20 ideas
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |