74 ideas
| 21405 | Cicero sees wisdom in terms of knowledge, but earlier Stoics saw it as moral [Cicero, by Long] |
| 20871 | Unfortunately we choose a way of life before we are old enough to think clearly [Cicero] |
| 5893 | A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero] |
| 5891 | Philosophy is the collection of rational arguments [Cicero] |
| 2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
| 2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
| 2673 | There cannot be more than one truth [Cicero] |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 21677 | How can the not-true fail to be false, or the not-false fail to be true? [Cicero] |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 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] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
| 2665 | How can there be a memory of what is false? [Cicero] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 20800 | Every true presentation can have a false one of the same quality [Cicero] |
| 5879 | The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero] |
| 5884 | How can one mind perceive so many dissimilar sensations? [Cicero] |
| 5887 | The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero] |
| 5886 | Like the eye, the soul has no power to see itself, but sees other things [Cicero] |
| 6029 | Whoever knows future causes knows everything that will be [Cicero] |
| 2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
| 5885 | Souls contain no properties of elements, and elements contain no properties of souls [Cicero] |
| 21667 | Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero] |
| 20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
| 21678 | If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero] |
| 2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |
| 5890 | We should not share the distress of others, but simply try to relieve it [Cicero] |
| 5894 | All men except philosophers fear poverty [Cicero] |
| 6031 | The essence of propriety is consistency [Cicero] |
| 5895 | If one despises illiterate mechanics individually, they are not worth more collectively [Cicero] |
| 2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
| 2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
| 2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
| 2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
| 2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
| 2636 | Many primitive people know nothing of the gods [Cicero] |
| 2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
| 2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
| 2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
| 2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
| 2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
| 2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
| 2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
| 2641 | Why believe in gods if you have never seen them? [Cicero] |
| 2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
| 2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |