Combining Texts

All the ideas for 'Philosophical Explanations', 'What are Sets and What are they For?' and 'Proslogion'

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21 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3570 Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
2748 A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
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]