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. |
| 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. |
| 13152 | We can talk of 'innumerable number', about the infinite points on a line [Newton] |
| Full Idea: If any man shall take the words number and sum in a larger sense, to understand things which are numberless and sumless (such as the infinite points on a line), I could allow him the contradictious phrase 'innumerable number' without absurdity. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |
| A reaction: [compressed] I take the key point here to be the phrase of taking number 'in a larger sense'. Like the word 'atom' in physics, the word 'number' retains its traditional reference, but has considerably shifted its scope. Amateurs must live with this. |
| 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) |
| 13151 | Not all infinites are equal [Newton] |
| Full Idea: It is an error that all infinites are equal. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |
| A reaction: There follows a discussion of the mathematicians' view of infinity. Cantor was not the first to notice that there is more than one sort of of infinity. |
| 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. |
| 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. |
| 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. |
| 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)? |
| 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. |
| 19906 | All countries are in a mutual state of nature [Locke] |
| Full Idea: All commonwealths are in a state of Nature one with another. | |
| From: John Locke (Second Treatise of Government [1690], 153) | |
| A reaction: A striking remark. It is easy to think that the state of nature no longer exists. International law attempts to rectify this, but diplomacy is much more like negotiations in nature than it is like obedience to laws. |
| 19882 | We are not created for solitude, but are driven into society by our needs [Locke] |
| Full Idea: God, having made man such a creature that, in His own judgement, it was not good for him to be alone, put him under strong obligations of necessity, convenience, and inclination, to drive him into society. | |
| From: John Locke (Second Treatise of Government [1690], 077) | |
| A reaction: This is almost Aristotelian, apart from the individualistic assumption that we are 'driven' into society. The only time I see other people looking generally happy is when they are sitting around at leisure and talking to other people. |
| 19864 | In nature men can dispose of possessions and their persons in any way that is possible [Locke] |
| Full Idea: The estate all men are naturally in is perfect freedom to order their actions, and dispose of their possessions and persons as they think fit, within the bounds of the laws of nature. | |
| From: John Locke (Second Treatise of Government [1690], 004) | |
| A reaction: Note that they have possessions, so property is not an invention of society, but something which society should protect. Presumably Locke thinks they could sell themselves into slavery, which Rousseau rejects. |
| 19865 | There is no subjection in nature, and all creatures of the same species are equal [Locke] |
| Full Idea: Creatures of the same species and rank, promiscuously born to all the same advantages of Nature, are also equal one among another, without subordination or subjection. | |
| From: John Locke (Second Treatise of Government [1690], 004) | |
| A reaction: The birds in my garden don't behave as if that were true. Physical strength is surely a natural inequality. |
| 19866 | The rational law of nature says we are all equal and independent, and should show mutual respect [Locke] |
| Full Idea: The state of Nature has a law of Nature to govern it, which obliges everyone, and reason, which is that law, teaches mankind that all being equal and independent, no one ought to harm another in his life, health, liberty or possessions. | |
| From: John Locke (Second Treatise of Government [1690], 006) | |
| A reaction: He adds that this is because we are all the property of God. Locke is more optimistic than Hobbes or Rousseau about this, since he thinks we have a natural obligation to be nice. |
| 19872 | The animals and fruits of the earth belong to mankind [Locke] |
| Full Idea: All the fruits the earth naturally produces, and beasts it feeds, belong to mankind in common, as they are produced by the spontaneous hand of Nature. | |
| From: John Locke (Second Treatise of Government [1690], 026) | |
| A reaction: Not a popular view among 21st century ecologists, I guess, but this remains the implicit belief of anyone who goes hunting in the woods, and our enclosed gardens seem to endorse the idea. |
| 19907 | There is a natural right to inheritance within a family [Locke] |
| Full Idea: Every man is born with a right before any other man, to inherit, with his brethren, his father's goods. | |
| From: John Locke (Second Treatise of Government [1690], 190) | |
| A reaction: If a child is fully grown, they may well have drifted into a state of partial ownership of the goods of the parent, of which it would be hard then to deprive them. It is hard to see this as a natural right of tiny orphaned infants. |
| 19863 | Politics is the right to make enforceable laws to protect property and the state, for the common good [Locke] |
| Full Idea: Political power is the right of making laws, with penalties up to death, for the preserving of property, employing the force of community in the execution of such laws, in defence of the commonwealth, and only for the common good. | |
| From: John Locke (Second Treatise of Government [1690], 003) | |
| A reaction: Since political power can be used for selfish corruption and genocide, this isn't very accurate, so I take it this is how power ought to be exercised! Notice that defence gets equal billing with his famous defence of property. |
| 5654 | The Second Treatise explores the consequences of the contractual view of the state [Locke, by Scruton] |
| Full Idea: In his second Treatise, Locke gave us perhaps the first extended account of the true logical consequences of Hobbes's contractual view of the state. | |
| From: report of John Locke (Second Treatise of Government [1690]) by Roger Scruton - Short History of Modern Philosophy Ch.14 | |
| A reaction: The issue seems to boil down to an opposition between the Cartesian and the Aristotelian view of the individual, with Locke following Descartes. The alternative, endorsed by Hegel, which I prefer, is that the state is part of human nature. |
| 19888 | A society only begins if there is consent of all the individuals to join it [Locke] |
| Full Idea: The beginning of politic society depends upon the consent of the individuals to join into and make one society. | |
| From: John Locke (Second Treatise of Government [1690], 106) | |
| A reaction: This is the dramatic new political idea (originating with Hobbes), that all of the members must (at some point) consent to the state. In practice we are all born into a state, so it is not clear what this means in real life. |
| 6702 | If anyone enjoys the benefits of government (even using a road) they give tacit assent to its laws [Locke] |
| Full Idea: Every man, that hath an possession, or enjoyment, of any part of the dominions of any government, doth thereby give his tacit consent, and is obliged to obedience to the laws, ..whether it be barely travelling on the highway. | |
| From: John Locke (Second Treatise of Government [1690], 119), quoted by Gordon Graham - Eight Theories of Ethics Ch.8 | |
| A reaction: Locke's famous assertion of an unspoken and inescapable contract, to which we are all subject. Hume gave an effective reply (Idea 6703). Locke has a point though. The more you accept, the more obliged you are. I accept the law more as I get older. |
| 19909 | A politic society is created from a state of nature by a unanimous agreement [Locke] |
| Full Idea: That which makes the community, and brings men out of the loose state of Nature into one politic society, is the agreement that everyone has with the rest to incorporate and act as one body. | |
| From: John Locke (Second Treatise of Government [1690], 211) | |
| A reaction: Geography usually keeps commonwealths in place once they have been established, but some of them become disfunctional hell holes because they are trapped in perpetual disagreement. |
| 19910 | A single will creates the legislature, which is duty-bound to preserve that will [Locke] |
| Full Idea: The essence and union of the society consisting in having one will; the legislative, when once established by the majority, has the declaring and, as it were, keeping of that will. | |
| From: John Locke (Second Treatise of Government [1690], 212) | |
| A reaction: Not far from Rousseau's big idea, apart from the emphasis on the 'majority'. Rousseau reduced the role of the general will to preliminaries and basics, but wanted close to unanimity, so that everyone accepts being a subject, to government and law. |
| 19893 | Anyone who enjoys the benefits of a state has given tacit consent to be part of it [Locke] |
| Full Idea: Every man that hath any possession or enjoyment of any part of the dominions of any government doth thereby give his tacit consent, and is as far forth obliged to obedience to the laws of that government, during such enjoyment. | |
| From: John Locke (Second Treatise of Government [1690], 119) | |
| A reaction: I wondered at the age of about 18 whether I had given tacit consent to be a British citizen. Locke says you only have to travel freely down the highways to give consent! We are all free, of course, to apply for citizenship elsewhere. But Idea 19894. |
| 19894 | You can only become an actual member of a commonwealth by an express promise [Locke] |
| Full Idea: Nothing can make any man a subject or member of a commonwealth but his actually entering into it by positive engagement, and express promise and compact. | |
| From: John Locke (Second Treatise of Government [1690], 122) | |
| A reaction: In practice the indigenous population never do this. But it a clear distinction for foreign residents in any country. States cannot induct resident foreigners into their army, or allow them to vote. |
| 19892 | Children are not born into citizenship of a state [Locke] |
| Full Idea: It is plain, by the practices of governments themselves, as well as by the laws of right reason, that a child is born a subject of no country nor government. | |
| From: John Locke (Second Treatise of Government [1690], 118) | |
| A reaction: At what age do they become citizens, given that there is no induction ceremony? If a small British child were attacked overseas, we would expect the British government to defend its rights. |
| 19885 | Absolute monarchy is inconsistent with civil society [Locke] |
| Full Idea: Absolute monarchy, which by some men is counted for the only government in the world, is inconsistent with civil society, and so can be no form of civil government at all. | |
| From: John Locke (Second Treatise of Government [1690], 090) | |
| A reaction: This is because citizens do not have a 'decisive' power to appeal for redress of injuries. Rousseau thought that there could be an absolute monarchy, as long as the general will agreed it, and its term of office could be brought to an end by the assembly. |
| 19886 | The idea that absolute power improves mankind is confuted by history [Locke] |
| Full Idea: He that thinks absolute power purifies men's blood, and corrects the baseness of human nature, need but read the history of this, or any other age, to be convinced to the contrary. | |
| From: John Locke (Second Treatise of Government [1690], 092) | |
| A reaction: I can't imagine who proposed the view that Locke is attacking, but it will have been some real 17th century thinker. Attitudes to monarchy changed drastically in England, but Louis XIV was still ruling in France. |
| 19903 | Despotism is arbitrary power to kill, based neither on natural equality, nor any social contract [Locke] |
| Full Idea: Despotical power is an absolute, arbitrary power one man over another, to take away his life whenever he pleases; and this is a power which neither Nature gives, for it has made no such distinction between one man and another, nor compact can convey. | |
| From: John Locke (Second Treatise of Government [1690], 172) | |
| A reaction: Colonies of seals, walruses and apes seem to display despotism, based on physical strength, though that is largely to do with mating. There could be such a compact, but Locke would regard it as invalid. |
| 19905 | People stripped of their property are legitimately subject to despotism [Locke] |
| Full Idea: Forfeiture gives despotical power to lords for their own benefit over those who are stripped of all property. ...Despotical power is over such as have no property at all. | |
| From: John Locke (Second Treatise of Government [1690], 173) | |
| A reaction: Nasty! Shylock is stripped of his property by Venice, so these things happened. This is taking the significance of property a long way beyond its role at the beginning of Locke's book. Property is the start of society, but then becomes your passport. |
| 19904 | Legitimate prisoners of war are subject to despotism, because that continues the state of war [Locke] |
| Full Idea: Captives, taken in a just and lawful war, and such only, are subject to a despotical power, which, as it arises not from compact, so neither is it capable of any, but is the state of war continued. | |
| From: John Locke (Second Treatise of Government [1690], 205) | |
| A reaction: How long after a war finishes is such despotism legitimate? What happened to the German prisoners in Russia in 1945? Locke defined despotism as the right to kill, but that is expressly contrary to the rules of war, look you. |
| 19895 | Even the legislature must be preceded by a law which gives it power to make laws [Locke] |
| Full Idea: The first and fundamental positive law of all commonwealths is the establishing of the legislative power, as the first and fundamental natural law which is to govern even the legislative. | |
| From: John Locke (Second Treatise of Government [1690], 134) | |
| A reaction: I think Rousseau says that there cannot be a law which enables the general will to set up legislative powers. It just seems to be something which happens. Locke is threatened with an infinite regress. What legitimises the enabling law? |
| 19900 | The executive must not be the legislature, or they may exempt themselves from laws [Locke] |
| Full Idea: It may be too great temptation to human frailty, apt to grasp at power, for the same persons to have the power of making laws to also have in their hands the power to execute them, whereby they may exempt themselves. | |
| From: John Locke (Second Treatise of Government [1690], 143) | |
| A reaction: The main principles of modern constitutions are devised to avoid corruption. If people were incorruptible (yeah, right) the world would presumably be run very differently, and rather more efficiently, like a good family. |
| 19902 | Any obstruction to the operation of the legislature can be removed forcibly by the people [Locke] |
| Full Idea: Having erect a legislative with the power of making laws, when they are hindered by any force from what is so necessary to society, and wherein the safety and preservation of the people consists, the people have a right to remove it by force. | |
| From: John Locke (Second Treatise of Government [1690], 155) | |
| A reaction: I doubt if he was thinking of the French Revolution, but this will clearly have application to the English events of 1642. The Speaker of the Commons was held down in his chair in the 1620s, so that some legislation could be enacted. |
| 19908 | Rebelling against an illegitimate power is no sin [Locke] |
| Full Idea: It is plain that shaking off a power which force, and not right, hath set over any one, though it have the name of rebellion, yet it is no offence against God. | |
| From: John Locke (Second Treatise of Government [1690], 196) | |
| A reaction: [He cites Hezekiah at 2 Kings 18.7] At this time the English Civil War was referred to as the 'Great Rebellion' (so this is an interesting and brave remark of Locke's), though few people would think that Charles I had illegitimate power. |
| 19911 | If legislators confiscate property, or enslave people, they are no longer owed obedience [Locke] |
| Full Idea: Whenever the legislators endeavour to take away and destroy the property of the people, or reduce them to slavery under arbitrary power, they put themselves into a state of war with the people, who are thereupon absolved from any further obedience. | |
| From: John Locke (Second Treatise of Government [1690], 222) | |
| A reaction: This might fit Louis XVI in 1788. Locke was certainly not averse to consideration the situations in which revolution might be justified. He was trying to be even-handed about 1642. Locke seems to think that without property you ARE a slave. |
| 19901 | The people have supreme power, to depose a legislature which has breached their trust [Locke] |
| Full Idea: There remains still in the people a supreme power to remove or alter the legislative, when they find the legislative act contrary to the trust reposed in them. | |
| From: John Locke (Second Treatise of Government [1690], 149) | |
| A reaction: This seems to be the most important aspect of representative democracy. It is not the power of people to make decisions, but the power to get rid of bad rulers. |
| 19887 | Unanimous consent makes a united community, which is then ruled by the majority [Locke] |
| Full Idea: When any number of men have, by the consent of every individual, made a community, they have thereby made that community into one body, with a power to act as one body, which is only by the will and determination of the majority. | |
| From: John Locke (Second Treatise of Government [1690], 096) | |
| A reaction: This seems to be presume democracy without discussion, although the formation of the community is by universal consent, which is the 'general will'. Rousseau has the constitution also made almost unanimously, not by a majority. |
| 19913 | A master forfeits ownership of slaves he abandons [Locke] |
| Full Idea: A master forfeits the dominion over his slaves whom he hath abandoned. | |
| From: John Locke (Second Treatise of Government [1690], 237) | |
| A reaction: How often did slave owners take a day off, I wonder? Presumably slaves will take back their freedom, even if the masters haven't 'forfeited' their ownership, so Locke's point is fairly academic. |
| 19883 | Slaves captured in a just war have no right to property, so are not part of civil society [Locke] |
| Full Idea: Slave are captives taken in a just war, and by right of Nature subjected to the absolute dominion and arbitrary power of their masters. ...Being not capable of any property, they cannot in that state be considered any part of civil society. | |
| From: John Locke (Second Treatise of Government [1690], 085) | |
| A reaction: If the test of citizenship is being capable of holding property, presumably children and mentally damaged people (including the very old) will also fail to qualify. I see no principled reason why slaves should not be allowed to vote. Note 'just' war. |
| 19870 | If you try to enslave me, you have declared war on me [Locke] |
| Full Idea: He who makes an attempt to enslave me thereby puts himself into a state of war with me. | |
| From: John Locke (Second Treatise of Government [1690], 017) | |
| A reaction: So presumably actual slaves are in a state of permanent war with their owners. What of a woman who is enslaved by her husband? |
| 19871 | Freedom is not absence of laws, but living under laws arrived at by consent [Locke] |
| Full Idea: Liberty of man in society is to be under no other legislative power but that established by consent in the commonwealth. Freedom is not (as Filmer suggests) doing what you please while not tied by any laws. | |
| From: John Locke (Second Treatise of Government [1690], 022) | |
| A reaction: That sounds plausible if the consent is unanimous, but a minority is not free if the laws made by a large majority are a sort of persecution. |
| 19880 | All value depends on the labour involved [Locke] |
| Full Idea: It is labour that puts the difference of value on everything. ...Whatever bread is worth more than acorns, wine than water, that is wholly owing to labour and industry. | |
| From: John Locke (Second Treatise of Government [1690], 040) | |
| A reaction: In capitalism this is nonsense. Supply and demand fix all the values. Locke has slid from labour bestowing ownership to labour bestowing value. No one gets paid on the basis of how hard they work, except on piece rates. |
| 19884 | There is only a civil society if the members give up all of their natural executive rights [Locke] |
| Full Idea: Wherever any number of men so unite into one society as to quite every one his executive power of the law of Nature, and to resign it to the public, there and there only is a civil society. | |
| From: John Locke (Second Treatise of Government [1690], 089) | |
| A reaction: This seems to mean that you must give up your active ('executive') natural rights, but not your passive ones (which are inviolable). |
| 19873 | We all own our bodies, and the work we do is our own [Locke] |
| Full Idea: Every man has a 'property' in his own 'person'. This nobody has any right to it but himself. The 'labour' of his body and the 'work' of his hands, we may say, are properly his. | |
| From: John Locke (Second Treatise of Government [1690], 027) | |
| A reaction: He doesn't have any grounds for this claim. Why doesn't a cow own its body? He slides from my ownership of my laborious efforts to my ownership of what I have been working on. I can't acquire your car by servicing it. |
| 6580 | Locke (and Marx) held that ownership of objects is a natural relation, based on the labour put into it [Locke, by Fogelin] |
| Full Idea: Locke thought that property ownership reflected a natural relationship; for him the primordial notion of the ownership of an object is a function of the labour that one puts into it; Marx held a similar view. | |
| From: report of John Locke (Second Treatise of Government [1690]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
| A reaction: Marx would have to think that, in order to believe that capitalist ownership of the means of production used by the workers was a fundamental injustice. A deeper Marxism might see the whole idea of 'ownership' as a capitalist (or feudal) conspiracy. |
| 20520 | Locke says 'mixing of labour' entitles you to land, as well as nuts and berries [Wolff,J on Locke] |
| Full Idea: The great advantage of Locke's 'labour-mixing' argument is that it seems it can justify the appropriation of land, as well as nuts and berries. | |
| From: comment on John Locke (Second Treatise of Government [1690]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 5 'Locke' | |
| A reaction: The argument is dubious at best, and plausibly downright wicked. How much labour achieves ownership? What of previous people who worked the land but never thought to claim 'ownership'? Suppose I do more labour than you on 'your' land? |
| 19875 | A man's labour gives ownership rights - as long as there are fair shares for all [Locke] |
| Full Idea: The 'labour' being the unquestionable property of the labourer, no man but he can have a right to what that is once joined to, at least where there is enough, and as good left in common for others. | |
| From: John Locke (Second Treatise of Government [1690], 027) | |
| A reaction: The qualification at the end is a crucial (and problematic) addition to his theory. What is the situation when an area of wilderness is 98% owned? What of the single source of water? Who gets the best parts? Getting there first seems crucial. |
| 19874 | If a man mixes his labour with something in Nature, he thereby comes to own it [Locke] |
| Full Idea: Whatever a man removes out of the state that Nature hath provided and left it in, he hath mixed his labour with it, and joined something to it that is his own, and thereby makes it his property. ...This excludes the common right of other men. | |
| From: John Locke (Second Treatise of Government [1690], 027) | |
| A reaction: This is Locke's famous Labour Theory of Value. Does picking it up count as labour? Putting a fence round it? Paying someone else to do the labour? Do bees own their honey? Settlers in the wilderness own nothing on day one? |
| 19877 | Fountain water is everyone's, but a drawn pitcher of water has an owner [Locke] |
| Full Idea: Though the water running in the fountain be every one's, yet who can doubt but that in the pitcher is his only who drew it out? | |
| From: John Locke (Second Treatise of Government [1690], 029) | |
| A reaction: This would certainly be the normal consensus of a community, as long as there is plenty of water. The strong and fit gatherers get all the best firewood, so I suppose that is just tough on the others. |
| 19876 | Gathering natural fruits gives ownership; the consent of other people is irrelevant [Locke] |
| Full Idea: If the first gathering of acorns and apples made them not a man's, nothing else could. ...Will anyone say he had no right to them because he had not the consent of all mankind to make them his? | |
| From: John Locke (Second Treatise of Government [1690], 028) | |
| A reaction: The ideas of Nozick are all in this sentence. Does this idea justify the enclosure of common land? The first member of the community who thought of Locke's labour theory had a huge head's start. Liberal individualism rampant. |
| 19878 | Mixing labour with a thing bestows ownership - as long as the thing is not wasted [Locke] |
| Full Idea: How far has God given us all things 'to enjoy'? As much as any one can make use of to any advantage of his life before it spoils, so much he may by his labour fix a property in. | |
| From: John Locke (Second Treatise of Government [1690], 031) | |
| A reaction: This adds a very different value to Locke's theory, because the person seems to be answerable to fellow citizens if they harvest important resources and then waste them. Where do luxuries fit in? |
| 19879 | A man owns land if he cultivates it, to the limits of what he needs [Locke] |
| Full Idea: As much land as a man tills, plants, improves, cultivates, and can use the product of, so much is his property. | |
| From: John Locke (Second Treatise of Government [1690], 032) | |
| A reaction: Industrial farming rather changes this picture. Does the man himself decide how much he can use the product of, or do the neighbours tell him where his boundaries must be? 'Reason not the need', as King Lear said. What if he stops cultivating it? |
| 19898 | Soldiers can be commanded to die, but not to hand over their money [Locke] |
| Full Idea: The sergeant that can command a soldier to march up to the mouth of a cannon ...cannot command that soldier to give him one penny of his money. | |
| From: John Locke (Second Treatise of Government [1690], 139) | |
| A reaction: A very nice and accurate illustration of a principle which runs so deep that it does indeed look like a basis of society. |
| 19881 | The aim of law is not restraint, but to make freedom possible [Locke] |
| Full Idea: The end of law is not to abolish or restrain, but to preserve and enlarge freedom, for where there is no law there is no freedom. | |
| From: John Locke (Second Treatise of Government [1690], 057) | |
| A reaction: This fits both the liberal and the communitarian view of the matter. Talk of 'freedom' is commonplace in England by this date, where it is hardly mention 60 years earler. John Lilburne almost single-handedly brought this about. |
| 19868 | It is only by a law of Nature that we can justify punishing foreigners [Locke] |
| Full Idea: If by the law of Nature every man hath not a power to punish offences against [the state], as he soberly judges the case to require, I see not how the magistrates of any community can punish an alien of another country. | |
| From: John Locke (Second Treatise of Government [1690], 009) | |
| A reaction: This is a nice point. You can't expect to be above the law in a foreign country, but you have entered into no social contract, unless visiting a place is a sort of contract. Intrusions into air space are often accidental visits. |
| 19867 | Reparation and restraint are the only justifications for punishment [Locke] |
| Full Idea: Reparation and restraint are the only two reasons why one man may lawfully do harm to another, which is that we call punishment. | |
| From: John Locke (Second Treatise of Government [1690], 008) | |
| A reaction: But by 'reparation' does be mean retribution, or compensation? He doesn't rule out capital punishment, but that may qualify as maximum restraint. |
| 19912 | Self-defence is natural, but not the punishment of superiors by inferiors [Locke] |
| Full Idea: It is natural for us to defend life and limb, but that an inferior should punish a superior is against nature. | |
| From: John Locke (Second Treatise of Government [1690], 236) | |
| A reaction: He is obliquely referring to the execution of Charles I, even though he may have been legitimately overthrown. I wonder what exactly he means by 'superior' and 'inferior'. An idea from another age! |
| 19869 | Punishment should make crime a bad bargain, leading to repentance and deterrence [Locke] |
| Full Idea: Each transgression may be punished to that degree, and with so much severity, as will suffice to make it an ill bargain to the offender, give him cause to repent, and terrify others from doing the like. | |
| From: John Locke (Second Treatise of Government [1690], 012) | |
| A reaction: I gather that the consensus among experts is that the biggest deterrence is a high likelihood of being caught, rather than the severity of the punishment. |
| 19899 | The consent of the people is essential for any tax [Locke] |
| Full Idea: The legislative power must not raise taxes on the property of the people without the consent of the people given by themselves or their deputies. | |
| From: John Locke (Second Treatise of Government [1690], 142) | |
| A reaction: He will be thinking of the resistance to Ship Money in the 1630s, which was a step towards civil war. The people of Boston, Ma, may have read this sentence 80 years later! |
| 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. |
| 15863 | The principles of my treatise are designed to fit with a belief in God [Newton] |
| Full Idea: When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men, for the belief of a deity. | |
| From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |
| A reaction: Harré quotes this, and it shows that the rather passive view of nature Newton developed was to be supplemented by the active power of God. Without God, we need a more active view of nature. |
| 8340 | I do not pretend to know the cause of gravity [Newton] |
| Full Idea: You sometimes speak of gravity as essential and inherent in matter. Pray do no ascribe that notion to me; for the cause of gravity is what I do not pretend to know. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |
| A reaction: I take science to be a two-stage operation - first we discern the regularities, and then we explain them. Evolution was spotted, then explained by Darwin. Cancer from cigarettes was spotted, but hasn't been explained. Regularity is the beginning. |
| 13150 | The motions of the planets could only derive from an intelligent agent [Newton] |
| Full Idea: The motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent agent. | |
| From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |
| A reaction: He is writing to a cleric, but seems to be quite sincere about this. Elsewhere he just says he doesn't know what causes gravity. |
| 12178 | That gravity should be innate and essential to matter is absurd [Newton] |
| Full Idea: That gravity should be innate, inherent and essential to matter ...is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |
| A reaction: He is replying to some sermons, and he pays vague lip service to a possible divine force. Nevertheless, this is thoroughgoing anti-essentialism, and he talks of external 'laws' in the next sentence. Newton still sought the cause of gravity. |
| 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) |