39 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] |
| 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] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 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] |
| 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] |
| 22808 | Liberalism is minimal government, or individual rights, or equality [Avineri/De-Shalit] |
| 22803 | Can individualist theories justify an obligation to fight in a war? [Avineri/De-Shalit] |
| 22804 | Autonomy is better achieved within a community [Avineri/De-Shalit] |
| 22806 | Communitarians avoid oppression for the common good, by means of small mediating communities [Avineri/De-Shalit] |
| 22807 | If our values are given to us by society then we have no grounds to criticise them [Avineri/De-Shalit] |
| 16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |