151 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. |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
From: Plato (Parmenides [c.364 BCE], 135e) |
232 | Opposites are as unlike as possible [Plato] |
Full Idea: Opposites are as unlike as possible. | |
From: Plato (Parmenides [c.364 BCE], 159a) |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
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. |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
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. |
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. |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
From: Plato (Parmenides [c.364 BCE], 144a) | |
A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
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. |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
From: Plato (Parmenides [c.364 BCE], 155d) |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
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. |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
From: Plato (Parmenides [c.364 BCE], 134c) |
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. |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
From: Plato (Parmenides [c.364 BCE], 135c) |
227 | You must always mean the same thing when you utter the same name [Plato] |
Full Idea: You must always mean the same thing when you utter the same name. | |
From: Plato (Parmenides [c.364 BCE], 147d) |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
220 | The concept of a master includes the concept of a slave [Plato] |
Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
From: Plato (Parmenides [c.364 BCE], 133e) |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
From: Plato (Parmenides [c.364 BCE], 133c) |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
From: Plato (Parmenides [c.364 BCE], 149e) |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
From: Plato (Parmenides [c.364 BCE], 131b) |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
From: Plato (Parmenides [c.364 BCE], 132e) |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
From: Plato (Parmenides [c.364 BCE], 132c) |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
From: Plato (Parmenides [c.364 BCE], 131a) |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
From: Plato (Parmenides [c.364 BCE], 132a) |
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. |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
From: Plato (Parmenides [c.364 BCE], 157d) | |
A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
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. |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
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! |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
From: Plato (Parmenides [c.364 BCE], 146b) | |
A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
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)? |
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. |
23616 | Legal excuses are duress, ignorance, and diminished responsibility [McMahan] |
Full Idea: The common legal practice is to distinguish three broad categories of excuse: duress, epistemic limitation, and diminished responsibility. | |
From: Jeff McMahan (Killing in War [2009], 3.2.1) | |
A reaction: McMahan cites these with reference to soldiers in wartime, but they have general application. The third one seems particularly open to very wide interpretation. Presumably I can't be excused by just being irresponsible. |
23606 | Liberty Rights are permissions, and Claim Rights are freedom from intervention [McMahan] |
Full Idea: There are two types of right. A Liberty right is merely a permission, meaning it is not wrong to do it. But a Claim right is a right against intervention, meaning no one has a liberty right to prevent it. | |
From: Jeff McMahan (Killing in War [2009], 2.3) | |
A reaction: There must also be a third type of right, which requires other people to perform actions on your behalf. If you pay for a book in a shop, you must then be given the book. |
23620 | A person or state may be attacked if they are responsible for an unjustified threat [McMahan] |
Full Idea: It is a necessary condition of liability to defensive attack that one be morally responsible for posing an objectively unjustified threat. | |
From: Jeff McMahan (Killing in War [2009], 4.1.1) | |
A reaction: This implies that one may not actually be doing the threatening (but merely ordering it, or enabling it). McMahan aims to have the same criteria for wartime as for peacetime. He denies Anscombe's claim that merely posing the threat is enough. |
23598 | You (e.g. a police officer) are not liable to attack just because you pose a threat [McMahan] |
Full Idea: It is false that by posing a threat to another, one necessarily makes oneself liable to defensive action. A police officer who shoots an active murderer does not thereby by make herself liable to defensive action. | |
From: Jeff McMahan (Killing in War [2009], 1.2) | |
A reaction: This is one of his arguments against the moral equality of combatants. It is not morally OK to shoot all the local soldiers when you unjustly invade a territory. Sounds right to me. |
23594 | Wars can be unjust, despite a just cause, if they are unnecessary or excessive or of mixed cause [McMahan] |
Full Idea: Wars can be unjust despite having a just cause, because they are not actually needed, or they will cause excessive harm, or they also pursue some unjust causes. | |
From: Jeff McMahan (Killing in War [2009], 1.1) | |
A reaction: [compressed] The point is that older writers often think that a 'just cause' is sufficient. He is obviously right. |
23597 | Just war theory says all and only persons posing a threat are liable to attack [McMahan] |
Full Idea: In mainstream just war theory (Anscombe, Nagel, Walzer) the criterion of liability to attack is simply posing a threat. Since all combatants pose a threat to each other, they are morally liable to attack; because noncombatants do not, they are not liable. | |
From: Jeff McMahan (Killing in War [2009], 1.2) | |
A reaction: McMahan says that the distinction between legitimate and illegitimate targets rests mostly on this basis. The problem is that a huge range of unarmed people can also pose various degrees of threat. |
23595 | The worst unjustified wars have no aim at all [McMahan] |
Full Idea: The most serious reason why a war might be unjustified is that it lacks any justifying aim at all. | |
From: Jeff McMahan (Killing in War [2009], 1.1) | |
A reaction: It seems that Louis XIV invaded the Netherlands in around 1674 purely to enhance his own glory. That strikes me as worse. I supposed Ghenghis Khan invaded places simply because he enjoyed fighting. |
23619 | A defensive war is unjust, if it is responding to a just war [McMahan] |
Full Idea: It is possible for a defensive war to be unjust, when the defensive war to which it is a response is a just war. | |
From: Jeff McMahan (Killing in War [2009], 3.3.3) | |
A reaction: An example might be a state resisting an intervention from outside, when the state is in the process of exterminating some unwanted minority. Or perhaps the invaders are crossing the state's territory to achieve some admirable end. |
23600 | Proportionality in fighting can't be judged independently of the justice of each side [McMahan] |
Full Idea: There is simply no satisfactory understanding of proportionality in war that can be applied independently of whether the acts that are evaluated support a just or an unjust cause. | |
From: Jeff McMahan (Killing in War [2009], 1.3) | |
A reaction: He rejects traditional just war theory, which sees both sides as morally equal in combat, and hence equally subject to the principles of proportional response. But the just can then be harsher, when their just principles should make them milder. |
23603 | Can an army start an unjust war, and then fight justly to defend their own civilians? [McMahan] |
Full Idea: There is a paradox if the unjust are justified in fighting the just in order to protect their own civilians who have been endangered by the starting of an unjust war. | |
From: Jeff McMahan (Killing in War [2009], 2.1) | |
A reaction: [my summary of MacMahan pp.48-49] It suggests that in a war there may be local concepts of justice which are at odds with the general situation - which is the ad bellum/in bello distinction. But this is the justice of fighting, not how it is conducted. |
23611 | Soldiers cannot freely fight in unjust wars, just because they behave well when fighting [McMahan] |
Full Idea: We must stop reassuring soldiers that they act permissibly when they fight in an unjust war, provided that they conduct themselve honorably on the battlefield by fighting in accordance with the rules of engagement. | |
From: Jeff McMahan (Killing in War [2009], 2.8) | |
A reaction: This culminates McMahan's arguments against the moral equality of combatants, and against the sharp division of justice of war from justice in war. How rare it is for philosophy to culminate in a policy recommendation! |
23612 | The law of war differs from criminal law; attacking just combatants is immoral, but legal [McMahan] |
Full Idea: Unlike domestic criminal law, the law of war is designed not to protect moral rights but to prevent harm. …This means when unjust combatants attack just combatants they violate their moral rights, yet they act within their legal rights. | |
From: Jeff McMahan (Killing in War [2009], 3.1.1) | |
A reaction: He says we must bring the law of war much closer to the morality of war. If there is any hope of slowly eliminating war, it may lie in reforms such as these. |
23617 | If the unjust combatants are morally excused they are innocent, so how can they be killed? [McMahan] |
Full Idea: If most unjust combatants are morally innocent because they are excused, and if it is wrong to intentionally kill morally innocent people, then a contingent form of pacificism may be inescapable. | |
From: Jeff McMahan (Killing in War [2009], 3.3.1) | |
A reaction: A very nice argument against the moral equality of combatants. If I think we are the good guys, and the opposing troops are no morally different from us, how can I possibly kill them? |
23599 | You don't become a legitimate target, just because you violently resist an unjust attack [McMahan] |
Full Idea: It is hard to see how just combatants could become legitimate targets simply by offering violent resistance to unjust attacks by unjust coombatants. | |
From: Jeff McMahan (Killing in War [2009], 1.3) | |
A reaction: It is, however, hard to criticise a soldier who is dragged into fighting for an unjust cause, and then kills just defenders in the course of the fight. Once the bullets fly, normal morality seems to be suspended. Just survive. |
23596 | If all combatants are seen as morally equal, that facilitates starting unjust wars [McMahan] |
Full Idea: It would be naïve to doubt that the widespread acceptance of the moral equality of combatants has facilitated the ability of governments to fight unjust wars. | |
From: Jeff McMahan (Killing in War [2009], 1.1) | |
A reaction: The point is that their armies are both compliant and seeing their actions as guiltless, which makes them perfect tools for evil. McMahan's ideal is an army which asks sharp questions about the justification of the war, before they fight it. |
23604 | Volunteer soldiers accept the risk of attack, but they don't agree to it, or to their deaths [McMahan] |
Full Idea: When soldiers go to war, they undoubtedly assume a certain risk. They voluntarily expose themselves to a significant risk of being attacked. But this is entirely different from consenting to being attacked. | |
From: Jeff McMahan (Killing in War [2009], 2.2.1) | |
A reaction: This is his response to Walzer's thought that soldiers resemble people who volunteer for a boxing match. The sailors at Pearl Harbour obviously didn't consent to the attack, or accept the Japanese right to kill them. |
23608 | If being part of a big collective relieves soldiers of moral responsibility, why not the leaders too? [McMahan] |
Full Idea: If acting as an agent of a political collective justifies the combatants fighting an unjust war, that should also release the leaders from responsibility for their role in the fighting of that war. No one ever explains why this is not so. | |
From: Jeff McMahan (Killing in War [2009], 2.5) | |
A reaction: At the very least there seems to be a problem of the cut off point between innocent soldiers and culpable leaders. Which rank in the army or executive triggers the blame? |
23610 | If soldiers can't refuse to fight in unjust wars, can they choose to fight in just wars? [McMahan] |
Full Idea: There is a certain symmetry here. The permissibility of disobeying a command to fight in an unjust war suggests the permissibility of disobeying a command not to fight in a just war. | |
From: Jeff McMahan (Killing in War [2009], 2.7) | |
A reaction: The argument considered here is that since we could never allow soldiers to choose to fight in their own wars, we similarly cannot let them opt out of the official wars. Implying obedience is absolute. Soldiers don't get to 'choose' anything! |
23613 | Equality is both sides have permission, or both sides are justified, or one justified the other permitted [McMahan] |
Full Idea: Moral equality means either 1) because just combatants are permitted to fight in a just way, so are the unjust , or 2) because the just are justified, so are the unjust, or 3) because the just are justified, the unjust are therefore permitted. | |
From: Jeff McMahan (Killing in War [2009], 3.1.2) | |
A reaction: [summary] McMahan calls 1) the weak version, and 2) the strong. He suggests that although 3) is unusual, it is what most people believe - that if the good are justified, the bad are permitted to fight back. He rejects them all. |
23615 | Fighting unjustly under duress does not justify it, or permit it, but it may excuse it [McMahan] |
Full Idea: It is said that combatants are compelled to fight; they have no choice. But duress is not a justification; nor does it ground a permission - not even a subjective permission. It is, instead, an excusing condition. | |
From: Jeff McMahan (Killing in War [2009], 3.1.2) | |
A reaction: The 'subjective' permission is believing you are just, even if you aren't. A nice, accurate and true distinction made by McMahan, I think. It is roughly our postwar attitude to the Nazi army. |
23605 | Soldiers cannot know enough facts to evaluate the justice of their war [McMahan] |
Full Idea: When soldiers are commanded to fight, they cannot reasonably be expected to have the factual knowledge necessary to evaluate the war as just or unjust. | |
From: Jeff McMahan (Killing in War [2009], 2.3) | |
A reaction: This is part of the 'epistemic' justification for a soldier to fight in an unjust war. Sometimes soldiers do have enoough knowledge, especially if they join up late on in a war, when they have studied and observed its progress. |
23602 | Innocence implies not being morally responsible, rather than merely being guiltless [McMahan] |
Full Idea: My alternative conception is that one is 'innocent' if one is neither morally responsible for nor guilty of a wrong. Classical theory focused on guilt, but I think we should focus on moral responsibility (which is something less). | |
From: Jeff McMahan (Killing in War [2009], 1.4) | |
A reaction: This seems to make the supporters of evil equally liable to attack with its perpetrators. But you can observe perpetration a lot more easily than you can observe support. |
23618 | Unconditional surrender can't be demanded, since evil losers still have legitimate conditions [McMahan] |
Full Idea: Achieving unconditional surrender can never be a justification for the continuation of war, since there are always conditions that a vanquished adversary, no matter how evil, can be justified in demanding. | |
From: Jeff McMahan (Killing in War [2009], 3.3.1) | |
A reaction: McMahan is particularly discussing Hiroshima, but this also applies to the European war in 1945. Presumably a civilised victor will grant the conditions which the losers would have demanded, and that probably happened in 1945. It's about power. |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
From: Plato (Parmenides [c.364 BCE], 135a) |
225 | The unlimited has no shape and is endless [Plato] |
Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
From: Plato (Parmenides [c.364 BCE], 137e) |
233 | Some things do not partake of the One [Plato] |
Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
From: Plato (Parmenides [c.364 BCE], 159d) | |
A reaction: Compare Idea 231 |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
From: Plato (Parmenides [c.364 BCE], 138b) |
231 | Everything partakes of the One in some way [Plato] |
Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: Compare Idea 233. |
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. |
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. |
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) |
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) |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
From: Plato (Parmenides [c.364 BCE], 160d) |