80 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
23966 | The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie] |
1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
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] |
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] |
8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
24005 | We know other's emotions by explanation, contagion, empathy, imagination, or sympathy [Goldie] |
24006 | Empathy and imagining don't ensure sympathy, and sympathy doesn't need them [Goldie] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
23978 | 'Having an emotion' differs from 'being emotional' [Goldie] |
23973 | Unlike moods, emotions have specific objects, though the difference is a matter of degree [Goldie] |
23974 | Emotional intentionality as belief and desire misses out the necessity of feelings [Goldie] |
23972 | A long lasting and evolving emotion is still seen as a single emotion, such as love [Goldie] |
23992 | Some Aborigines have fifteen different words for types of fear [Goldie] |
23979 | Emotional responses can reveal to us our values, which might otherwise remain hidden [Goldie] |
23976 | If we have a 'feeling towards' an object, that gives the recognition a different content [Goldie] |
23977 | When actions are performed 'out of' emotion, they appear to be quite different [Goldie] |
23980 | It is best to see emotions holistically, as embedded in a person's life narrative [Goldie] |
23982 | If emotions are 'towards' things, they can't be bodily feelings, which lack aboutness [Goldie] |
23968 | If reasons are seen impersonally (as just causal), then feelings are an irrelevant extra [Goldie] |
23969 | We have feelings of which we are hardly aware towards things in the world [Goldie] |
23984 | An emotion needs episodes of feeling, but not continuously [Goldie] |
24001 | Moods can focus as emotions, and emotions can blur into moods [Goldie] |
23970 | Emotions are not avocado pears, with a rigid core and changeable surface [Goldie] |
23986 | Early Chinese basic emotions: joy, anger, sadness, fear, love, disliking, and liking [Goldie] |
23991 | Cross-cultural studies of facial expressions suggests seven basic emotions [Goldie] |
23985 | A basic emotion is the foundation of a hierarchy, such as anger for types of annoyance [Goldie] |
23967 | Some emotions are direct responses, and neither rational nor irrational [Goldie] |
23971 | Emotional thought is not rational, but it can be intelligible [Goldie] |
23975 | Learning an evaluative property like 'dangerous' is also learning an emotion [Goldie] |
23983 | We call emotions 'passions' because they are not as controlled as we would like [Goldie] |
23999 | Emotional control is hard, but we are responsible for our emotions over long time periods [Goldie] |
23994 | Emotions are not easily changed, as new knowledge makes little difference, and akrasia is possible [Goldie] |
23998 | Emotional control is less concerned with emotional incidents, and more with emotional tendencies [Goldie] |
23995 | Akrasia can be either overruling our deliberation, or failing to deliberate [Goldie] |
24000 | Justifying reasons say you were right; excusing reasons say your act was explicable [Goldie] |
24003 | Character traits are both possession of and lack of dispositions [Goldie] |
24002 | We over-estimate the role of character traits when explaining behaviour [Goldie] |
24004 | Psychologists suggest we are muddled about traits, and maybe they should be abandoned [Goldie] |
23993 | Our capabilities did not all evolve during the hunter gathering period [Goldie] |