Combining Texts
Ideas for
'Individuals without Sortals', 'The Problem of the Essential Indexical' and 'Introduction to Mathematical Logic'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758
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Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
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17755
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Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
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17756
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The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
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17760
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Two infinite ordinals can represent a single infinite cardinal [Walicki]
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17757
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Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518
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Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
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17516
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If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762
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In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754
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Inductive proof depends on the choice of the ordering [Walicki]
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