51 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] |
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] |
22518 | The actual must be possible, because it occurred [Aristotle] |
6181 | Necessity cannot be extracted from an empirical proposition [Kant] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
16566 | Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle] |
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] |