58 ideas
| 22140 | The greatest philosophers are methodical; it is what makes them great [Grice] |
| 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] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 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] |
| 22121 | The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont] |
| 22122 | Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont] |
| 16660 | Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau] |
| 16648 | Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus] |
| 22125 | Duns Scotus was a realist about universals [Duns Scotus, by Dumont] |
| 15386 | If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio] |
| 15387 | If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio] |
| 16632 | We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus] |
| 22127 | Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont] |
| 13094 | The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne] |
| 16650 | 'Unity' is a particularly difficult word, because things can have hidden unity [Duns Scotus] |
| 16770 | It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus] |
| 16776 | Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus] |
| 16626 | Substance is only grasped under the general heading of 'being' [Duns Scotus] |
| 16614 | Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus] |
| 10919 | What prevents a stone from being divided into parts which are still the stone? [Duns Scotus] |
| 22126 | Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont] |
| 16768 | Two things are different if something is true of one and not of the other [Duns Scotus] |
| 13856 | Conditionals are truth-functional, but we must take care with misleading ones [Grice, by Edgington] |
| 8948 | The odd truth table for material conditionals is explained by conversational conventions [Grice, by Fisher] |
| 13767 | Conditionals might remain truth-functional, despite inappropriate conversational remarks [Edgington on Grice] |
| 10990 | Conditionals are truth-functional, but unassertable in tricky cases? [Grice, by Read] |
| 14277 | A person can be justified in believing a proposition, though it is unreasonable to actually say it [Grice, by Edgington] |
| 22129 | Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont] |
| 22130 | Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont] |
| 22128 | Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont] |
| 22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
| 7751 | Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice] |
| 7752 | Only the utterer's primary intention is relevant to the meaning [Grice] |
| 7753 | We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice] |
| 22330 | Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock] |
| 18045 | Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor] |
| 18044 | Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor] |
| 10991 | Key conversational maxims are 'quality' (assert truth) and 'quantity' (leave nothing out) [Grice, by Read] |
| 18046 | Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor] |
| 22123 | The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont] |
| 22124 | We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont] |