26 ideas
7454 | Gassendi is the first great empiricist philosopher [Hacking] |
1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
7450 | In the medieval view, only deduction counted as true evidence [Hacking] |
7451 | Formerly evidence came from people; the new idea was that things provided evidence [Hacking] |
1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG] |
7459 | Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking] |
23221 | The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish] |