19 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
8594 | People have had good reasons for thinking that the circle has been squared [Shoemaker] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
8596 | Inability to measure equality doesn't make all lengths unequal [Shoemaker] |
8597 | We couldn't verify the earth's rotation if everyone simultaneously fell asleep [Shoemaker] |
8593 | Maybe billions of changeless years have elapsed since my last meal [Shoemaker] |
8598 | If things turn red for an hour and then explode, we wouldn't say the redness was the cause [Shoemaker] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
4226 | If three regions 'freeze' every three, four and five years, after sixty years everything stops for a year [Shoemaker, by Lowe] |
8595 | If three regions freeze every 3rd, 4th and 5th year, they all freeze together every 60 years [Shoemaker] |