147 ideas
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
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] |
24047 | An account is either a definition or a demonstration [Aristotle] |
24052 | From one thing alone we can infer its contrary [Aristotle] |
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] |
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] |
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] |
1729 | We perceive number by the denial of continuity [Aristotle] |
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] |
14162 | Mathematics doesn't care whether its entities exist [Russell] |
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] |
14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
24057 | What is prior is always potentially present in what is next in order [Aristotle] |
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] |
16752 | Sight is the essence of the eye, fitting its definition; the eye itself is just the matter [Aristotle] |
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] |
24058 | The substance is the cause of a thing's being [Aristotle] |
24055 | Matter is potential, form is actual [Aristotle] |
24040 | Scientists explain anger by the matter, dialecticians by the form and the account [Aristotle] |
14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
16157 | Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M] |
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] |
5051 | The intellect has potential to think, like a tablet on which nothing has yet been written [Aristotle] |
16723 | Perception of sensible objects is virtually never wrong [Aristotle] |
1724 | Perception necessitates pleasure and pain, which necessitates appetite [Aristotle] |
1730 | Why do we have many senses, and not just one? [Aristotle] |
17711 | Our minds take on the form of what is being perceived [Aristotle, by Mares] |
1725 | Why can't we sense the senses? And why do senses need stimuli? [Aristotle] |
1732 | Sense organs aren't the end of sensation, or they would know what does the sensing [Aristotle] |
1728 | Many objects of sensation are common to all the senses [Aristotle] |
1727 | Some objects of sensation are unique to one sense, where deception is impossible [Aristotle] |
1734 | In moral thought images are essential, to be pursued or avoided [Aristotle] |
1726 | We may think when we wish, but not perceive, because universals are within the mind [Aristotle] |
16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
1714 | Mind involves movement, perception, incorporeality [Aristotle] |
5507 | Aristotle led to the view that there are several souls, all somewhat physical [Aristotle, by Martin/Barresi] |
24051 | Soul is seen as what moves, or what is least physical, or a combination of elements [Aristotle] |
12086 | Psuché is the form and actuality of a body which potentially has life [Aristotle] |
16754 | The soul is the cause or source of movement, the essence of body, and its end [Aristotle] |
24046 | Understanding is impossible, if it involves the understanding having parts [Aristotle] |
1717 | If the soul is composed of many physical parts, it can't be a true unity [Aristotle] |
24053 | If a soul have parts, what unites them? [Aristotle] |
1721 | What unifies the soul would have to be a super-soul, which seems absurd [Aristotle] |
1735 | In a way the soul is everything which exists, through its perceptions and thoughts [Aristotle] |
24061 | If we divide the mind up according to its capacities, there are a lot of them [Aristotle] |
24062 | Self-moving animals must have desires, and that entails having imagination [Aristotle] |
1710 | Emotion involves the body, thinking uses the mind, imagination hovers between them [Aristotle] |
24039 | All the emotions seem to involve the body, simultaneously with the feeling [Aristotle] |
24056 | The soul (or parts of it) is not separable from the body [Aristotle] |
24050 | If soul is separate from body, why does it die when the body dies? [Aristotle] |
24049 | Thinkers place the soul within the body, but never explain how they are attached [Aristotle] |
1514 | Early thinkers concentrate on the soul but ignore the body, as if it didn't matter what body received the soul [Aristotle] |
2683 | Aristotle has a problem fitting his separate reason into the soul, which is said to be the form of the body [Ackrill on Aristotle] |
1718 | Does the mind think or pity, or does the whole man do these things? [Aristotle] |
13275 | The soul and the body are inseparable, like the imprint in some wax [Aristotle] |
1733 | Thinking is not perceiving, but takes the form of imagination and speculation [Aristotle] |
23307 | Aristotle makes belief a part of reason, but sees desires as separate [Aristotle, by Sorabji] |
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] |
24060 | Self-controlled follow understanding, when it is opposed to desires [Aristotle] |
4376 | Pleasure and pain are perceptions of things as good or bad [Aristotle] |
1740 | Nature does nothing in vain [Aristotle] |
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] |
24045 | Movement is spatial, alteration, withering or growth [Aristotle] |
1738 | Practical reason is based on desire, so desire must be the ultimate producer of movement [Aristotle] |
24044 | Movement can be intrinsic (like a ship) or relative (like its sailors) [Aristotle] |
14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
1739 | If all movement is either pushing or pulling, there must be a still point in between where it all starts [Aristotle] |
24064 | If something is pushed, it pushes back [Aristotle] |
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] |
24063 | What is born has growth, a prime, and a withering away [Aristotle] |