Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'The Philosophy of Logic' and 'Plurals and Complexes'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10680
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The theory of the transfinite needs the ordinal numbers [Hossack]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10684
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I take the real numbers to be just lengths [Hossack]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18200
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Very large sets should be studied in an 'if-then' spirit [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10674
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A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10681
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In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
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10685
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Set theory is the science of infinity [Hossack]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18199
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Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
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8857
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We must quantify over numbers for science; but that commits us to their existence [Putnam]
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