83 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] |
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] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
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] |
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] |
16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [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] |
9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
21910 | Our destiny is the highest pitch of world-weariness [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] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
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] |
7584 | Without risk there is no faith [Kierkegaard] |
7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |