34 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
13966 | Analytic philosophy loved the necessary a priori analytic, linguistic modality, and rigour [Soames] |
13974 | If philosophy is analysis of meaning, available to all competent speakers, what's left for philosophers? [Soames] |
15163 | The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
15158 | Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames] |
15157 | Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames] |
15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
13969 | Kripkean essential properties and relations are necessary, in all genuinely possible worlds [Soames] |
15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
15161 | There are more metaphysically than logically necessary truths [Soames] |
13973 | A key achievement of Kripke is showing that important modalities are not linguistic in source [Soames] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
13968 | Kripkean possible worlds are abstract maximal states in which the real world could have been [Soames] |
15152 | To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames] |
15153 | Tarski's account of truth-conditions is too weak to determine meanings [Soames] |
13965 | Semantics as theory of meaning and semantics as truth-based logical consequence are very different [Soames] |
13964 | Semantic content is a proposition made of sentence constituents (not some set of circumstances) [Soames] |
13972 | Two-dimensionalism reinstates descriptivism, and reconnects necessity and apriority to analyticity [Soames] |
15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |