58 ideas
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
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] |
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] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
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] |