88 ideas
| 16000 | Fixed ideas should be tackled aggressively [Kierkegaard] |
| 7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
| 22087 | Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle] |
| 22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
| 16012 | Philosophy can't be unbiased if it ignores language, as that is no more independent than individuals are [Kierkegaard] |
| 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] |
| 22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
| 15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
| 22094 | Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle] |
| 16005 | I recognise knowledge, but it is the truth by which I can live and die that really matters [Kierkegaard] |
| 5651 | Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton] |
| 20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
| 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] |
| 16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
| 16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
| 2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
| 20742 | The real subject is ethical, not cognitive [Kierkegaard] |
| 16002 | The self is a combination of pairs of attributes: freedom/necessity, infinite/finite, temporal/eternal [Kierkegaard] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 22098 | Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle] |
| 22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
| 16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
| 7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
| 7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
| 22090 | For me time stands still, and I with it [Kierkegaard, by Carlisle] |
| 22096 | Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle] |
| 22097 | The ultimate in life is learning to be anxious in the right way [Kierkegaard] |
| 21909 | Ultimate knowledge is being anxious in the right way [Kierkegaard] |
| 20758 | Anxiety is staring into the yawning abyss of freedom [Kierkegaard] |
| 21910 | Our destiny is the highest pitch of world-weariness [Kierkegaard] |
| 9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
| 5650 | Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton] |
| 22095 | There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle] |
| 20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
| 7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
| 20747 | What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard] |
| 16001 | Life may be understood backwards, but it has to be lived forwards [Kierkegaard] |
| 22093 | Life is a repetition when what has been now becomes [Kierkegaard] |
| 16009 | When we seek our own 'freedom' we are just trying to avoid responsibility [Kierkegaard] |
| 22091 | Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle] |
| 7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
| 16006 | Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard] |
| 7577 | Abraham was willing to suspend ethics, for a higher idea [Kierkegaard] |
| 20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
| 7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
| 16008 | The best way to be a Christian is without 'Christianity' [Kierkegaard] |
| 20735 | We need to see that Christianity cannot be understood [Kierkegaard] |
| 22088 | Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle] |
| 7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
| 7584 | Without risk there is no faith [Kierkegaard] |