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Ideas for 'fragments/reports', 'Laughter' and 'Plurals and Complexes'

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3 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10674 A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
     Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'.
     From: Keith Hossack (Plurals and Complexes [2000], 4)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10681 In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
     Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties.
     From: Keith Hossack (Plurals and Complexes [2000], 8)
10685 Set theory is the science of infinity [Hossack]
     Full Idea: Set theory is the science of infinity.
     From: Keith Hossack (Plurals and Complexes [2000], 10)