162 ideas
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
12865 | Analytic philosophers may prefer formal systems because natural language is such mess [Simons] |
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] |
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] |
12815 | Classical mereology doesn't apply well to the objects around us [Simons] |
12832 | Complement: the rest of the Universe apart from some individual, written x-bar [Simons] |
12834 | Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons] |
12819 | A 'part' has different meanings for individuals, classes, and masses [Simons] |
12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |
12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
12846 | A 'group' is a collection with a condition which constitutes their being united [Simons] |
12848 | The same members may form two groups [Simons] |
12861 | 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons] |
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] |
12876 | Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons] |
14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
12845 | Some natural languages don't distinguish between singular and plural [Simons] |
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] |
14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
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] |
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] |
14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
14141 | Ordinals are defined through mathematical induction [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] |
14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [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] |
14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
14147 | Denying mathematical induction gave us the transfinite [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] |
12838 | Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons] |
12842 | There are real relational changes, as well as bogus 'Cambridge changes' [Simons] |
12841 | I don't believe in processes [Simons] |
12836 | Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons] |
12882 | A wave is maintained by a process, but it isn't a process [Simons] |
12880 | Moments are things like smiles or skids, which are founded on other things [Simons] |
12883 | Moving disturbances are are moments which continuously change their basis [Simons] |
12881 | A smiling is an event with causes, but the smile is a continuant without causes [Simons] |
12840 | I do not think there is a general identity condition for events [Simons] |
12839 | Relativity has an ontology of things and events, not on space-time diagrams [Simons] |
12879 | Independent objects can exist apart, and maybe even entirely alone [Simons] |
12847 | Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons] |
12862 | Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons] |
12863 | Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons] |
12858 | Mixtures disappear if nearly all of the mixture is one ingredient [Simons] |
12859 | A mixture can have different qualities from its ingredients. [Simons] |
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] |
12850 | To individuate something we must pick it out, but also know its limits of variation [Simons] |
12860 | Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons] |
14164 | The only unities are simples, or wholes composed of parts [Russell] |
12886 | A whole requires some unique relation which binds together all of the parts [Simons] |
14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
12835 | Does Tibbles remain the same cat when it loses its tail? [Simons] |
12857 | Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons] |
12820 | Without extensional mereology two objects can occupy the same position [Simons] |
12866 | Composition is asymmetric and transitive [Simons] |
12867 | A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons] |
12864 | We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons] |
12814 | Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons] |
12817 | 'Mereological extensionality' says objects with the same parts are identical [Simons] |
12833 | If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons] |
12849 | Sums are more plausible for pluralities and masses than they are for individuals [Simons] |
12877 | Sums of things in different categories are found within philosophy. [Simons] |
12888 | The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons] |
12871 | Objects have their essential properties because of the kind of objects they are [Simons] |
12870 | We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons] |
12873 | Original parts are the best candidates for being essential to artefacts [Simons] |
12874 | An essential part of an essential part is an essential part of the whole [Simons] |
14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
12837 | Four dimensional-objects are stranger than most people think [Simons] |
12856 | Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons] |
12885 | Objects like chess games, with gaps in them, are thereby less unified [Simons] |
12854 | An entrepreneur and a museum curator would each be happy with their ship at the end [Simons] |
12855 | The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons] |
12872 | The zygote is an essential initial part, for a sexually reproduced organism [Simons] |
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] |
12889 | The limits of change for an individual depend on the kind of individual [Simons] |
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] |
19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
14111 | A proposition is a unity, and analysis destroys it [Russell] |
12843 | With activities if you are doing it you've done it, with performances you must finish to have done it [Simons] |
12875 | One false note doesn't make it a performance of a different work [Simons] |
467 | A virtue is a combination of intelligence, strength and luck [Ion] |
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] |