79 ideas
7893 | Our life is the creation of our mind [Anon (Dham)] |
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] |
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] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
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] |
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] |
7898 | The world is just the illusion of an appearance [Anon (Dham)] |
4363 | The word 'person' is useless in ethics, because what counts as a good or bad self-conscious being? [Hursthouse] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
4355 | There may be inverse akrasia, where the agent's action is better than their judgement recommends [Hursthouse] |
4325 | Must all actions be caused in part by a desire, or can a belief on its own be sufficient? [Hursthouse] |
4351 | It is a fantasy that only through the study of philosophy can one become virtuous [Hursthouse] |
4340 | You are not a dishonest person if a tragic dilemma forces you to do something dishonest [Hursthouse] |
4329 | After a moral dilemma is resolved there is still a 'remainder', requiring (say) regret [Hursthouse] |
4330 | Deontologists resolve moral dilemmas by saying the rule conflict is merely apparent [Hursthouse] |
4341 | Involuntary actions performed in tragic dilemmas are bad because they mar a good life [Hursthouse] |
7894 | Hate is conquered by love [Anon (Dham)] |
4358 | Virtue may be neither sufficient nor necessary for eudaimonia [Hursthouse] |
4337 | Teenagers are often quite wise about ideals, but rather stupid about consequences [Hursthouse] |
4324 | Animals and plants can 'flourish', but only rational beings can have eudaimonia [Hursthouse] |
7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
4359 | When it comes to bringing up children, most of us think that the virtues are the best bet [Hursthouse] |
20195 | Eudaimonia first; virtue is a trait which promotes it; right acts are what virtues produce [Hursthouse, by Zagzebski] |
4336 | Any strict ranking of virtues or rules gets abandoned when faced with particular cases [Hursthouse] |
4334 | Virtue ethics is open to the objection that it fails to show priority among the virtues [Hursthouse] |
4361 | Good animals can survive, breed, feel characteristic pleasure and pain, and contribute to the group [Hursthouse] |
4349 | Virtuous people may not be fully clear about their reasons for action [Hursthouse] |
4352 | Performing an act simply because it is virtuous is sufficient to be 'morally motivated' or 'dutiful' [Hursthouse] |
4353 | If moral motivation is an all-or-nothing sense of duty, how can children act morally? [Hursthouse] |
7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
4346 | The emotions of sympathy, compassion and love are no guarantee of right action or acting well [Hursthouse] |
4339 | According to virtue ethics, two agents may respond differently, and yet both be right [Hursthouse] |
4354 | Maybe in a deeply poisoned character none of their milder character traits could ever be a virtue [Hursthouse] |
4364 | Being unusually virtuous in some areas may entail being less virtuous in others [Hursthouse] |
4356 | We are puzzled by a person who can show an exceptional virtue and also behave very badly [Hursthouse] |
7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
4327 | Deontologists do consider consequences, because they reveal when a rule might apply [Hursthouse] |
4335 | 'Codifiable' morality give rules for decisions which don't require wisdom [Hursthouse] |
4328 | Preference utilitarianism aims to be completely value-free, or empirical [Hursthouse] |
4343 | We are torn between utilitarian and deontological views of lying, depending on the examples [Hursthouse] |
4338 | Deontologists usually accuse utilitarians of oversimplifying hard cases [Hursthouse] |
4365 | We are distinct from other animals in behaving rationally - pursuing something as good, for reasons [Hursthouse] |
4350 | If people are virtuous in obedience to God, would they become wicked if they lost their faith? [Hursthouse] |
7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |