Combining Texts

All the ideas for 'Concerning the Author', 'Proslogion' and 'Model Theory'

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22 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
14767 The demonstrations of the metaphysicians are all moonshine [Peirce]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
14764 I am saturated with the spirit of physical science [Peirce]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14768 Infallibility in science is just a joke [Peirce]
12. Knowledge Sources / D. Empiricism / 2. Associationism
14765 Association of ideas is the best philosophical idea of the prescientific age [Peirce]
14. Science / B. Scientific Theories / 1. Scientific Theory
14766 Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce]
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]