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Single Idea 10685

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory ]

Full Idea

Set theory is the science of infinity.

Gist of Idea

Set theory is the science of infinity

Source

Keith Hossack (Plurals and Complexes [2000], 10)

Book Ref

-: 'British Soc for the Philosophy of Science' [-], p.433

The 29 ideas from Keith Hossack

23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
23623 Predicativism says only predicated sets exist [Hossack]
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
10663 A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
10665 Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
10664 Complex particulars are either masses, or composites, or sets [Hossack]
10666 Plural reference will refer to complex facts without postulating complex things [Hossack]
10669 Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
10668 We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
10671 Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
10675 A plural comprehension principle says there are some things one of which meets some condition [Hossack]
10673 Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
10674 A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
10676 The Axiom of Choice is a non-logical principle of set-theory [Hossack]
10677 Extensional mereology needs two definitions and two axioms [Hossack]
10678 The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
10682 The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
10681 In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
10680 The theory of the transfinite needs the ordinal numbers [Hossack]
10684 I take the real numbers to be just lengths [Hossack]
10683 We could ignore space, and just talk of the shape of matter [Hossack]
10685 Set theory is the science of infinity [Hossack]
10686 The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
10687 Maybe we reduce sets to ordinals, rather than the other way round [Hossack]