Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Commentary on Euclid's 'Elements'' and 'The Central Questions of Philosophy'

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21 ideas

2. Reason / E. Argument / 3. Analogy
5331 You can't infer that because you have a hidden birth-mark, everybody else does [Ayer]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
2611 It is currently held that quantifying over something implies belief in its existence [Ayer]
9. Objects / D. Essence of Objects / 3. Individual Essences
16520 We see properties necessary for a kind (in the definition), but not for an individual [Ayer]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
13165 Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
2613 The theory of other minds has no rival [Ayer]
5328 Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer]
5330 Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
5326 Qualia must be united by a subject, because they lead to concepts and judgements [Ayer]
5325 Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5324 Bodily identity and memory work together to establish personal identity [Ayer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
5322 Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
5327 Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5329 Why shouldn't we say brain depends on mind? Better explanation! [Ayer]
18. Thought / E. Abstraction / 1. Abstract Thought
9569 The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
19. Language / D. Propositions / 6. Propositions Critique
2610 Talk of propositions is just shorthand for talking about equivalent sentences [Ayer]