25 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] |
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
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] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
8488 | A concept is a function whose value is always a truth-value [Frege] |
9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |