86 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
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] |
15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
15409 | All occurrences of variables in atomic formulas are free [Burgess] |
15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
15412 | Models leave out meaning, and just focus on truth values [Burgess] |
15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
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] |
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] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
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] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |
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] |