155 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] |
6779 | Instrumentalists say distinctions between observation and theory vanish with ostensive definition [Bird] |
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] |
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] |
6780 | Anti-realism is more plausible about laws than about entities and theories [Bird] |
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] |
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] |
6796 | Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird] |
6797 | Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird] |
22303 | It makes no sense to say that a true proposition could have been false [Russell] |
6800 | Many philosophers rate justification as a more important concept than knowledge [Bird] |
6786 | As science investigates more phenomena, the theories it needs decreases [Bird] |
6792 | If theories need observation, and observations need theories, how do we start? [Bird] |
6757 | Explanation predicts after the event; prediction explains before the event [Bird] |
6777 | Realists say their theories involve truth and the existence of their phenomena [Bird] |
6804 | There is no agreement on scientific method - because there is no such thing [Bird] |
6805 | Relativity ousted Newtonian mechanics despite a loss of simplicity [Bird] |
6778 | Instrumentalists regard theories as tools for prediction, with truth being irrelevant [Bird] |
6775 | Induction is inference to the best explanation, where the explanation is a law [Bird] |
6791 | If Hume is right about induction, there is no scientific knowledge [Bird] |
6790 | Anything justifying inferences from observed to unobserved must itself do that [Bird] |
6738 | Any conclusion can be drawn from an induction, if we use grue-like predicates [Bird] |
6739 | Several months of observing beech trees supports the deciduous and evergreen hypotheses [Bird] |
6799 | We normally learn natural kinds from laws, but Goodman shows laws require prior natural kinds [Bird] |
6798 | Bayesianism claims to find rationality and truth in induction, and show how science works [Bird] |
6752 | The objective component of explanations is the things that must exist for the explanation [Bird] |
6754 | We talk both of 'people' explaining things, and of 'facts' explaining things [Bird] |
6750 | Explanations are causal, nomic, psychological, psychoanalytic, Darwinian or functional [Bird] |
6761 | Contrastive explanations say why one thing happened but not another [Bird] |
6758 | 'Covering law' explanations only work if no other explanations are to be found [Bird] |
6759 | Livers always accompany hearts, but they don't explain hearts [Bird] |
6756 | Probabilistic-statistical explanations don't entail the explanandum, but makes it more likely [Bird] |
6760 | An operation might reduce the probability of death, yet explain a death [Bird] |
6785 | Inference to the Best Explanation is done with facts, so it has to be realist [Bird] |
6788 | Maybe bad explanations are the true ones, in this messy world [Bird] |
6787 | Which explanation is 'best' is bound to be subjective, and no guide to truth [Bird] |
6751 | Maybe explanation is so subjective that it cannot be a part of science [Bird] |
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] |
6776 | Natural kinds are those that we use in induction [Bird] |
6767 | Rubies and sapphires are both corundum, with traces of metals varying their colours [Bird] |
6768 | Tin is not one natural kind, but appears to be 21, depending on isotope [Bird] |
6770 | Membership of a purely random collection cannot be used as an explanation [Bird] |
6771 | Natural kinds may overlap, or be sub-kinds of one another [Bird] |
6773 | If F is a universal appearing in a natural law, then Fs form a natural kind [Bird] |
6769 | In the Kripke-Putnam view only nuclear physicists can know natural kinds [Bird] |
6774 | Darwinism suggests that we should have a native ability to detect natural kinds [Bird] |
6764 | Nominal essence of a natural kind is the features that make it fit its name [Bird] |
6766 | Jadeite and nephrite are superficially identical, but have different composition [Bird] |
6808 | Reference to scientific terms is by explanatory role, not by descriptions [Bird] |
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] |
6753 | Laws are more fundamental in science than causes, and laws will explain causes [Bird] |
6762 | Newton's laws cannot be confirmed individually, but only in combinations [Bird] |
6763 | Parapsychology is mere speculation, because it offers no mechanisms for its working [Bird] |
6772 | Existence requires laws, as inertia or gravity are needed for mass or matter [Bird] |
6740 | 'All uranium lumps are small' is a law, but 'all gold lumps are small' is not [Bird] |
6741 | There can be remarkable uniformities in nature that are purely coincidental [Bird] |
6742 | A law might have no instances, if it was about things that only exist momentarily [Bird] |
6743 | If laws are just instances, the law should either have gaps, or join the instances arbitrarily [Bird] |
6744 | Where is the regularity in a law predicting nuclear decay? [Bird] |
6747 | Laws cannot explain instances if they are regularities, as something can't explain itself [Bird] |
6746 | There may be many laws, each with only a few instances [Bird] |
6748 | Similar appearance of siblings is a regularity, but shared parents is what links them [Bird] |
6749 | We can only infer a true regularity if something binds the instances together [Bird] |
6803 | If we only infer laws from regularities among observations, we can't infer unobservable entities. [Bird] |
6801 | Accidental regularities are not laws, and an apparent regularity may not be actual [Bird] |
6745 | A regularity is only a law if it is part of a complete system which is simple and strong [Bird] |
6802 | With strange enough predicates, anything could be made out to be a regularity [Bird] |
6789 | If flame colour is characteristic of a metal, that is an empirical claim needing justification [Bird] |
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] |
6807 | In Newton mass is conserved, but in Einstein it can convert into energy [Bird] |
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] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |