Combining Texts
Ideas for
'fragments/reports', 'Metaphysical Dependence' and 'Plurals and Complexes'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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10680
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The theory of the transfinite needs the ordinal numbers [Hossack]
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Full Idea:
The theory of the transfinite needs the ordinal numbers.
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From:
Keith Hossack (Plurals and Complexes [2000], 8)
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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10684
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I take the real numbers to be just lengths [Hossack]
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Full Idea:
I take the real numbers to be just lengths.
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From:
Keith Hossack (Plurals and Complexes [2000], 9)
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A reaction:
I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged.
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
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10674
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A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
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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...'.
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From:
Keith Hossack (Plurals and Complexes [2000], 4)
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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10681
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In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
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Full Idea:
In arithmetic singularists need sets as the instantiator of numeric properties.
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From:
Keith Hossack (Plurals and Complexes [2000], 8)
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10685
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Set theory is the science of infinity [Hossack]
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Full Idea:
Set theory is the science of infinity.
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From:
Keith Hossack (Plurals and Complexes [2000], 10)
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