Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction
- 1 Beginnings and Puzzles
- 2 Mathematical Preliminaries
- 3 Some Cases Discussed
- 4 Space, Time, and Spacetime
- 5 Physical Infinities
- 6 Probability and Decision Theory
- 7 Mereology
- 8 Some Philosophical Considerations
- 9 Infinite Regress and Sufficient Reason
- Conclusion
- References
- Index
7 - Mereology
Published online by Cambridge University Press: 31 July 2009
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction
- 1 Beginnings and Puzzles
- 2 Mathematical Preliminaries
- 3 Some Cases Discussed
- 4 Space, Time, and Spacetime
- 5 Physical Infinities
- 6 Probability and Decision Theory
- 7 Mereology
- 8 Some Philosophical Considerations
- 9 Infinite Regress and Sufficient Reason
- Conclusion
- References
- Index
Summary
Mereology is the theory of the part/whole relation. The basic principles of the theory of the part/whole relation may seem to be utterly straightforward. However, as we shall see, there are various different ways in which questions about infinity impose themselves on the investigation of the general nature of part/whole relations.
We begin with the “proofs” in Kant's Second Antinomy, which concern the part/whole structure of the world. On the one hand, he offers a “proof” of the claim that the world – and everything in it – either is something that has no parts (i.e., a simple) or is composed without remainder from things that have no parts. On the other hand, he offers a “proof” of the claim that there are no simples, that is, there are no things that have no parts. In each case, the object of “proof” is a strong modal thesis – that it is necessary that any object either has no parts or else is composed without remainder of objects that themselves have no parts, that it is necessary that there are no things that have no parts – from which the desired results can be inferred by a simple application of the T-axiom (if it is necessary that [w3], then [w3]).
After this warm-up, we turn to a formal presentation of the basic concepts and axioms of mereology, and then to a discussion of the various ways in which questions about infinity bear on these concepts and axioms.
- Type
- Chapter
- Information
- Philosophical Perspectives on Infinity , pp. 201 - 230Publisher: Cambridge University PressPrint publication year: 2006