76 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] |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 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] |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 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] |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| 6181 | Necessity cannot be extracted from an empirical proposition [Kant] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 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] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| 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] |