56 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] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 6181 | Necessity cannot be extracted from an empirical proposition [Kant] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 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] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 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] |