Combining Texts

All the ideas for 'The Scientific Revolution 1500-1800', 'Elements of Set Theory' and 'Significance of the Kripkean Nec A Posteriori'

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15 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / c. Modern philosophy mid-period
Analytic philosophy loved the necessary a priori analytic, linguistic modality, and rigour [Soames]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
If philosophy is analysis of meaning, available to all competent speakers, what's left for philosophers? [Soames]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
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
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
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
We can only define functions if Choice tells us which items are involved [Enderton]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Kripkean essential properties and relations are necessary, in all genuinely possible worlds [Soames]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
A key achievement of Kripke is showing that important modalities are not linguistic in source [Soames]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Kripkean possible worlds are abstract maximal states in which the real world could have been [Soames]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
Two-dimensionalism reinstates descriptivism, and reconnects necessity and apriority to analyticity [Soames]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The idea of laws of nature arose in the Middle Ages [Hall,AR, by Ellis]