Combining Texts

All the ideas for 'A Defense of Presentism', 'Elements of Set Theory' and 'Sources of Knowledge of Mathematics'

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22 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
14001 People who use science to make philosophical points don't realise how philosophical science is [Markosian]
3. Truth / B. Truthmakers / 9. Making Past Truths
13991 Presentism has the problem that if Socrates ceases to exist, so do propositions about him [Markosian]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9545 Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14002 Possible worlds must be abstract, because two qualitatively identical worlds are just one world [Markosian]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
14000 'Grabby' truth conditions first select their object, unlike 'searchy' truth conditions [Markosian]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
13990 Presentism is the view that only present objects exist [Markosian]
13992 Presentism says if objects don't exist now, we can't have attitudes to them or relations with them [Markosian]
13994 Presentism seems to entail that we cannot talk about other times [Markosian]
13995 Serious Presentism says things must exist to have relations and properties; Unrestricted version denies this [Markosian]
13996 Maybe Presentists can refer to the haecceity of a thing, after the thing itself disappears [Markosian]
13997 Maybe Presentists can paraphrase singular propositions about the past [Markosian]
13993 Special Relativity denies the absolute present which Presentism needs [Markosian]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
13998 Objects in the past, like Socrates, are more like imaginary objects than like remote spatial objects [Markosian]
13999 People are mistaken when they think 'Socrates was a philosopher' says something [Markosian]