33 ideas
| 20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
| 6675 | The heart has its reasons of which reason knows nothing [Pascal] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 22011 | The first principles of truth are not rational, but are known by the heart [Pascal] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
| 20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
| 6681 | We only want to know things so that we can talk about them [Pascal] |
| 6676 | Painting makes us admire things of which we do not admire the originals [Pascal] |
| 6680 | It is a funny sort of justice whose limits are marked by a river [Pascal] |
| 6677 | Imagination creates beauty, justice and happiness, which is the supreme good [Pascal] |
| 6678 | We live for the past or future, and so are never happy in the present [Pascal] |
| 20732 | If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal] |
| 6682 | Majority opinion is visible and authoritative, although not very clever [Pascal] |
| 6679 | It is not good to be too free [Pascal] |
| 7455 | Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking] |
| 7457 | Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal] |
| 7456 | The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal] |
| 6684 | If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal] |
| 5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |