83 ideas
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
10354 | Correspondence could be with other beliefs, rather than external facts [Kusch] |
10353 | Tarskians distinguish truth from falsehood by relations between members of sets [Kusch] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [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] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [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] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
18459 | Diversity arises from the power of unity [Porphyry] |
10337 | We can have knowledge without belief, if others credit us with knowledge [Kusch] |
10357 | Methodological Solipsism assumes all ideas could be derived from one mind [Kusch] |
18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
10339 | Foundations seem utterly private, even from oneself at a later time [Kusch] |
10331 | Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch] |
10338 | The coherentist restricts the space of reasons to the realm of beliefs [Kusch] |
10340 | Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch] |
10345 | Individual coherentism cannot generate the necessary normativity [Kusch] |
10350 | Cultures decide causal routes, and they can be critically assessed [Kusch] |
10343 | Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch] |
10341 | Justification depends on the audience and one's social role [Kusch] |
10334 | Testimony is an area in which epistemology meets ethics [Kusch] |
10336 | Powerless people are assumed to be unreliable, even about their own lives [Kusch] |
10324 | Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch] |
10327 | Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch] |
10329 | Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch] |
10330 | A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch] |
10325 | Vindicating testimony is an expression of individualism [Kusch] |
10335 | Myths about lonely genius are based on epistemological individualism [Kusch] |
10323 | Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch] |
10348 | Private justification is justification to imagined other people [Kusch] |
18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
10349 | To be considered 'an individual' is performed by a society [Kusch] |
18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
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] |
10358 | Often socialising people is the only way to persuade them [Kusch] |
18464 | Justice is each person fulfilling his function [Porphyry] |
18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
10333 | Communitarianism in epistemology sees the community as the primary knower [Kusch] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
10351 | Natural kinds are social institutions [Kusch] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
10332 | Omniscience is incoherent, since knowledge is a social concept [Kusch] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |