2000 | Plurals and Complexes |
1 | p.411 | 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs |
1 | p.412 | 10664 | Complex particulars are either masses, or composites, or sets |
1 | p.413 | 10666 | Plural reference will refer to complex facts without postulating complex things |
1 | p.413 | 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules |
2 | p.414 | 10668 | We are committed to a 'group' of children, if they are sitting in a circle |
2 | p.415 | 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise |
3 | p.416 | 10671 | Plural definite descriptions pick out the largest class of things that fit the description |
3 | p.417 | 10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence |
4 | p.420 | 10673 | Plural language can discuss without inconsistency things that are not members of themselves |
4 | p.420 | 10674 | A plural language gives a single comprehensive induction axiom for arithmetic |
4 | p.421 | 10675 | A plural comprehension principle says there are some things one of which meets some condition |
4 n8 | p.421 | 10676 | The Axiom of Choice is a non-logical principle of set-theory |
5 | p.423 | 10677 | Extensional mereology needs two definitions and two axioms |
7 | p.427 | 10678 | The relation of composition is indispensable to the part-whole relation for individuals |
8 | p.429 | 10681 | In arithmetic singularists need sets as the instantiator of numeric properties |
8 | p.429 | 10680 | The theory of the transfinite needs the ordinal numbers |
8 | p.430 | 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles |
9 | p.432 | 10683 | We could ignore space, and just talk of the shape of matter |
9 | p.432 | 10684 | I take the real numbers to be just lengths |
10 | p.433 | 10685 | Set theory is the science of infinity |
10 | p.436 | 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals |
10 | p.436 | 10687 | Maybe we reduce sets to ordinals, rather than the other way round |