12 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
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] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
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] |
579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
13159 | Only God sees contingent truths a priori [Leibniz] |
5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |