66 ideas
| 21422 | Moral self-knowledge is the beginning of all human wisdom [Kant] |
| 21408 | For any subject, its system of non-experiential concepts needs a metaphysics [Kant] |
| 21416 | Philosophers should not offer multiple proofs - suggesting the weakness of each of them [Kant] |
| 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] |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| 21410 | That a concept is not self-contradictory does not make what it represents possible [Kant] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 462 | One vision is produced by both eyes [Empedocles] |
| 21421 | Within nature man is unimportant, but as moral person he is above any price [Kant] |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| 21415 | Duty is impossible without prior moral feeling, conscience, love and self-respect [Kant] |
| 21409 | Moral principles do not involve feelings [Kant] |
| 21431 | The love of man is required in order to present the world as a beautiful and perfect moral whole [Kant] |
| 21437 | All morality directs the will to love of others' ends, and respect for others' rights [Kant] |
| 21429 | The duty of love is to makes the ends of others one's own [Kant] |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| 21411 | A duty of virtue is a duty which is also an end [Kant] |
| 21413 | Virtue is strong maxims for duty [Kant] |
| 21414 | The supreme principle of virtue is to find universal laws for ends [Kant] |
| 21436 | We are obliged to show the social virtues, but at least they make a virtuous disposition fashionable [Kant] |
| 21419 | If virtue becomes a habit, that is a loss of the freedom needed for adopting maxims [Kant] |
| 21417 | How do we distinguish a mean? The extremes can involve quite different maxims [Kant] |
| 21420 | If virtue is the mean between vices, then virtue is just the vanishing of vice [Kant] |
| 21418 | There is one principle of virtues; the virtues are distinguished by their objects [Kant] |
| 21425 | We can love without respect, and show respect without love [Kant] |
| 21427 | Respect is limiting our self-esteem by attending to the human dignity of other persons [Kant] |
| 21430 | Disrespect is using a person as a mere means to my own ends [Kant] |
| 21428 | Respect is purely negative (of not exalting oneself over others), and is thus a duty of Right [Kant] |
| 21426 | Love urges us to get closer to people, but respect to keep our distance [Kant] |
| 21434 | We must respect the humanity even in a vicious criminal [Kant] |
| 21412 | Humans are distinguished from animals by their capacity to set themselves any sort of end [Kant] |
| 21435 | Man is both social, and unsociable [Kant] |
| 21433 | Violation of rights deserves punishment, which is vengeance, rather than restitution [Kant] |
| 21423 | Men can only have duties to those who qualify as persons [Kant] |
| 21424 | Cruelty to animals is bad because it dulls our empathy for pain in humans [Kant] |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| 459 | All change is unity through love or division through hate [Empedocles] |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| 466 | God is pure mind permeating the universe [Empedocles] |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |