90 ideas
| 6200 | Wisdom is knowing the highest good, and conforming the will to it [Kant] |
| 6207 | What fills me with awe are the starry heavens above me and the moral law within me [Kant] |
| 6184 | Consistency is the highest obligation of a philosopher [Kant] |
| 6203 | Metaphysics is just a priori universal principles of physics [Kant] |
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
| 14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| 14443 | The British parliament has one representative selected from each constituency [Russell] |
| 14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
| 14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
| 14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| 14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| 8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
| 14452 | All the propositions of logic are completely general [Russell] |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
| 7311 | The only genuine proper names are 'this' and 'that' [Russell] |
| 14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
| 14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
| 14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
| 13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
| 14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
| 14439 | A complex number is simply an ordered couple of real numbers [Russell] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |
| 14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
| 14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
| 14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
| 14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
| 14425 | A number is something which characterises collections of the same size [Russell] |
| 14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| 13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
| 14449 | There is always something psychological about inference [Russell] |
| 14463 | Existence can only be asserted of something described, not of something named [Russell] |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| 6181 | Necessity cannot be extracted from an empirical proposition [Kant] |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 6183 | Can pure reason determine the will, or are empirical conditions relevant? [Kant] |
| 6191 | The will is the faculty of purposes, which guide desires according to principles [Kant] |
| 6190 | The sole objects of practical reason are the good and the evil [Kant] |
| 12156 | Aesthetics has risen and fallen with Romanticism [Scruton] |
| 12158 | Aesthetic experience informs the world with the values of the observer [Scruton] |
| 18235 | Only human reason can confer value on our choices [Kant, by Korsgaard] |
| 6196 | People cannot come to morality through feeling, because morality must not be sensuous [Kant] |
| 18675 | Kant may rate two things as finally valuable: having a good will, and deserving happiness [Orsi on Kant] |
| 22007 | An autonomous agent has dignity [Würde], which has absolute worth [Kant, by Pinkard] |
| 18234 | The good will is unconditionally good, because it is the only possible source of value [Kant, by Korsgaard] |
| 6192 | Good or evil cannot be a thing, but only a maxim of action, making the person good or evil [Kant] |
| 6197 | Morality involves duty and respect for law, not love of the outcome [Kant] |
| 6193 | Our happiness is all that matters, not as a sensation, but as satisfaction with our whole existence [Kant] |
| 1452 | Happiness is the condition of a rational being for whom everything goes as they wish [Kant] |
| 1454 | Morality is not about making ourselves happy, but about being worthy of happiness [Kant] |
| 6194 | The highest worth for human beings lies in dispositions, not just actions [Kant] |
| 6198 | Virtue is the supreme state of our pursuit of happiness, and so is supreme good [Kant] |
| 1456 | Moral law is holy, and the best we can do is achieve virtue through respect for the law [Kant] |
| 6185 | No one would lend money unless a universal law made it secure, even after death [Kant] |
| 6187 | Universality determines the will, and hence extends self-love into altruism [Kant] |
| 6201 | Everyone (even God) must treat rational beings as ends in themselves, and not just as means [Kant] |
| 6186 | A holy will is incapable of any maxims which conflict with the moral law [Kant] |
| 6195 | Reason cannot solve the problem of why a law should motivate the will [Kant] |
| 6188 | A permanent natural order could not universalise a rule permitting suicide [Kant] |
| 6199 | Obligation does not rest on the existence of God, but on the autonomy of reason [Kant] |
| 1453 | We have to postulate something outside nature which makes happiness coincide with morality [Kant] |
| 1455 | Belief in justice requires belief in a place for justice (heaven), a time (eternity), and a cause (God) [Kant, by PG] |
| 6205 | To know if this world must have been created by God, we would need to know all other possible worlds [Kant] |
| 6204 | Using God to explain nature is referring to something inconceivable to explain what is in front of you [Kant] |
| 6206 | From our limited knowledge we can infer great virtues in God, but not ultimate ones [Kant] |
| 6202 | In all naturalistic concepts of God, if you remove the human qualities there is nothing left [Kant] |