139 ideas
| 19336 | Wisdom involves the desire to achieve perfection [Leibniz] |
| 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] |
| 6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
| 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] |
| 6064 | Regresses are only vicious in the context of an explanation [McGinn] |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| 6088 | Truth is a method of deducing facts from propositions [McGinn] |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| 6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
| 6085 | The idea of truth is built into the idea of correspondence [McGinn] |
| 6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| 6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
| 6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
| 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] |
| 6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
| 6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
| 6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
| 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] |
| 6042 | The quantifier is overrated as an analytical tool [McGinn] |
| 6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| 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] |
| 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] |
| 6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
| 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] |
| 7696 | Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette] |
| 19341 | There must be a straining towards existence in the essence of all possible things [Leibniz] |
| 19428 | Because something does exist, there must be a drive in possible things towards existence [Leibniz] |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| 6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
| 6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
| 6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
| 6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
| 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] |
| 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] |
| 6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
| 6053 | Identity is as basic as any concept could ever be [McGinn] |
| 6043 | Type-identity is close similarity in qualities [McGinn] |
| 6044 | Qualitative identity is really numerical identity of properties [McGinn] |
| 6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
| 6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
| 6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
| 6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
| 6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
| 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] |
| 6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
| 6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
| 6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
| 5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
| 6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
| 6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
| 6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
| 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] |
| 6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
| 6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
| 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] |
| 19343 | We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz] |
| 19429 | The principle of determination in things obtains the greatest effect with the least effort [Leibniz] |
| 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] |
| 6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
| 6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |