77 ideas
19250 | Everything interesting should be recorded, with records that can be rearranged [Peirce] |
19228 | Sciences concern existence, but philosophy also concerns potential existence [Peirce] |
19241 | An idea on its own isn't an idea, because they are continuous systems [Peirce] |
19227 | Philosophy is a search for real truth [Peirce] |
19218 | Metaphysics is pointless without exact modern logic [Peirce] |
19229 | Metaphysics is the science of both experience, and its general laws and types [Peirce] |
19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
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] |
19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
1553 | No perceptible object is truly straight or curved [Protagoras] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [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] |
19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
19240 | Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce] |
19239 | There may be no reality; it's just our one desperate hope of knowing anything [Peirce] |
19252 | Objective chance is the property of a distribution [Peirce] |
19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
1549 | Everything that exists consists in being perceived [Protagoras] |
19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
19235 | How does induction get started? [Peirce] |
19236 | Induction can never prove that laws have no exceptions [Peirce] |
19251 | The worst fallacy in induction is generalising one recondite property from a sample [Peirce] |
19222 | Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce] |
19220 | We may think animals reason very little, but they hardly ever make mistakes! [Peirce] |
19255 | Generalisation is the great law of mind [Peirce] |
19242 | Generalization is the true end of life [Peirce] |
19249 | 'Know yourself' is not introspection; it is grasping how others see you [Peirce] |
19257 | Whatever is First must be sentient [Peirce] |
19248 | Reasoning involves observation, experiment, and habituation [Peirce] |
19221 | Everybody overrates their own reasoning, so it is clearly superficial [Peirce] |
19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
19230 | People should follow what lies before them, and is within their power [Peirce] |
1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
532 | Successful education must go deep into the soul [Protagoras] |
19245 | We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce] |
1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
19254 | Our laws of nature may be the result of evolution [Peirce] |
1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |