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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 nonlogical principle of settheory

5

p.423

10677

Extensional mereology needs two definitions and two axioms

7

p.427

10678

The relation of composition is indispensable to the partwhole 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 oneone 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 ordersensitive meaning, as 'and then'
