23 ideas
13941 | Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R] |
13942 | Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R] |
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] |
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] |
13945 | A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R] |
19440 | How do you know you have conceived a thing deeply enough to assess its possibility? [Vaidya] |
13948 | For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R] |
13950 | People don't assert the meaning of the words they utter [Cartwright,R] |
13944 | We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R] |
13947 | 'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R] |
13943 | We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R] |
13946 | To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R] |
13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |