Combining Texts

All the ideas for 'Proslogion', 'The Theory of Logical Types' and 'The Nature of Mathematics'

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22 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
14782 Philosophy is an experimental science, resting on common experience [Peirce]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
14787 Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
14783 Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
14788 Mathematics is close to logic, but is even more abstract [Peirce]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
10. Modality / B. Possibility / 1. Possibility
14786 Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
14789 Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
14785 The world is one of experience, but experiences are always located among our ideas [Peirce]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
14784 Ethics is the science of aims [Peirce]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
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]
21243 An existing thing is even greater if its non-existence is inconceivable [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]