Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Summa quaestionum super Sententias' and 'What is Cantor's Continuum Problem?'

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13 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
8. Modes of Existence / A. Relations / 1. Nature of Relations
16659 Relations do not add anything to reality, though they are real aspects of the world [Olivi]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16673 Quantity just adds union and location to the extension of parts [Olivi]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
27. Natural Reality / G. Biology / 5. Species
16663 Things are limited by the species to certain modes of being [Olivi]