38 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] |
16456 | For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker] |
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] |
2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
2735 | Could you have a single belief on its own? [Audi,R] |
2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
2741 | The principles of justification have to be a priori [Audi,R] |
2725 | To remember something is to know it [Audi,R] |
2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
2734 | A consistent madman could have a very coherent belief system [Audi,R] |
2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |