60 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] |
16541 | All the intrinsic properties of a thing should be deducible from its definition [Spinoza] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
6181 | Necessity cannot be extracted from an empirical proposition [Kant] |
13073 | To understand the properties we must know the essence, as with a circle [Spinoza] |
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] |
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] |