Ideas from 'Parts of Classes' by David Lewis [1991], by Theme Structure
[found in 'Parts of Classes' by Lewis,David [Blackwell 1991,063117656x]].
green numbers give full details 
back to texts

expand these ideas
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 membersingleton 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 secondorder 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

Troutturkeys 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 catfusions 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
