green numbers give full details.     |    back to list of philosophers     |     expand these ideas

Ideas of Keith Hossack, by Text

[British, fl. 2007, Lecturer at Birkbeck College, London.]

2000 Plurals and Complexes
1 p.411 A thought can refer to many things, but only predicate a universal and affirm a state of affairs
1 p.412 Complex particulars are either masses, or composites, or sets
1 p.413 Leibniz's Law argues against atomism - water is wet, unlike water molecules
1 p.413 Plural reference will refer to complex facts without postulating complex things
2 p.414 We are committed to a 'group' of children, if they are sitting in a circle
2 p.415 Plural reference is just an abbreviation when properties are distributive, but not otherwise
3 p.416 Plural definite descriptions pick out the largest class of things that fit the description
4 p.420 A plural language gives a single comprehensive induction axiom for arithmetic
4 p.420 Plural language can discuss without inconsistency things that are not members of themselves
4 p.421 A plural comprehension principle says there are some things one of which meets some condition
4 n8 p.421 The Axiom of Choice is a non-logical principle of set-theory
5 p.423 Extensional mereology needs two definitions and two axioms
7 p.427 The relation of composition is indispensable to the part-whole relation for individuals
8 p.429 The theory of the transfinite needs the ordinal numbers
8 p.429 In arithmetic singularists need sets as the instantiator of numeric properties
8 p.430 The fusion of five rectangles can decompose into more than five parts that are rectangles
9 p.432 We could ignore space, and just talk of the shape of matter
9 p.432 I take the real numbers to be just lengths
10 p.433 Set theory is the science of infinity
10 p.436 Maybe we reduce sets to ordinals, rather than the other way round
10 p.436 The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
2020 Knowledge and the Philosophy of Number
Intro p.1 Numbers are properties, not sets (because numbers are magnitudes)
Intro 2 p.3 We can only mentally construct potential infinities, but maths needs actual infinities
02.3 p.26 Predicativism says only predicated sets exist
09.9 p.146 The iterative conception has to appropriate Replacement, to justify the ordinals
09.9 p.147 Limitation of Size justifies Replacement, but then has to appropriate Power Set
10.1 p.152 Transfinite ordinals are needed in proof theory, and for recursive functions and computability
10.3 p.157 'Before' and 'after' are not two relations, but one relation with two orders
10.4 p.158 The connective 'and' can have an order-sensitive meaning, as 'and then'