23 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
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] |
4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
14759 | A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad] |
11842 | If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad] |
4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
8160 | The present and past exist, but the future does not [Broad, by Dummett] |
14609 | We could say present and past exist, but not future, so that each event adds to the total history [Broad] |
22933 | We imagine the present as a spotlight, moving across events from past to future [Broad] |