31 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] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 22180 | Multiple realisability is said to make reduction impossible [Okasha] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
| 22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
| 22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
| 22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
| 22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
| 22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
| 22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
| 22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
| 22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |