148 ideas
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| Full Idea: Though analysis gives us the truth, and nothing but the truth, yet it can never give us the whole truth | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §138) |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| Full Idea: The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §046) | |
| A reaction: This is a dangerous tendency, which has led to some daft linguistic philosophy, but Russell himself was never guilty of losing the correct perspective on the matter. |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| Full Idea: It is said that analysis is falsification, that the complex is not equivalent to the sum of its constituents and is changed when analysed into these. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: Not quite Moore's Paradox of Analysis, but close. Russell is articulating the view we now call 'holism' - that the whole is more than the sum of its parts - which I can never quite believe. |
| 24047 | An account is either a definition or a demonstration [Aristotle] |
| Full Idea: Every account is either a definition or a demonstration. | |
| From: Aristotle (De Anima [c.329 BCE], 407a24) | |
| A reaction: That is, it is either a summary of the thing's essential nature, or it is a proof of some natural fact, starting from first principles. |
| 24052 | From one thing alone we can infer its contrary [Aristotle] |
| Full Idea: One member of a pair of contraries is sufficient to discern both itself and its opposite. | |
| From: Aristotle (De Anima [c.329 BCE], 411a02) | |
| A reaction: This obviously requires prior knowledge of what the opposite is. He says you can infer the crooked from the straight. You can hardly use light in isolation to infer dark [see DA 418b17]. What's the opposite of a pig? |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| Full Idea: A definition as an analysis of an idea into its constituents is inconvenient and, I think, useless; it overlooks the fact that wholes are not, as a rule, determinate when their constituents are given. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §108) | |
| A reaction: The influence of Leibniz seems rather strong here, since he was obsessed with explaining what creates true unities. |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| Full Idea: The statement that a class is to be represented by a symbol is a definition in mathematics, and says nothing about mathematical entities. Any formula can be stated in terms of primitive ideas, so the definitions are superfluous. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §412) | |
| A reaction: [compressed wording] I'm not sure that everyone would agree with this (e.g. Kit Fine), as certain types of numbers seem to be introduced by stipulative definitions. |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| Full Idea: In the objectionable kind of infinite regress, some propositions join to constitute the meaning of some proposition, but one of them is similarly compounded, and so ad infinitum. This comes from circular definitions, where the term defined reappears. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §329) |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| Full Idea: Every proposition function …has, in addition to its range of truth, a range of significance, i.e. a range within which x must lie if φ(x) is to be a proposition at all, whether true or false. This is the first point of the theory of types. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App B:523), quoted by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: Magidor quotes this as the origin of the idea of a 'category mistake'. It is the basis of the formal theory of types, but is highly influential in philosophy generally, especially as a criterion for ruling many propositions as 'meaningless'. |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| Full Idea: I hold that what is true or false is not in general mental, and requiring a name for the true or false as such, this name can scarcely be other than 'propositions'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], Pref) | |
| A reaction: This is the Fregean and logicians' dream that that there is some fixed eternal realm of the true and the false. I think true and false concern the mental. We can talk about the 'facts' which are independent of minds, but not the 'truth'. |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| Full Idea: "The death of Caesar is true" is not, I think, the same proposition as "Caesar died". | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §478) | |
| A reaction: I suspect that it was this remark which provoked Ramsey into rebellion, because he couldn't see the difference. Nowadays we must talk first of conversational implicature, and then of language and metalanguage. |
| 14113 | The null class is a fiction [Russell] |
| Full Idea: The null class is a fiction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §079) | |
| A reaction: This does not commit him to regarding all classes as fictions - though he seems to have eventually come to believe that. The null class seems to have a role something like 'Once upon a time...' in story-telling. You can then tell truth or fiction. |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| Full Idea: Russell was the inventor of the naïve set theory so often attributed to Cantor. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| Full Idea: The two sources of order are 'between' and 'separation'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §204) |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| Full Idea: All order depends upon transitive asymmetrical relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §208) |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| Full Idea: The relation of whole and part is, it would seem, an indefinable and ultimate relation, or rather several relations, often confounded, of which one at least is indefinable. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §135) | |
| A reaction: This is before anyone had produced a mathematical account of mereology (qv). |
| 14106 | Implication cannot be defined [Russell] |
| Full Idea: A definition of implication is quite impossible. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §016) |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §037) | |
| A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'. |
| 14167 | The only classes are things, predicates and relations [Russell] |
| Full Idea: The only classes appear to be things, predicates and relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §440) | |
| A reaction: This is the first-order logic view of reality, which has begun to look incredibly impoverished in modern times. Processes certainly demand a hearing, as do modal facts. |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| Full Idea: The number of logical constants is not great: it appears, in fact, to be eight or nine. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §012) | |
| A reaction: There is, of course, lots of scope for interdefinability. No one is going to disagree greatly with his claim, so it is an interesting fact, which invites some sort of (non-platonic) explanation. |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3 | |
| A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value? |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| Full Idea: A constant is something absolutely definite, concerning which there is no ambiguity whatever. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §006) |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| Full Idea: A variable is not any term simply, but any term as entering into a propositional function. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §093) | |
| A reaction: So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107). |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| Full Idea: The word 'any' is preferable to the word 'all' where infinite classes are concerned. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §284) | |
| A reaction: The reason must be that it is hard to quantify over 'all' of the infinite members, but it is easier to say what is true of any one of them. |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| Full Idea: When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §321) | |
| A reaction: Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle. |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| Full Idea: Burali-Forti didn't discover any paradoxes, though his work suggested a paradox to Russell. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| Full Idea: The approach to practical geometry of the idealists, and especially of Kant, was that we must be certain of the premisses on their own account. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| Full Idea: Geometry no longer throws any direct light on the nature of actual space. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: This was 1903. Minkowski then contributed a geometry of space which was used in Einstein's General Theory. It looks to me as if geometry reveals the possibilities for actual space. |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| Full Idea: As a branch of pure mathematics, geometry is strictly deductive, indifferent to the choice of its premises, and to the question of whether there strictly exist such entities. It just deals with series of more than one dimension. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §352) | |
| A reaction: This seems to be the culmination of the seventeenth century reduction of geometry to algebra. Russell admits that there is also the 'study of actual space'. |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| Full Idea: The approach to practical geometry of the empiricists, notably Mill, was to show that no other set of premisses would give results consistent with experience. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: The modern phrase might be that geometry just needs to be 'empirically adequate'. The empiricists are faced with the possibility of more than one successful set of premisses, and the idealist don't know how to demonstrate truth. |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| Full Idea: Two points will define the line that joins them ('descriptive' geometry), the distance between them ('metrical' geometry), and the whole of the extended line ('projective' geometry). | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], §362) by PG - Db (ideas) | |
| A reaction: [a summary of Russell's §362] Projective Geometry clearly has the highest generality, and the modern view seems to make it the master subject of geometry. |
| 1729 | We perceive number by the denial of continuity [Aristotle] |
| Full Idea: Number we perceive by the denial of continuity. | |
| From: Aristotle (De Anima [c.329 BCE], 425a19) | |
| A reaction: This is a key thought. A being (call it 'Parmenides') which sees all Being as One would make no distinctions of identity, and so could not count anything. Why would they want numbers? |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| Full Idea: Russell defined the rationals as ratios of integers, and was therefore forced to treat the real number 5/8 as an object distinct from the rational 5/8. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| Full Idea: Ordinal numbers result from likeness among relations, as cardinals from similarity among classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §293) |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| Full Idea: It is claimed that ordinals are prior to cardinals, because they form the progression which is relevant to mathematics, but they both form progressions and have the same ordinal properties. There is nothing to choose in logical priority between them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §230) | |
| A reaction: We have an intuitive notion of the size of a set without number, but you can't actually start counting without number, so the ordering seems to be the key to the business, which (I would have thought) points to ordinals as prior. |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| Full Idea: Ordinals presuppose serial and one-one relations, whereas cardinals only presuppose one-one relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §232) | |
| A reaction: This seems to award the palm to the cardinals, for their greater logical simplicity, but I have already given the award to the ordinals in the previous idea, and I am not going back on that. |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| Full Idea: The properties of number must be capable of proof without appeal to the general properties of progressions, since cardinals can be independently defined, and must be seen in a progression before theories of progression are applied to them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §243) | |
| A reaction: Russell says there is no logical priority between ordinals and cardinals, but it is simpler to start an account with cardinals. |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| Full Idea: The ordinal numbers are defined by some relation to mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| Full Idea: The finite ordinals may be conceived as types of series; ..the ordinal number may be taken as 'n terms in a row'; this is distinct from the 'nth', and logically prior to it. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Worth nothing, because the popular and traditional use of 'ordinal' (as in learning a foreign language) is to mean the nth instance of something, rather than a whole series. |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| Full Idea: Unlike the transfinite cardinals, the transfinite ordinals do not obey the commutative law, and their arithmetic is therefore quite different from elementary arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| Full Idea: In his most recent article Cantor speaks of ordinals as types of order, not as numbers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §298) | |
| A reaction: Russell likes this because it supports his own view of ordinals as classes of serial relations. It has become orthodoxy to refer to heaps of things as 'numbers' when the people who introduced them may not have seen them that way. |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| Full Idea: We do not know that of any two different cardinal numbers one must be the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §300) | |
| A reaction: This was 1903, and I don't know whether the situation has changed. I find this thought extremely mind-boggling, given that cardinals are supposed to answer the question 'how many?' Presumably they can't be identical either. See Burali-Forti. |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| Full Idea: Real numbers are not really numbers at all, but something quite different; ...a real number, so I shall contend, is nothing but a certain class of rational numbers. ...A segment of rationals is a real number. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §258) |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| Full Idea: Some quantities cannot be measured (such as pain), and some things which are not quantities can be measured (such as certain series). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §150) |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| Full Idea: Quantity, though philosophers seem to think it essential to mathematics, does not occur in pure mathematics, and does occur in many cases not amenable to mathematical treatment. The place of quantity is taken by order. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §405) | |
| A reaction: He gives pain as an example of a quantity which cannot be treated mathematically. |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| Full Idea: The process of counting gives us no indication as to what the numbers are, as to why they form a series, or as to how it is to be proved that there are n numbers from 1 to n. Hence counting is irrelevant to the foundations of arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §129) | |
| A reaction: I take it to be the first truth in the philosophy of mathematics that if there is a system of numbers which won't do the job of counting, then that system is irrelevant. Counting always comes first. |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| Full Idea: It is possible, without the notion of unity, to define what is meant by one-to-one. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: This is the trick which enables the Greek account of numbers, based on units, to be abandoned. But when you have arranged the boys and the girls one-to-one, you have not yet got a concept of number. |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| Full Idea: It is not at present known whether, of two different infinite numbers, one must be greater and the other less. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §118) | |
| A reaction: This must refer to cardinal numbers, as ordinal numbers have an order. The point is that the proper subset is equal to the set (according to Dedekind). |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| Full Idea: The theory of infinity has two forms, cardinal and ordinal, of which the former springs from the logical theory of numbers; the theory of continuity is purely ordinal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §249) |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| Full Idea: There are two differences of infinite numbers from finite: that they do not obey mathematical induction (both cardinals and ordinals), and that the whole contains a part consisting of the same number of terms (applying only to ordinals). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §250) |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| Full Idea: The ordinal representing the whole series must be different from what represents a segment of itself, with no immediate predecessor, since the series has no last term. ω names the class progression, or generating relation of series of this class. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §291) | |
| A reaction: He is paraphrasing Cantor's original account of ω. |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| Full Idea: It must not be supposed that we can obtain a new transfinite cardinal by merely adding one to it, or even by adding any finite number, or aleph-0. On the contrary, such puny weapons cannot disturb the transfinite cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §288) | |
| A reaction: If you add one, the original cardinal would be a subset of the new one, and infinite numbers have their subsets equal to the whole, so you have gone nowhere. You begin to wonder whether transfinite cardinals are numbers at all. |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| Full Idea: For every transfinite cardinal there is an infinite collection of transfinite ordinals, although the cardinal number of all ordinals is the same as or less than that of all cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Sort that one out, and you are beginning to get to grips with the world of the transfinite! Sounds like there are more ordinals than cardinals, and more cardinals than ordinals. |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| Full Idea: The Axiom of Archimedes asserts that, given any two magnitudes of a kind, some finite multiple of the lesser exceeds the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §168 n*) |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| Full Idea: What Russell tried to show [at this time] was that Peano's Postulates (based on 'zero', 'number' and 'successor') could in turn be dispensed with, and the whole edifice built upon nothing more than the notion of 'class'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: (See Idea 5897 for Peano) Presumably you can't afford to lose the notion of 'successor' in the account. If you build any theory on the idea of classes, you are still required to explain why a particular is a member of that class, and not another. |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| Full Idea: Dedekind's demonstrations nowhere - not even where he comes to cardinals - involve any property distinguishing numbers from other progressions. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903], p.249) by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Shapiro notes that his sounds like Frege's Julius Caesar problem, of ensuring that your definition really does capture a number. Russell is objecting to mathematical structuralism. |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| Full Idea: The transfinite was obtained by denying mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §310) | |
| A reaction: This refers to the work of Dedekind and Cantor. This raises the question (about which thinkers have ceased to care, it seems), of whether it is rational to deny mathematical induction. |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| Full Idea: Finite numbers obey the law of mathematical induction: infinite numbers do not. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §183) |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| Full Idea: It used to be common to define numbers by means of 1, with 2 being 1+1 and so on. But this method was only applicable to finite numbers, made a tiresome different between 1 and the other numbers, and left + unexplained. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: Am I alone in hankering after the old approach? The idea of a 'unit' is what connected numbers to the patterns of the world. Russell's approach invites unneeded platonism. + is just 'and', and infinities are fictional extrapolations. Sounds fine to me. |
| 14117 | Numbers are properties of classes [Russell] |
| Full Idea: Numbers are to be regarded as properties of classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: If properties are then defined extensionally as classes, you end up with numbers as classes of classes. |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| Full Idea: It is impossible that the ordinals should be, as Dedekind suggests, nothing but the terms of such relations as constitute a progression. If they are anything at all, they must be intrinsically something. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §242) | |
| A reaction: This is the obvious platonist response to the incipient doctrine of structuralism. We have a chicken-and-egg problem. Bricks need intrinsic properties to make a structure. A structure isomorphic to numbers is not thereby the numbers. |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| Full Idea: Mathematics is throughout indifferent to the question whether its entities exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §434) | |
| A reaction: There is an 'if-thenist' attitude in this book, since he is trying to reduce mathematics to logic. Total indifference leaves the problem of why mathematics is applicable to the real world. |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| Full Idea: Pure mathematics is the class of all propositions of the form 'p implies q', where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §001) | |
| A reaction: Linnebo calls Russell's view here 'deductive structuralism'. Russell gives (§5) as an example that Euclid is just whatever is deduced from his axioms. |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| Full Idea: In his 1903 theory of types he distinguished between individuals, ranges of individuals, ranges of ranges of individuals, and so on. Each level was a type, and it was stipulated that for 'x is a u' to be meaningful, u must be one type higher than x. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App) | |
| A reaction: Russell was dissatisfied because this theory could not deal with Cantor's Paradox. Is this the first time in modern philosophy that someone has offered a criterion for whether a proposition is 'meaningful'? |
| 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] |
| Full Idea: Russell argues that in a statement of the form 'x is a u' (and correspondingly, 'x is a not-u'), 'x must be of different types', and hence that ''x is an x' must in general be meaningless'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], App B:524) by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: " 'Word' is a word " comes to mind, but this would be the sort of ascent to a metalanguage (to distinguish the types) which Tarski exploited. It is the simple point that a classification can't be the same as a member of the classification. |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| Full Idea: Being is that which belongs to every conceivable, to every possible object of thought. | |
| From: Bertrand Russell (The Principles of Mathematics [1903]), quoted by Stephen Read - Thinking About Logic Ch.5 | |
| A reaction: I take Russell's (or anyone's) attempt to distinguish two different senses of the word 'being' or 'exist' to be an umitigated metaphysical disaster. |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| Full Idea: Numbers, the Homeric gods, relations, chimeras and four-dimensional space all have being, for if they were not entities of a kind, we could not make propositions about them. Existence, on the contrary, is the prerogative of some only amongst the beings. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §427) | |
| A reaction: This is the analytic philosophy account of being (a long way from Heidegger). Contemporary philosophy seems to be full of confusions on this, with many writers claiming existence for things which should only be awarded 'being' status. |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| Full Idea: It would seem that whatever exists at any part of time has causal relations. This is not a distinguishing characteristic of what exists, since we have seen that two non-existent terms may be cause and effect. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Presumably he means that the non-existence of something (such as a safety rail) might the cause of an event. This is a problem for Alexander's Principle, in Idea 3534. I think we could redescribe his problem cases, to save Alexander. |
| 24057 | What is prior is always potentially present in what is next in order [Aristotle] |
| Full Idea: What is prior is always potentially present in what is next in order … - for example, the triangle in the quadrilateral, or the nutritive part of animate things in the perceptual part. | |
| From: Aristotle (De Anima [c.329 BCE], 414a28) | |
| A reaction: 'Prior' seems to be a value for Aristotle, which is never present in modern discussions of ontological relations and structure. Priority tracks back to first principles. |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| Full Idea: Among terms which appear to exist, there are, we may say, four great classes: 1) instants, 2) points, 3) terms which occupy instants but not points, 4) terms which occupy both points and instants. Analysis cannot explain 'occupy'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §437) | |
| A reaction: This is a massively reductive scientific approach to categorising existence. Note that it homes in on 'terms', which seems a rather linguistic approach, although Russell is cautious about such things. |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| Full Idea: Relations were regarded with suspicion, until philosophers working in logic and mathematics advanced reasons to doubt that we could provide anything like an adequate description of the world without developing a relational vocabulary. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], Ch.26) by John Heil - Relations | |
| A reaction: [Heil cites Russell as the only reference] A little warning light, that philosophers describing the world managed to do without real relations, and it was only for the abstraction of logic and maths that they became essential. |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| Full Idea: The property of a relation which insures that it holds between a term and itself is called by Peano 'reflexiveness', and he has shown, contrary to what was previously believed, that this property cannot be inferred from symmetry and transitiveness. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §209) | |
| A reaction: So we might say 'this is a sentence' has a reflexive relation, and 'this is a wasp' does not. While there are plenty of examples of mental properties with this property, I'm not sure that it makes much sense of a physical object. Indexicality... |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| Full Idea: Relations which are both symmetrical and transitive are formally of the nature of equality. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §209) | |
| A reaction: This is the key to the whole equivalence approach to abstraction and Frege's definition of numbers. Establish equality conditions is the nearest you can get to saying what such things are. Personally I think we can say more, by revisiting older views. |
| 16752 | Sight is the essence of the eye, fitting its definition; the eye itself is just the matter [Aristotle] |
| Full Idea: If the eye were an animal, sight would have been its soul, for sight is the substance or essence of the eye which corresponds to the formula, the eye being merely the matter of seeing; when seeing is removed it is no longer an eye,except in name. | |
| From: Aristotle (De Anima [c.329 BCE], 412b18) | |
| A reaction: This is a drastic view of form as merely function, which occasionally appears in Aristotle. To say a blind eye is not an eye is a tricky move in metaphysics. So what is it? In some sense it is still an eye. |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| Full Idea: Whatever may be an object of thought, or occur in a true or false proposition, or be counted as one, I call a term. This is the widest word in the philosophical vocabulary, which I use synonymously with unit, individual, entity (being one, and existing). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §047) | |
| A reaction: The claim of existence begs many questions, such as whether the non-existence of the Loch Ness Monster is an 'object' of thought. |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| Full Idea: It is sufficient to observe that all unities are propositions or propositional concepts, and that consequently nothing that exists is a unity. If, therefore, it is maintained that things are unities, we must reply that no things exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: The point, I presume, is that you end up as a nihilist about identities (like van Inwagen and Merricks) by mistakenly thinking (as Aristotle and Leibniz did) that everything that exists needs to have something called 'unity'. |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| Full Idea: The only kind of unity to which I can attach any precise sense - apart from the unity of the absolutely simple - is that of a whole composed of parts. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: This comes from a keen student of Leibniz, who was obsessed with unity. Russell leaves unaddressed the question of what turns some parts into a whole. |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| Full Idea: In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §070) | |
| A reaction: This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes. |
| 24058 | The substance is the cause of a thing's being [Aristotle] |
| Full Idea: The cause of its being for everything is its substance. | |
| From: Aristotle (De Anima [c.329 BCE], 415b12) | |
| A reaction: It sounds as if 'substance' here means essence. We no longer see the cause of something's being as intrinsic to the thing. Only previous causes produce things. The 'form' must be the intrinsic cause of being. |
| 24055 | Matter is potential, form is actual [Aristotle] |
| Full Idea: Matter is potentiality, whereas form is actuality. | |
| From: Aristotle (De Anima [c.329 BCE], 412a09) | |
| A reaction: Plato said mud has no Form. What did Aristotle think of that? I only ask because to me mud looks like unformed actuality. |
| 24040 | Scientists explain anger by the matter, dialecticians by the form and the account [Aristotle] |
| Full Idea: For a dialectician anger is a desire for retaliation or something like that, where for a natural scientist it is a boiling of the blood and hoot stuff around the heart. The scientist gives the matter, where the dialectician give the form and the account. | |
| From: Aristotle (De Anima [c.329 BCE], 403a30) | |
| A reaction: A nice illumination of hylomorphism. Notice that the dialectician also give the account [logos]. |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| Full Idea: The notion of change is obscured by the doctrine of substance, by a thing's nature versus its external relations, and by subject-predicate form, so that things can be different and the same. Hence the useless distinction between essential and accidental. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §443) | |
| A reaction: He goes on to object to vague unconscious usage of 'essence' by modern thinkers, but allows (teasingly) that medieval thinkers may have been precise about it. It is a fact, in common life, that things can change and be the same. Explain it! |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| Full Idea: Two terms are identical when the second belongs to every class to which the first belongs. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §026) |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| Full Idea: Russell's definition of '=' is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has a sense). | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Tractatus Logico-Philosophicus 5.5302 | |
| A reaction: This is what now seems to be a standard denial of the bizarre Leibniz claim that there never could be two things with identical properties, even, it seems, in principle. What would Leibniz made of two electrons? |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| Full Idea: There seems to be no true proposition of which it makes sense to say that it might have been false. One might as well say that redness might have been a taste and not a colour. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §430), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 29 'Analy' | |
| A reaction: Few thinkers agree with this rejection of counterfactuals. It seems to rely on Moore's idea that true propositions are facts. It also sounds deterministic. Does 'he is standing' mean he couldn't have been sitting (at t)? |
| 5051 | The intellect has potential to think, like a tablet on which nothing has yet been written [Aristotle] |
| Full Idea: The intellect is in a way potentially the object of thought, but nothing in actuality before it thinks, and the potentiality is like that of the tablet on which there is nothing actually written. | |
| From: Aristotle (De Anima [c.329 BCE], 429b31) | |
| A reaction: This passage is referred to by Leibniz, and is the origin of the concept of the 'tabula rasa'. Aristotle need not be denying innate ideas, but merely describing the phenomenology of the moment before a train of thought begins. |
| 16723 | Perception of sensible objects is virtually never wrong [Aristotle] |
| Full Idea: Perception of the special objects of sense is never in error or admits the least possible amount of falsehood. | |
| From: Aristotle (De Anima [c.329 BCE], 428b19) | |
| A reaction: This is, surprisingly, the view which was raised and largely rejected in 'Theaetetus'. It became a doctrine of Epicureanism, and seems to make Aristotle a thoroughgoing empiricist, though that is not so clear elsewhere. I think Aristotle is right. |
| 1724 | Perception necessitates pleasure and pain, which necessitates appetite [Aristotle] |
| Full Idea: Where there is perception there is also pleasure and pain, and where there are these, of necessity also appetite. | |
| From: Aristotle (De Anima [c.329 BCE], 413b23) |
| 1730 | Why do we have many senses, and not just one? [Aristotle] |
| Full Idea: A possible line of inquiry would be into the question for what purpose we have many senses and not just one. | |
| From: Aristotle (De Anima [c.329 BCE], 425b04) |
| 17711 | Our minds take on the form of what is being perceived [Aristotle, by Mares] |
| Full Idea: Aristotle famously holds that in perception our minds take on the form of what is being perceived. | |
| From: report of Aristotle (De Anima [c.329 BCE]) by Edwin D. Mares - A Priori 08.2 | |
| A reaction: [References in Aristotle needed here...] |
| 1725 | Why can't we sense the senses? And why do senses need stimuli? [Aristotle] |
| Full Idea: Why is there not also a sense of the senses themselves? And why don't the senses produce sensation without external bodies, since they contain elements? | |
| From: Aristotle (De Anima [c.329 BCE], 417a03) |
| 1732 | Sense organs aren't the end of sensation, or they would know what does the sensing [Aristotle] |
| Full Idea: Flesh is not the ultimate sense-organ. To suppose that it is requires the supposition that on contact with the object the sense-organ itself discerns what is doing the discerning. | |
| From: Aristotle (De Anima [c.329 BCE], 426b16) |
| 1728 | Many objects of sensation are common to all the senses [Aristotle] |
| Full Idea: Common sense-objects are movement, rest, number, shape and size, which are not special to any one sense, but common to all. | |
| From: Aristotle (De Anima [c.329 BCE], 418a18) |
| 1727 | Some objects of sensation are unique to one sense, where deception is impossible [Aristotle] |
| Full Idea: Now I call that sense-object 'special' that does not admit of being perceived by another sense and about which it is impossible to be deceived. | |
| From: Aristotle (De Anima [c.329 BCE], 418a15) |
| 1734 | In moral thought images are essential, to be pursued or avoided [Aristotle] |
| Full Idea: In the thinking soul, images play the part of percepts, and the assertion or negation of good or bad is invariably accompanied by avoidance or pursuit, which is the reason for the soul's never thinking without an image. | |
| From: Aristotle (De Anima [c.329 BCE], 431a15) |
| 1726 | We may think when we wish, but not perceive, because universals are within the mind [Aristotle] |
| Full Idea: Perception is of particular things, but knowledge is of universals, which are in a way in the soul itself. Thus a man may think whenever he wishes, but not perceive. | |
| From: Aristotle (De Anima [c.329 BCE], 417b22) |
| 16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
| Full Idea: In demonstration a definition of the essence is required as starting point, so that definitions which do not enable us to discover the derived properties, or which fail to facilitate even a conjecture about them, must obviously be dialectical and futile. | |
| From: Aristotle (De Anima [c.329 BCE], 402b25) | |
| A reaction: Interesting to see 'dialectical' used as a term of abuse! Illuminating. For scientific essentialism, then, demonstration is filling out the whole story once the essence has been inferred. It is circular, because essence is inferred from accidents. |
| 24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
| Full Idea: Demonstrations are both from a starting-point and have a sort of end, namely the deduction or the conclusion. | |
| From: Aristotle (De Anima [c.329 BCE], 407a25) | |
| A reaction: A starting point has to be a first principle [arché]. It has been observed that Aristotle explains demonstration very carefully, but rarely does it in his writings. |
| 16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
| Full Idea: In mathematics it is useful for the understanding of the property of the equality of the interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and the plane. | |
| From: Aristotle (De Anima [c.329 BCE], 402b18) | |
| A reaction: Although Aristotle was cautious about this, he clearly endorses here the idea that essences play an explanatory role in geometry. The caution is in the word 'useful', rather than 'vital'. How else can we arrive at this result, though? |
| 1714 | Mind involves movement, perception, incorporeality [Aristotle] |
| Full Idea: The soul seems to be universally defined by three features, so to speak, the production of movement, perception and incorporeality. | |
| From: Aristotle (De Anima [c.329 BCE], 405b12) | |
| A reaction: 'Incorporeality' begs the question, but its appearance is a phenomenon that needs explaining. 'Movement' is an interesting Greek view. Nowadays we would presumably added intentional states, and the contents and meaning of thoughts. No 'reason'? |
| 5507 | Aristotle led to the view that there are several souls, all somewhat physical [Aristotle, by Martin/Barresi] |
| Full Idea: On the later views inspired by Aristotle's 'De Anima' there was no longer just one soul, but several, and each of them had a great deal in common with the body. | |
| From: report of Aristotle (De Anima [c.329 BCE]) by R Martin / J Barresi - Introduction to 'Personal Identity' p.17 | |
| A reaction: Is this based on the faculties of sophia, episteme, nous, techne and phronesis, or is it based on the vegetative, appetitive and rational parts? The latter, I presume. Not so interesting, not so modular. |
| 24051 | Soul is seen as what moves, or what is least physical, or a combination of elements [Aristotle] |
| Full Idea: Three ways have been handed down in which people define the soul: what is most capable of moving things, since it moves itself; or a body which is the most fine-grained and least corporeal; or that it is composed of the elements. | |
| From: Aristotle (De Anima [c.329 BCE], 409b19) | |
| A reaction: A nice example of Aristotle beginning an investigation by idenfying the main explanations which have been 'handed down' from previous generations. These three aren't really in competition, and might all be true. |
| 12086 | Psuché is the form and actuality of a body which potentially has life [Aristotle] |
| Full Idea: Soul is substance as the form of a natural body which potentially has life, and since this substance is actuality, soul will be the actuality of such a body. | |
| From: Aristotle (De Anima [c.329 BCE], 412a20) | |
| A reaction: To understand what Aristotle means by 'form' you must, I'm afraid, read the 'Metaphysics'. Form isn't shape, but rather the essence which bestows the individual identity on the thing. 'Psuche is the essence of man' might be a better slogan. |
| 16754 | The soul is the cause or source of movement, the essence of body, and its end [Aristotle] |
| Full Idea: The soul is the cause [aitia] of its body alike in three senses which we explicitly recognise. It is (a) the source or origin of movement, it is (b) the end, and it is (c) the essence of the whole living body. | |
| From: Aristotle (De Anima [c.329 BCE], 415b09) | |
| A reaction: 'Aitia' also means explanation, so these are three ways to explain a human being, by what it does, why what it is for, and by what it intrinsically is. Activity, purpose and nature. |
| 24046 | Understanding is impossible, if it involves the understanding having parts [Aristotle] |
| Full Idea: How could a spatial understanding understand anything? Wiil it do so with parts, seen as magnitudes or as points? If it is points, the understanding will never get through them all. If magnitudes, it will understand things an unlimited number of times. | |
| From: Aristotle (De Anima [c.329 BCE], 407a09) | |
| A reaction: This seems to be a strong commitment to the idea that the mind is not physical because it is necessarily non-spatial. |
| 1717 | If the soul is composed of many physical parts, it can't be a true unity [Aristotle] |
| Full Idea: If the soul is composed of parts of the body, or the harmony of the elements composing the body, there will be many souls, and everywhere in the body. | |
| From: Aristotle (De Anima [c.329 BCE], 408a15) | |
| A reaction: We will ignore "everywhere in the body", but the rest seems to me exactly right. The idea of the unity of the soul is an understandable and convenient assumption, but it leads to all sorts of confusion. A crowd remains unified if half its members leave. |
| 24053 | If a soul have parts, what unites them? [Aristotle] |
| Full Idea: What is it that holds the soul together, if it by nature has parts? For surely it cannot be the body. For it seems on the contrary that it is rather the soul that holds the body together? | |
| From: Aristotle (De Anima [c.329 BCE], 411b05) | |
| A reaction: This is the hylomorphic view of a human, that the soul is the form that give unity to the matter. To do the job, presumably the form or soul need an intrinsic unity of its own, and hence cannot have parts. Apart from the need for unifying glue. |
| 1721 | What unifies the soul would have to be a super-soul, which seems absurd [Aristotle] |
| Full Idea: If soul has parts, what holds them together? Not body, because that is united by soul. If a thing unifies the soul, then THAT is the soul (unless it too has parts, which would lead to an infinite regress). Best to say the soul is a unity. | |
| From: Aristotle (De Anima [c.329 BCE], 411b10) | |
| A reaction: You don't need a 'thing' to unify something (like a crowd). I say the body holds the soul together, not physically, but because the body's value permeates thought. The body is the focused interest of the soul, like parents kept together by their child. |
| 1735 | In a way the soul is everything which exists, through its perceptions and thoughts [Aristotle] |
| Full Idea: The soul is in a way all the things that exist, for all the things that exist are objects either of perception or of thought. | |
| From: Aristotle (De Anima [c.329 BCE], 431b20) | |
| A reaction: Sounds very like Berkeley's empirical version of idealism. It also seems to imply modern externalist (anti-individualist) understandings of the mind (which strike me as false). |
| 24061 | If we divide the mind up according to its capacities, there are a lot of them [Aristotle] |
| Full Idea: For those who divide the soul into parts, and divide and separate them in accord with their capacities, the parts turn out to be very many. | |
| From: Aristotle (De Anima [c.329 BCE], 433a32) | |
| A reaction: I accept the warning. The capacities which interest me are those which seem to generate our basic ontology, but if the capacities become fine-grained, they are legion. |
| 24062 | Self-moving animals must have desires, and that entails having imagination [Aristotle] |
| Full Idea: If an animal has a desiring part, it is capable of moving itself. A desiring part, however, cannot exist without an imagination, and all imagination is either rationally calculative or perceptual. Hence in the latter the other animals also have a share. | |
| From: Aristotle (De Anima [c.329 BCE], 433b27) | |
| A reaction: Maybe if you asked people whether other animals are imaginative they would say no, but this argument is strong support for the positive view. |
| 1710 | Emotion involves the body, thinking uses the mind, imagination hovers between them [Aristotle] |
| Full Idea: Most affections (like anger) seem to involve the body, but thinking seems distinctive of the soul. But if this requires imagination, it too involves the body. Only pure mental activity would prove the separation of the two. | |
| From: Aristotle (De Anima [c.329 BCE], 403a08-) | |
| A reaction: What an observant man! Modern neuroscience is bringing out the fact that emotion is central to all mental life. We can't recognise faces without it. I say imagination is essential to pure reason, and that seems emotional too. Reason is physical. |
| 24039 | All the emotions seem to involve the body, simultaneously with the feeling [Aristotle] |
| Full Idea: The affections of the soul - spiritedness, fear, pity, confidence, joy, loving, hating - would all seem to involve the body, since at the same time as these the body is affected in a certain way. | |
| From: Aristotle (De Anima [c.329 BCE], 403a16) | |
| A reaction: Aristotle was not a physicalist, but this resembles the pilot-in-the-ship passage in Descartes, accepting the very close links. |
| 24056 | The soul (or parts of it) is not separable from the body [Aristotle] |
| Full Idea: That the soul is not separable from the body - or that certain parts of it are not, if it naturally has parts - is quite clear. | |
| From: Aristotle (De Anima [c.329 BCE], 413a04) | |
| A reaction: This doesn't make him a physicalist. I've seen him described in modern terms as a functionalist, but that makes the mind abstract and the body concrete. Perhaps he is an 'Integrationist' (as Descartes might be in his 'pilot' passage). |
| 24050 | If soul is separate from body, why does it die when the body dies? [Aristotle] |
| Full Idea: If the soul is something distinct from the mixture, why then are the being for flesh and for the other parts of the animal destroyed at the same time? | |
| From: Aristotle (De Anima [c.329 BCE], 408a25) | |
| A reaction: An obvious response to this reasonable question is to say that we see the body die, but not the soul, so the soul doesn't die. The problem is then to find some evidence for the soul's continued existence. |
| 24049 | Thinkers place the soul within the body, but never explain how they are attached [Aristotle] |
| Full Idea: There is another absurdity which follows, …since they attach the soul to a body, and place it in the body, without further determining the cause due to which this attachment comes about. …Yet this seems necessary, because this association produces action. | |
| From: Aristotle (De Anima [c.329 BCE], 407b14) | |
| A reaction: A clear statement of the interaction objection to full substance dualism. Critics say that dualists have to invoke a 'miracle' at this point. |
| 1514 | Early thinkers concentrate on the soul but ignore the body, as if it didn't matter what body received the soul [Aristotle] |
| Full Idea: Early thinkers try only to describe the soul, but they fail to go into any kind of detail about the body which is to receive the soul, as if it were possible (as it is in the Pythagorean tales) for just any old soul to be clothed in just any old body. | |
| From: Aristotle (De Anima [c.329 BCE], 407b20) | |
| A reaction: Precisely. Anyone who seriously believes that a human mind can be reincarnated in a flea needs their mind examined. Actually they need their brain examined, but that probably wouldn't impress them. I can, of course, imagine moving into a flea. |
| 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] |
| Full Idea: In 'De Anima' Aristotle cannot fit his account of separable reason - which is not the form of a body - into his general theory that the soul is the form of the body. | |
| From: comment on Aristotle (De Anima [c.329 BCE]) by J.L. Ackrill - Aristotle on Eudaimonia p.33 | |
| A reaction: A penetrating observation. Possibly the biggest challenge for a modern physicalist is to give a reductive account of 'pure' reason, in terms of brain events or brain functions. |
| 1718 | Does the mind think or pity, or does the whole man do these things? [Aristotle] |
| Full Idea: Perhaps it would be better not to say that the soul pities or learns or thinks, but that the man does in virtue of the soul. | |
| From: Aristotle (De Anima [c.329 BCE], 408b12) | |
| A reaction: This can be seen as incipient behaviourism in Aristotle's view. It echoes the functionalist view that what matters is not what the mind is, or is made of, but what it does. |
| 13275 | The soul and the body are inseparable, like the imprint in some wax [Aristotle] |
| Full Idea: We should not enquire whether the soul and the body are one thing, any more than whether the wax and its imprint are, or in general whether the matter of each thing is one with that of which it is the matter. | |
| From: Aristotle (De Anima [c.329 BCE], 412b06) | |
| A reaction: This is his hylomorphist view of objects, so that the soul is the 'form' which bestows identity (and power) on the matter of which it is made. This remark is thoroughly physicalist. |
| 1733 | Thinking is not perceiving, but takes the form of imagination and speculation [Aristotle] |
| Full Idea: Thinking, then, is something other than perceiving, and its two kinds are held to be imagination and supposition. | |
| From: Aristotle (De Anima [c.329 BCE], 427b28) |
| 23307 | Aristotle makes belief a part of reason, but sees desires as separate [Aristotle, by Sorabji] |
| Full Idea: Aristotle insists [against Plato] that desires, even rational desires, are a capacity distinct from reason, as is perception. Belief is included within reason. And he sometimes distinguishes steps of reasoning from insight. | |
| From: report of Aristotle (De Anima [c.329 BCE], 428-432) by Richard Sorabji - Rationality 'Shifting' | |
| A reaction: So the standard picture of desire as permanently in conflict with reason comes from Aristotle. Maybe Plato is right on that one (though he doesn't say much about it). Since objectivity needs knowledge, reason does need belief. |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| Full Idea: The relations in an abstraction principle are always constituted by possession of a common property (which is imprecise as it relies on 'predicate'), ..so we say a common property of two terms is any third term to which both have the same relation. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: This brings out clearly the linguistic approach of the modern account of abstraction, where the older abstractionism was torn between the ontology and the epistemology (that is, the parts of objects, or the appearances of them in the mind). |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| Full Idea: The principle of Abstraction says that whenever a relation with instances is symmetrical and transitive, then the relation is not primitive, but is analyzable into sameness of relation to some other term. ..This is provable and states a common assumption. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: At last I have found someone who explains the whole thing clearly! Bertrand Russell was wonderful. See other ideas on the subject from this text, for a proper understanding of abstraction by equivalence. |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| Full Idea: The possession of a common property of a certain type always leads to a symmetrical transitive relation. The principle of Abstraction asserts the converse, that such relations only spring from common properties of the above type. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: The type of property is where only one term is applicable to it, such as the magnitude of a quantity, or the time of an event. So symmetrical and transitive relations occur if and only if there is a property of that type. |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| Full Idea: A proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §051) | |
| A reaction: Russell says in his Preface that he took over this view of propositions from G.E. Moore. They are now known as 'Russellian' propositions, which are mainly distinguished by not being mental event, but by being complexes out in the world. |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| Full Idea: Russell often treated propositions as facts, but discovered that correspondence then became useless for explaining truth, since every meaningful expression, true or false, expresses a proposition. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Donald Davidson - Truth and Predication 6 | |
| A reaction: So 'pigs fly' would have to mean pigs actually flying (which they don't). They might correspond to possible situations, but only if pigs might fly. What do you make of 'circles are square'? Russell had many a sleepless night over that. |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| Full Idea: A proposition is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §054) | |
| A reaction: The question of the 'unity of the proposition' led to a prolonged debate. |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| Full Idea: Moore and Russell reacted strongly against the idea that the unity of the proposition depended on human acts of judgement. ...Russell decided that unless the unity is explained in terms of the proposition itself, there can be no objective truth. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], p.42) by Donald Davidson - Truth and Predication 5 | |
| A reaction: Put like this, the Russellian view strikes me as false. Effectively he is saying that a unified proposition is the same as a fact. I take a proposition to be a brain event, best labelled by Frege as a 'thought'. Thoughts may not even have parts. |
| 24060 | Self-controlled follow understanding, when it is opposed to desires [Aristotle] |
| Full Idea: Self-controlled people, even when they desire and have an appetite for things, do not do these things for which they have the desire, but instead follow the understanding. | |
| From: Aristotle (De Anima [c.329 BCE], 433a06) | |
| A reaction: If modern discussions would stop talking of 'weakness of will', and talk instead of 'control' and its lack, the whole issue would become clearer. Akrasia is then seen, for example, as an action of the whole person, not of some defective part. |
| 4376 | Pleasure and pain are perceptions of things as good or bad [Aristotle] |
| Full Idea: To experience pleasure or pain is to be active with the perceptive mean in relation to good or bad as such. | |
| From: Aristotle (De Anima [c.329 BCE], 431a10) | |
| A reaction: A bizarre view which is interesting, but strikes me as wrong. We are drawn towards pleasure, but judgement can pull us away again, and 'good' is in the judgement, not in the feeling. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 1740 | Nature does nothing in vain [Aristotle] |
| Full Idea: Nature does nothing in vain. | |
| From: Aristotle (De Anima [c.329 BCE], 434a31) |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| Full Idea: On the whole it is not worthwhile preserving the word 'cause': it is enough to say, what is far less misleading, that any two configurations allow us to infer any other. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §460) | |
| A reaction: Russell spelled this out fully in a 1912 paper. This sounds like David Hume, but he prefers to talk of 'habit' rather than 'inference', which might contain a sneaky necessity. |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| Full Idea: Some people would hold that two moments of time, or two points of space, imply each other's existence; yet the relation between these cannot be said to be causal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Famously, Russell utterly rejected causation a few years after this. The example seems clearer if you say that two points or moments can imply at least one point or instant between them, without causing them. |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| Full Idea: For us, as pure mathematicians, the laws of motion and the law of gravitation are not properly laws at all, but parts of the definition of a certain kind of matter. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §459) | |
| A reaction: The 'certain kind of matter' is that which has 'mass'. Since these are paradigm cases of supposed laws, this is the beginning of the end for real laws of nature, and good riddance say I. See Mumford on this. |
| 24045 | Movement is spatial, alteration, withering or growth [Aristotle] |
| Full Idea: There a four sorts of movement - spatial movement, alteration, withering and growth. | |
| From: Aristotle (De Anima [c.329 BCE], 406a12) | |
| A reaction: Large parts of Aristotle's writings attempt to explain these four. |
| 1738 | Practical reason is based on desire, so desire must be the ultimate producer of movement [Aristotle] |
| Full Idea: There seem to be two producers of movement, either desire or practical intellect, but practical reason begins in desire. | |
| From: Aristotle (De Anima [c.329 BCE], 433a16) |
| 24044 | Movement can be intrinsic (like a ship) or relative (like its sailors) [Aristotle] |
| Full Idea: It is not necessary for what moves things to be itself moving. For a thing can be moving in two ways - with reference to something else, or intrinsically. A ship is moving intrinsically, but sailors move because they are in something that is moving. | |
| From: Aristotle (De Anima [c.329 BCE], 406a03) | |
| A reaction: I love the way that Aristotle is desperate to explain the puzzle of movement, yet we just take it for granted. Very illuminating about puzzles. Newton's First Law of Motion. |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| Full Idea: The concept of motion is logically subsequent to that of occupying as place at a time, and also to that of change. Motion is the occupation, by one entity, of a continuous series of places at a continuous series of times. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) | |
| A reaction: This is Russell's famous theory of motion, which came to be called the 'At-At' theory (at some place at some time). It seems to mathematically pin down motion all right, but seems a bit short on the poetry of the thing. |
| 1739 | If all movement is either pushing or pulling, there must be a still point in between where it all starts [Aristotle] |
| Full Idea: Every movement being either a push or a pull, there must be a still point as with the circle, and this will be the point of departure for the movement. | |
| From: Aristotle (De Anima [c.329 BCE], 433b26) |
| 24064 | If something is pushed, it pushes back [Aristotle] |
| Full Idea: What has pushed something else makes the latter push as well. | |
| From: Aristotle (De Anima [c.329 BCE], 435b30) | |
| A reaction: Aristotle seems to have spotted that this is intrinsic to massive bodies, and is not just friction etc. Newton adds a vector to Aristotle's insight. |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| Full Idea: A force is the supposed cause of acceleration, ...but an acceleration is a mere mathematical fiction, a number, not a physical fact. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §448) | |
| A reaction: This rests on his at-at theory of motion, in Idea 14168. I'm not sure that if I fell off a cliff I could be reassured on the way down that my acceleration was just a mathematical fiction. |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| Full Idea: I won't discuss whether points are unities or simple terms, but whether space is an aggregate of them. ..There is no geometry without points, nothing against them, and logical reasons in their favour. Space is the extension of the concept 'point'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §423) |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| Full Idea: To the mathematician as such there is no relevant distinction between the instants of time and the points on a line. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §387) | |
| A reaction: This is the germ of the modern view of space time, which is dictated by the mathematics, rather than by our intuitions or insights into what is actually going on. |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| Full Idea: The universe is a somewhat ambiguous term: it may mean all the things that exist at a single moment, or all things that ever have existed or will exist, or the common quality of whatever exists. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) |
| 24063 | What is born has growth, a prime, and a withering away [Aristotle] |
| Full Idea: What has been born must have growth, a prime of life, and a time of withering away. | |
| From: Aristotle (De Anima [c.329 BCE], 434a23) | |
| A reaction: Modern biologists don't seem much interested in the 'prime of life', but for Aristotle it is crucial, as the fulfilment of a thing's essential nature. Nietzsche would probably agree with Aristotle on this. We dread seeing one period of life as 'superior'. |