43 ideas
3600 | Slow and accurate thought makes the greatest progress [Descartes] |
3601 | Most things in human life seem vain and useless [Descartes] |
3602 | Almost every daft idea has been expressed by some philosopher [Descartes] |
3603 | Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
3612 | Clear and distinct conceptions are true because a perfect God exists [Descartes] |
3610 | Truth is clear and distinct conception - of which it is hard to be sure [Descartes] |
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] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
12462 | Only the finite can bring certainty to the infinite [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] |
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] |
3605 | We can believe a thing without knowing we believe it [Descartes] |
1583 | In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
3607 | In thinking everything else false, my own existence remains totally certain [Descartes] |
3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
3611 | Understanding, rather than imagination or senses, gives knowledge [Descartes] |
3606 | I was searching for reliable rock under the shifting sand [Descartes] |
3604 | When rebuilding a house, one needs alternative lodgings [Descartes] |
3618 | Only experiments can settle disagreements between rival explanations [Descartes] |
3615 | Little reason is needed to speak, so animals have no reason at all [Descartes] |
3609 | I am a thinking substance, which doesn't need a place or material support [Descartes] |
3608 | I can deny my body and the world, but not my own existence [Descartes] |
3613 | Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes] |
3616 | The soul must unite with the body to have appetites and sensations [Descartes] |
3614 | A machine could speak in response to physical stimulus, but not hold a conversation [Descartes] |
1581 | Greeks elevate virtues enormously, but never explain them [Descartes] |
16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |