64 ideas
| 7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
| 22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
| 6891 | Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner] |
| 6310 | Enquiry needs a conceptual scheme, so we should retain the best available [Quine] |
| 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] |
| 20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 12798 | Plurals can in principle be paraphrased away altogether [Quine] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| 16462 | The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine] |
| 15723 | Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine] |
| 15490 | Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB] |
| 8504 | Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt] |
| 8464 | Physical objects in space-time are just events or processes, no matter how disconnected [Quine] |
| 7924 | The notion of a physical object is by far the most useful one for science [Quine] |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| 17594 | We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine] |
| 15725 | Normal conditionals have a truth-value gap when the antecedent is false. [Quine] |
| 15722 | Conditionals are pointless if the truth value of the antecedent is known [Quine] |
| 15719 | We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine] |
| 15721 | Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine] |
| 15720 | What stays the same in assessing a counterfactual antecedent depends on context [Quine] |
| 15724 | Counterfactuals have no place in a strict account of science [Quine] |
| 4630 | Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl] |
| 20742 | The real subject is ethical, not cognitive [Kierkegaard] |
| 3131 | Quine expresses the instrumental version of eliminativism [Quine, by Rey] |
| 3988 | Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine] |
| 6311 | The firmer the links between sentences and stimuli, the less translations can diverge [Quine] |
| 6312 | We can never precisely pin down how to translate the native word 'Gavagai' [Quine] |
| 6313 | Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine] |
| 6317 | Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine] |
| 6315 | We should be suspicious of a translation which implies that a people have very strange beliefs [Quine] |
| 6314 | Weird translations are always possible, but they improve if we impose our own logic on them [Quine] |
| 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] |
| 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] |
| 7586 | God does not think or exist; God creates, and is eternal [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] |
| 7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
| 7584 | Without risk there is no faith [Kierkegaard] |