135 ideas
| 22396 | We take courage, temperance, wisdom and justice as moral, but Aristotle takes wisdom as intellectual [Foot] |
| 22496 | Wisdom only implies the knowledge achievable in any normal lifetime [Foot] |
| 22397 | Wisdom is open to all, and not just to the clever or well trained [Foot] |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 22462 | We should speak the truth, but also preserve and pursue it [Foot] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 22449 | When we say 'is red' we don't mean 'seems red to most people' [Foot] |
| 22371 | Determinism threatens free will if actions can be causally traced to external factors [Foot] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 23438 | Full rationality must include morality [Foot] |
| 23437 | Practical reason is goodness in choosing actions [Foot] |
| 22480 | Possessing the virtue of justice disposes a person to good practical rationality [Foot] |
| 23694 | All criterions of practical rationality derive from goodness of will [Foot] |
| 22372 | Not all actions need motives, but it is irrational to perform troublesome actions with no motive [Foot] |
| 22393 | I don't understand the idea of a reason for acting, but it is probably the agent's interests or desires [Foot] |
| 23436 | It is an odd Humean view to think a reason to act must always involve caring [Foot] |
| 22481 | There is no restitution after a dilemma, if it only involved the agent, or just needed an explanation [Foot, by PG] |
| 22482 | I can't understand how someone can be necessarily wrong whatever he does [Foot] |
| 22465 | We see a moral distinction between doing and allowing to happen [Foot] |
| 22384 | A 'double effect' is a foreseen but not desired side-effect, which may be forgivable [Foot] |
| 22385 | The doctrine of double effect can excuse an outcome because it wasn't directly intended [Foot] |
| 22386 | Double effect says foreseeing you will kill someone is not the same as intending it [Foot] |
| 22387 | Without double effect, bad men can make us do evil by threatening something worse [Foot] |
| 22388 | Double effect seems to rely on a distinction between what we do and what we allow [Foot] |
| 22466 | We see a moral distinction between our aims and their foreseen consequences [Foot] |
| 22467 | Acts and omissions only matter if they concern doing something versus allowing it [Foot] |
| 4692 | It is not true that killing and allowing to die (or acts and omissions) are morally indistinguishable [Foot] |
| 4694 | Making a runaway tram kill one person instead of five is diverting a fatal sequence, not initiating one [Foot] |
| 22445 | Morality shows murder is wrong, but not what counts as a murder [Foot] |
| 22444 | A moral system must deal with the dangers and benefits of life [Foot] |
| 23683 | Moral norms are objective, connected to facts about human goods [Foot, by Hacker-Wright] |
| 22392 | Morality is inescapable, in descriptive words such as 'dishonest', 'unjust' and 'uncharitable' [Foot] |
| 22451 | All people need affection, cooperation, community and help in trouble [Foot] |
| 22485 | Non-cognitivists give the conditions of use of moral sentences as facts about the speaker [Foot] |
| 22474 | Unlike aesthetic evaluation, moral evaluation needs a concept of responsibility [Foot] |
| 23684 | Morality gives everyone reasons to act, irrespective of their desires [Foot, by Hacker-Wright] |
| 23690 | We all have reason to cultivate the virtues, even when we lack the desire [Foot, by Hacker-Wright] |
| 23685 | Reason is not a motivator of morality [Foot, by Hacker-Wright] |
| 23691 | Rejecting moral rules may be villainous, but it isn't inconsistent [Foot] |
| 23686 | Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright] |
| 23693 | Practical rationality must weigh both what is morally and what is non-morally required [Foot] |
| 7258 | The forefather of modern intuitionism is Richard Price [Price,R, by Dancy,J] |
| 23431 | Human defects are just like plant or animal defects [Foot] |
| 23687 | Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright] |
| 22477 | Calling a knife or farmer or speech or root good does not involve attitudes or feelings [Foot] |
| 22486 | The mistake is to think good grounds aren't enough for moral judgement, which also needs feelings [Foot] |
| 22492 | Virtues are as necessary to humans as stings are to bees [Foot] |
| 23433 | Humans need courage like a plant needs roots [Foot] |
| 23432 | Concepts such as function, welfare, flourishing and interests only apply to living things [Foot] |
| 22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
| 22493 | Sterility is a human defect, but the choice to be childless is not [Foot] |
| 22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
| 22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
| 22487 | Moral arguments are grounded in human facts [Foot] |
| 22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |
| 22491 | Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot] |
| 23434 | There is no fact-value gap in 'owls should see in the dark' [Foot] |
| 22447 | Saying something 'just is' right or wrong creates an illusion of fact and objectivity [Foot] |
| 22452 | Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot] |
| 23439 | Principles are not ultimate, but arise from the necessities of human life [Foot] |
| 23435 | If you demonstrate the reason to act, there is no further question of 'why should I?' [Foot] |
| 22381 | Being a good father seems to depend on intentions, rather than actual abilities [Foot] |
| 22379 | The meaning of 'good' and other evaluations must include the object to which they attach [Foot] |
| 22458 | Consequentialists can hurt the innocent in order to prevent further wickedness [Foot] |
| 22460 | Why might we think that a state of affairs can be morally good or bad? [Foot] |
| 22461 | Good outcomes are not external guides to morality, but a part of virtuous actions [Foot] |
| 22464 | The idea of a good state of affairs has no role in the thought of Aristotle, Rawls or Scanlon [Foot] |
| 22497 | Deep happiness usually comes from the basic things in life [Foot] |
| 22498 | Happiness is enjoying the pursuit and attainment of right ends [Foot] |
| 23695 | Good actions can never be justified by the good they brings to their agent [Foot] |
| 22470 | A good moral system benefits its participants, and so demands reciprocity [Foot] |
| 22499 | We all know that just pretending to be someone's friend is not the good life [Foot] |
| 22402 | Most people think virtues can be displayed in bad actions [Foot] |
| 23145 | Virtues are intended to correct design flaws in human beings [Foot, by Driver] |
| 22401 | Actions can be in accordance with virtue, but without actually being virtuous [Foot] |
| 22398 | Virtues are corrective, to resist temptation or strengthen motivation [Foot] |
| 22478 | The essential thing is the 'needs' of plants and animals, and their operative parts [Foot] |
| 23692 | Good and bad are a matter of actions, not of internal dispositions [Foot] |
| 22468 | Virtues can have aims, but good states of affairs are not among them [Foot] |
| 22373 | People can act out of vanity without being vain, or even vain about this kind of thing [Foot] |
| 22495 | Someone is a good person because of their rational will, not their body or memory [Foot] |
| 22456 | Maybe virtues conflict with each other, if some virtue needs a vice for its achievement [Foot] |
| 22469 | Some virtues imply rules, and others concern attachment [Foot] |
| 22403 | Temperance is not a virtue if it results from timidity or excessive puritanism [Foot] |
| 22472 | The practice of justice may well need a recognition of human equality [Foot] |
| 22479 | Observing justice is necessary to humans, like hunting to wolves or dancing to bees [Foot] |
| 22400 | Courage overcomes the fears which should be overcome, and doesn't overvalue personal safety [Foot] |
| 22391 | Saying we 'ought to be moral' makes no sense, unless it relates to some other system [Foot] |
| 22389 | Morality no more consists of categorical imperatives than etiquette does [Foot] |
| 22395 | Moral judgements are hypothetical, because they depend on interests and desires [Foot] |
| 22448 | We sometimes just use the word 'should' to impose a rule of conduct on someone [Foot] |
| 22463 | Morality is seen as tacit legislation by the community [Foot] |
| 22459 | For consequentialism, it is irrational to follow a rule which in this instance ends badly [Foot] |
| 22502 | Refraining from murder is not made good by authenticity or self-fulfilment [Foot] |
| 4693 | The right of non-interference (with a 'negative duty'), and the right to goods/services ('positive') [Foot] |
| 22383 | Abortion is puzzling because we do and don't want the unborn child to have rights [Foot] |
| 22446 | In the case of something lacking independence, calling it a human being is a matter of choice [Foot] |
| 22380 | Some words, such as 'knife', have a meaning which involves its function [Foot] |