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Ideas of Keith Hossack, by Text

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

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 10665 Leibniz's Law argues against atomism - water is wet, unlike water molecules
1 p.413 10666 Plural reference will refer to complex facts without postulating complex things
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
4 p.420 10674 A plural language gives a single comprehensive induction axiom for arithmetic
4 p.420 10673 Plural language can discuss without inconsistency things that are not members of themselves
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 10680 The theory of the transfinite needs the ordinal numbers
8 p.429 10681 In arithmetic singularists need sets as the instantiator of numeric properties
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 10687 Maybe we reduce sets to ordinals, rather than the other way round
10 p.436 10686 The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
2020 Knowledge and the Philosophy of Number
Intro p.1 23621 Numbers are properties, not sets (because numbers are magnitudes)
Intro 2 p.3 23622 We can only mentally construct potential infinities, but maths needs actual infinities
02.3 p.26 23623 Predicativism says only predicated sets exist
09.9 p.146 23624 The iterative conception has to appropriate Replacement, to justify the ordinals
09.9 p.147 23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set
10.1 p.152 23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability
10.3 p.157 23627 'Before' and 'after' are not two relations, but one relation with two orders
10.4 p.158 23628 The connective 'and' can have an order-sensitive meaning, as 'and then'