23 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
19067 | A successful proof requires recognition of truth at every step [Dummett] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |