183 ideas
| 2136 | Philosophers become as divine and orderly as possible, by studying divinity and order [Plato] |
| 23767 | The winds of the discussion should decide its destination [Plato] |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 23682 | It would be absurd to be precise about the small things, but only vague about the big things [Plato] |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| 2151 | Dialectic is the only method of inquiry which uproots the things which it takes for granted [Plato] |
| 2154 | The ability to take an overview is the distinguishing mark of a dialectician [Plato] |
| 4011 | For Plato, rationality is a vision of and love of a cosmic rational order [Plato, by Taylor,C] |
| 2093 | You must never go against what you actually believe [Plato] |
| 2130 | People often merely practice eristic instead of dialectic, because they don't analyse the subject-matter [Plato] |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| 2145 | In mathematics certain things have to be accepted without further explanation [Plato] |
| 14113 | The null class is a fiction [Russell] |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| 14106 | Implication cannot be defined [Russell] |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| 14167 | The only classes are things, predicates and relations [Russell] |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| 8726 | Geometry can lead the mind upwards to truth and philosophy [Plato] |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 14117 | Numbers are properties of classes [Russell] |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| 9863 | We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato] |
| 9864 | In pure numbers, all ones are equal, with no internal parts [Plato] |
| 8727 | Geometry is not an activity, but the study of unchanging knowledge [Plato] |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| 9861 | The same thing is both one and an unlimited number at the same time [Plato] |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| 9862 | To become rational, philosophers must rise from becoming into being [Plato] |
| 21818 | Being depends on the Good, which is not itself being, but superior to being [Plato] |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| 2061 | The best things (gods, healthy bodies, good souls) are least liable to change [Plato] |
| 6562 | Plato's reality has unchanging Parmenidean forms, and Heraclitean flux [Plato, by Fogelin] |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| 2142 | The plurality of beautiful things must belong to a single class, because they have a single particular character [Plato] |
| 5094 | Plato's Forms are said to have no location in space [Plato, by Aristotle] |
| 12043 | Forms are not universals, as they don't cover every general term [Plato, by Annas] |
| 2159 | Craftsmen making furniture refer to the form, but no one manufactures the form of furniture [Plato] |
| 17 | A Form applies to a set of particular things with the same name [Plato] |
| 12122 | Plato mistakenly thought forms were totally abstracted away from matter [Bacon on Plato] |
| 5574 | Plato's Forms not only do not come from the senses, but they are beyond possibility of sensing [Plato, by Kant] |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 2133 | Knowledge must be of the permanent unchanging nature of things [Plato] |
| 2162 | If theory and practice conflict, the best part of the mind accepts theory, so the other part is of lower grade [Plato] |
| 2140 | True belief without knowledge is like blind people on the right road [Plato] |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| 2096 | Is the function of the mind management, authority and planning - or is it one's whole way of life? [Plato] |
| 6009 | Psychic conflict is clear if appetite is close to the body and reason fairly separate [Plato, by Modrak] |
| 6041 | There is a third element to the mind - spirit - lying between reason and appetite [Plato] |
| 2127 | The mind has parts, because we have inner conflicts [Plato] |
| 1737 | The soul seems to have an infinity of parts [Aristotle on Plato] |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| 5945 | The 'Republic' is a great work of rhetorical theory [Lawson-Tancred on Plato] |
| 23316 | For Plato and Aristotle there is no will; there is only rational desire for what is seen as good [Plato, by Frede,M] |
| 16 | We avoid evil either through a natural aversion, or because we have acquired knowledge [Plato] |
| 16565 | Without the surface decoration, poetry shows only appearances and nothing of what is real [Plato] |
| 2160 | Representation is two steps removed from the truth [Plato] |
| 2163 | Artists should be excluded from a law-abiding community, because they destroy the rational mind [Plato] |
| 2135 | Truth is closely related to proportion [Plato] |
| 2141 | I suggest that we forget about trying to define goodness itself for the time being [Plato] |
| 1869 | The good cannot be expressed in words, but imprints itself upon the soul [Plato, by Celsus] |
| 4115 | Plato found that he could only enforce rational moral justification by creating an authoritarian society [Williams,B on Plato] |
| 4547 | Plato measured the degree of reality by the degree of value [Nietzsche on Plato] |
| 2094 | A thing's function is what it alone can do, or what it does better than other things [Plato] |
| 2095 | If something has a function then it has a state of being good [Plato] |
| 2129 | Goodness is mental health, badness is mental sickness [Plato] |
| 12 | If we were invisible, would the just man become like the unjust? [Plato] |
| 2168 | Clever criminals do well at first, but not in the long run [Plato] |
| 2137 | The main aim is to understand goodness, which gives everything its value and advantage [Plato] |
| 2139 | Every person, and every activity, aims at the good [Plato] |
| 4007 | For Plato we abandon honour and pleasure once we see the Good [Plato, by Taylor,C] |
| 2143 | Good has the same role in the world of knowledge as the sun has in the physical world [Plato] |
| 2147 | The sight of goodness leads to all that is fine and true and right [Plato] |
| 2144 | Goodness makes truth and knowledge possible [Plato] |
| 2164 | Bad is always destructive, where good preserves and benefits [Plato] |
| 2138 | Pleasure is commonly thought to be the good, though the more ingenious prefer knowledge [Plato] |
| 2070 | Even people who think pleasure is the good admit that there are bad pleasures [Plato] |
| 2157 | Nice smells are intensive, have no preceding pain, and no bad after-effect [Plato] |
| 2134 | Philosophers are concerned with totally non-physical pleasures [Plato] |
| 2156 | There are three types of pleasure, for reason, for spirit and for appetite [Plato] |
| 2158 | Pleasure-seekers desperately seek illusory satisfaction, like filling a leaky vessel [Plato] |
| 2123 | Excessive pleasure deranges people, making the other virtues impossible [Plato] |
| 2166 | We should behave well even if invisible, for the health of the mind [Plato] |
| 2097 | Isn't it better to have a reputation for goodness than to actually be good? [Plato] |
| 19946 | Morality is a compromise, showing restraint, to avoid suffering wrong without compensation [Plato] |
| 5 | Justice is merely the interests of the stronger party [Plato] |
| 7 | Surely you don't return a borrowed weapon to a mad friend? [Plato] |
| 8 | Is right just the interests of the powerful? [Plato] |
| 15 | Sin first, then sacrifice to the gods from the proceeds [Plato] |
| 5944 | For Plato, virtue is its own reward [Lawson-Tancred on Plato] |
| 2155 | True goodness requires mental unity and harmony [Plato] |
| 2126 | A good community necessarily has wisdom, courage, self-discipline and morality [Plato] |
| 23562 | If the parts of our soul do their correct work, we will be just people, and will act justly [Plato] |
| 2092 | Simonides said morality is helping one's friends and harming one's enemies [Plato] |
| 19889 | People need society because the individual has too many needs [Plato] |
| 19890 | All exchanges in a community are for mutual benefit [Plato] |
| 10 | After a taste of mutual harm, men make a legal contract to avoid it [Plato] |
| 23561 | People doing their jobs properly is the fourth cardinal virtue for a city [Plato] |
| 2149 | Reluctant rulers make a better and more unified administration [Plato] |
| 2132 | Only rule by philosophers of integrity can keep a community healthy [Plato] |
| 2131 | Is there anything better for a community than to produce excellent people? [Plato] |
| 2152 | Dialectic is the highest and most important part of the curriculum [Plato] |
| 2148 | To gain knowledge, turn away from the world of change, and focus on true goodness [Plato] |
| 2153 | Compulsory intellectual work never remains in the mind [Plato] |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| 2630 | If Plato's God is immaterial, he will lack consciousness, wisdom, pleasure and movement, which are essential to him [Cicero on Plato] |
| 14 | If the gods are non-existent or indifferent, why bother to deceive them? [Plato] |
| 2165 | Something is unlikely to be immortal if it is imperfectly made from diverse parts [Plato] |
| 13 | Is the supreme reward for virtue to be drunk for eternity? [Plato] |
| 2120 | God is responsible for the good things, but we must look elsewhere for the cause of the bad things [Plato] |