1975 | The Emergence of Probability |
Ch.1 | p.1 | 7447 | Probability was fully explained between 1654 and 1812 |
Ch.1 | p.1 | 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) |
Ch.10 | p.86 | 7459 | Follow maths for necessary truths, and jurisprudence for contingent truths |
Ch.2 | p.14 | 7449 | Epistemological probability based either on logical implications or coherent judgments |
Ch.3 | p.22 | 7450 | In the medieval view, only deduction counted as true evidence |
Ch.4 | p.32 | 7451 | Formerly evidence came from people; the new idea was that things provided evidence |
Ch.4 | p.35 | 7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection |
Ch.5 | p.46 | 7454 | Gassendi is the first great empiricist philosopher |
1979 | What is Logic? |
§02 | p.227 | 13829 | If logical truths essentially depend on logical constants, we had better define the latter |
§06.2 | p.233 | 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction |
§06.3 | p.233 | 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' |
§08 | p.235 | 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with |
§09 | p.238 | 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically |
§10 | p.239 | 13838 | A decent modern definition should always imply a semantics |
§11 | p.242 | 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers |
§13 | p.245 | 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem |
§13 | p.246 | 13842 | Second-order completeness seems to need intensional entities and possible worlds |
§13 | p.246 | 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it |
§13 | p.247 | 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers |
§15 | p.250 | 13845 | The various logics are abstractions made from terms like 'if...then' in English |