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'fragments/reports', 'Replies on 'Limits of Abstraction'' and 'Causal Powers'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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15273
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Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]
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10573
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Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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15274
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Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]
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10575
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Why should a Dedekind cut correspond to a number? [Fine,K]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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10574
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Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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10560
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Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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10568
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Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
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15211
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There is not an exclusive dichotomy between the formal and the logical [Harré/Madden]
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