Potentialism

Bibliography

11 - Indispensability

Summary

3 - Putnamian Potentialism: Putnam and Hellman

Summary

Part II

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

42 results

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary

Summary