79 ideas
| 5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
| 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] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [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] |
| 5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
| 6346 | The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz] |
| 6351 | Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz] |
| 6374 | To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz] |
| 6355 | Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz] |
| 6359 | Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz] |
| 6366 | Perception causes beliefs in us, without inference or justification [Pollock/Cruz] |
| 6362 | Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz] |
| 6371 | Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz] |
| 6373 | Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz] |
| 6353 | People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz] |
| 6361 | Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz] |
| 6357 | Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz] |
| 6363 | Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz] |
| 6365 | Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz] |
| 6354 | Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz] |
| 6367 | Coherence theories isolate justification from the world [Pollock/Cruz] |
| 6370 | Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz] |
| 6358 | One belief may cause another, without being the basis for the second belief [Pollock/Cruz] |
| 6364 | We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz] |
| 6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
| 6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
| 6360 | Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz] |
| 23872 | 'Society determines consciousness' is contradictory; society only exists in minds [Weil on Marx/Engels] |
| 5277 | Life is not determined by consciousness, but consciousness by life [Marx/Engels] |
| 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] |
| 5280 | Language co-exists with consciousness, and makes it social [Marx/Engels] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 5281 | Consciousness is a social product [Marx/Engels] |
| 5276 | The nature of an individual coincides with what they produce and how they produce it [Marx/Engels] |
| 5289 | When aristocracy or the bourgeoisie dominate, certain values dominate with them [Marx/Engels] |
| 5274 | Young Hegelians proposed changing our present consciousness for liberating critical consciousness [Marx/Engels] |
| 21992 | Producing their own subsistence distinguishes men from animals [Marx/Engels] |
| 5275 | Men distinguish themselves from animals when they begin to produce their means of subsistence [Marx/Engels] |
| 5292 | Individuals are mutually hostile unless they group together in competition with other groups [Marx/Engels] |
| 5293 | Only in community are people able to cultivate their gifts, and therefore be free [Marx/Engels] |
| 5273 | Young Hegelians think consciousness is chains for men, where old Hegelians think it the bond of society [Marx/Engels] |
| 5282 | If the common interest imposes on the individual, his actions become alienated and enslaving [Marx/Engels] |
| 5283 | In communist society we are not trapped in one activity, but can act freely [Marx/Engels] |
| 5288 | The class controlling material production also controls mental production [Marx/Engels] |
| 5290 | The revolutionary class is opposed to 'class', and represents all of society [Marx/Engels] |
| 5294 | To assert themselves as individuals, the proletarians must overthrow the State [Marx/Engels] |
| 5285 | Slavery cannot be abolished without the steam-engine [Marx/Engels] |
| 5284 | Communism abolishes private property and dissolves the powerful world market [Marx/Engels] |
| 5291 | The law says private property is the result of the general will [Marx/Engels] |
| 5279 | Human history must always be studied in relation to industry and exchange [Marx/Engels] |
| 5286 | Most historians are trapped in the illusions of their own epoch [Marx/Engels] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |