Parts and Wholes: Spatial to Modal

Description

The Odd Universe Argument aims to show that from four intuitive assumptions about parts and wholes, we can conclude a priori that there is an odd number of things in the universe. This Element investigates how this is so and where things might have gone awry. Section 1 gives an overview of general methodology, basic mereology, and plural logic. Section 2 explores questions about the nature of composition and decomposition. Does composition always occur? Never? Sometimes? Is the universe, at rock bottom, just many partless bits (simples)? Or do the parts have parts all the way down (gunk)? Section 3 looks at arguments for and against the thesis that composition is identity, with a healthy bias in its favor. In the wake of this discussion, we reconsider our methods of counting. We conclude with a return to the odd universe argument and suggestions on how best to resist it. Cover Title page Copyright page Parts and Wholes Contents Introduction: An Odd Universe 1 Parts and Plurals 1.1 Methodology 1.2 Mereology 1.2.1 Axioms and Definitions 1.2.2 Sets and Sums 1.2.3 Ontological Innocence 1.2.4 Topic Neutrality and Univocality 1.3 Plurals 2 Composition and Decomposition 2.1 Always 2.2 Never 2.3 Sometimes 2.4 All the Way Down 2.4.1 Infinite Simples 2.4.2 Gunk 2.4.3 Zeno 3 Identity and Counting 3.1 Advantages of CI 3.2 Leibniz’s Law and Hybrid Identity 3.3 Objections to CI 3.3.1 Invalid and Unsound 3.3.2 Persistence Worries 3.3.3 Numerical Worries 3.4 Counting 3.4.1 Singular 3.4.2 Relative 3.4.3 Count Conclusion References Acknowledgements