Combining Texts

All the ideas for 'Notebooks 1914-1916', 'The Principles of Art' and 'Investigations in the Foundations of Set Theory I'

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26 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
18274 Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein]
2. Reason / D. Definition / 8. Impredicative Definition
15924 Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17608 We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
17607 Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10870 ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
13012 Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
17609 Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13017 Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13015 Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13020 The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
16908 We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18276 A statement's logical form derives entirely from its constituents [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
6563 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178 For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627 Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
23472 The sense of propositions relies on the world's basic logical structure [Wittgenstein]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
23500 My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
22323 The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
23481 Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20420 The emotion expressed is non-conscious, but feels oppressive until expression relieves it [Collingwood]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20421 Art exists ideally, purely as experiences in the mind of the perceiver [Collingwood, by Kemp]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
20406 Art clarifies the artist's mind and feelings, thus leading to self-knowledge [Collingwood, by Davies,S]
25. Social Practice / F. Life Issues / 4. Suicide
4678 Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein]