Combining Texts

All the ideas for 'Defending the Axioms', 'Proslogion' and 'Internalism Exposed'

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21 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
6871 We can't only believe things if we are currently conscious of their justification - there are too many [Goldman]
6872 Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman]
6874 Internal justification needs both mental stability and time to compute coherence [Goldman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
6873 Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6875 Reliability involves truth, and truth is external [Goldman]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
21243 An existing thing is even greater if its non-existence is inconceivable [Anselm]
21244 Conceiving a greater being than God leads to absurdity [Anselm]
21241 Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm]
21242 If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm]
1421 A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm]
21245 The word 'God' can be denied, but understanding shows God must exist [Anselm]
21246 Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm]
21247 Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
1420 Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm]