### Ideas from 'Parts of Classes' by David Lewis [1991], by Theme Structure

#### [found in 'Parts of Classes' by Lewis,David [Blackwell 1991,0-631-17656-x]].

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###### 4. Formal Logic / F. Set Theory ST / 1. Set Theory
 18395 Sets are mereological sums of the singletons of their members [Armstrong]
 15496 We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton
###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
 15500 Classes divide into subclasses in many ways, but into members in only one way
 15499 A subclass of a subclass is itself a subclass; a member of a member is not in general a member
###### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
 15503 We needn't accept this speck of nothingness, this black hole in the fabric of Reality!
 15498 We can accept the null set, but there is no null class of anything
 15502 There are four main reasons for asserting that there is an empty set
###### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
 15506 If we don't understand the singleton, then we don't understand classes
 15497 We can replace the membership relation with the member-singleton relation (plus mereology)
 15511 If singleton membership is external, why is an object a member of one rather than another?
 15513 Maybe singletons have a structure, of a thing and a lasso?
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
 15507 Set theory has some unofficial axioms, generalisations about how to understand it
 10191 Set theory reduces to a mereological theory with singletons as the only atoms [MacBride]
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
 15508 If singletons are where their members are, then so are all sets
 15514 A huge part of Reality is only accepted as existing if you have accepted set theory
 15523 Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it
###### 5. Theory of Logic / G. Quantification / 6. Plural Quantification
 15525 Plural quantification lacks a complete axiom system
 15518 I like plural quantification, but am not convinced of its connection with second-order logic
###### 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
 15524 Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory
###### 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
 15517 Giving up classes means giving up successful mathematics because of dubious philosophy
###### 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
 15515 To be a structuralist, you quantify over relations
###### 7. Existence / A. Nature of Existence / 2. Types of Existence
 15520 Existence doesn't come in degrees; once asserted, it can't then be qualified
###### 7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
 15501 We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture
 15504 Atomless gunk is an individual whose parts all have further proper parts
###### 8. Modes of Existence / B. Properties / 11. Properties as Sets
 15516 A property is any class of possibilia
###### 9. Objects / C. Structure of Objects / 5. Composition of an Object
 14748 The many are many and the one is one, so they can't be identical
 6129 Lewis affirms 'composition as identity' - that an object is no more than its parts [Merricks]
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
 15512 In mereology no two things consist of the same atoms
 15519 Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power
 15521 Given cats, a fusion of cats adds nothing further to reality
 15522 The one has different truths from the many; it is one rather than many, one rather than six
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
 14244 Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions [Oliver/Smiley]
 10660 A commitment to cat-fusions is not a further commitment; it is them and they are it
 10566 Lewis prefers giving up singletons to giving up sums [Fine,K]
###### 12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
 15509 Some say qualities are parts of things - as repeatable universals, or as particulars