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] |
20189 | Belief is a feeling, independent of the will, which arises from uncontrolled and unknown causes [Hume] |
21309 | A proposition cannot be intelligible or consistent, if the perceptions are not so [Hume] |
15755 | Hume needs a notion which includes degrees of resemblance [Shoemaker on Hume] |
5323 | Experiences are logically separate, but factually linked by simultaneity or a feeling of continuousness [Ayer on Hume] |
21311 | Are self and substance the same? Then how can self remain if substance changes? [Hume] |
21312 | Perceptions are distinct, so no connection between them can ever be discovered [Hume] |
21308 | We have no impression of the self, and we therefore have no idea of it [Hume] |
21310 | Does an oyster with one perception have a self? Would lots of perceptions change that? [Hume] |
23115 | We have no natural love of mankind, other than through various relationships [Hume] |
21058 | Enlightenment requires the free use of reason in the public realm [Kant] |
16946 | Causation is just invariance, as long as it is described in general terms [Quine on Hume] |
15250 | If impressions, memories and ideas only differ in vivacity, nothing says it is memory, or repetition [Whitehead on Hume] |