131 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'. |
| 15557 | Verisimilitude has proved hard to analyse, and seems to have several components [Lewis] |
| Full Idea: The analysis of verisimilitude has been much debated. Some plausible analyses have failed disastrously, others conflict with one another. One conclusion is that verisimilitude seems to consist of several distinguishable virtues. | |
| From: David Lewis (Causal Explanation [1986], V n7) | |
| A reaction: Presumably if it is complex, you can approach truth in one respect while receding from it in another. It seems clear enough if you are calculating pi by some iterative process. |
| 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. |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| Full Idea: Russell defined the rationals as ratios of integers, and was therefore forced to treat the real number 5/8 as an object distinct from the rational 5/8. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| Full Idea: Ordinal numbers result from likeness among relations, as cardinals from similarity among classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §293) |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| Full Idea: It is claimed that ordinals are prior to cardinals, because they form the progression which is relevant to mathematics, but they both form progressions and have the same ordinal properties. There is nothing to choose in logical priority between them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §230) | |
| A reaction: We have an intuitive notion of the size of a set without number, but you can't actually start counting without number, so the ordering seems to be the key to the business, which (I would have thought) points to ordinals as prior. |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| Full Idea: Ordinals presuppose serial and one-one relations, whereas cardinals only presuppose one-one relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §232) | |
| A reaction: This seems to award the palm to the cardinals, for their greater logical simplicity, but I have already given the award to the ordinals in the previous idea, and I am not going back on that. |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| Full Idea: The properties of number must be capable of proof without appeal to the general properties of progressions, since cardinals can be independently defined, and must be seen in a progression before theories of progression are applied to them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §243) | |
| A reaction: Russell says there is no logical priority between ordinals and cardinals, but it is simpler to start an account with cardinals. |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| Full Idea: The ordinal numbers are defined by some relation to mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| Full Idea: The finite ordinals may be conceived as types of series; ..the ordinal number may be taken as 'n terms in a row'; this is distinct from the 'nth', and logically prior to it. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Worth nothing, because the popular and traditional use of 'ordinal' (as in learning a foreign language) is to mean the nth instance of something, rather than a whole series. |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| Full Idea: Unlike the transfinite cardinals, the transfinite ordinals do not obey the commutative law, and their arithmetic is therefore quite different from elementary arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| Full Idea: In his most recent article Cantor speaks of ordinals as types of order, not as numbers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §298) | |
| A reaction: Russell likes this because it supports his own view of ordinals as classes of serial relations. It has become orthodoxy to refer to heaps of things as 'numbers' when the people who introduced them may not have seen them that way. |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| Full Idea: We do not know that of any two different cardinal numbers one must be the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §300) | |
| A reaction: This was 1903, and I don't know whether the situation has changed. I find this thought extremely mind-boggling, given that cardinals are supposed to answer the question 'how many?' Presumably they can't be identical either. See Burali-Forti. |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| Full Idea: Real numbers are not really numbers at all, but something quite different; ...a real number, so I shall contend, is nothing but a certain class of rational numbers. ...A segment of rationals is a real number. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §258) |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| Full Idea: Some quantities cannot be measured (such as pain), and some things which are not quantities can be measured (such as certain series). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §150) |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| Full Idea: Quantity, though philosophers seem to think it essential to mathematics, does not occur in pure mathematics, and does occur in many cases not amenable to mathematical treatment. The place of quantity is taken by order. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §405) | |
| A reaction: He gives pain as an example of a quantity which cannot be treated mathematically. |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| Full Idea: The process of counting gives us no indication as to what the numbers are, as to why they form a series, or as to how it is to be proved that there are n numbers from 1 to n. Hence counting is irrelevant to the foundations of arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §129) | |
| A reaction: I take it to be the first truth in the philosophy of mathematics that if there is a system of numbers which won't do the job of counting, then that system is irrelevant. Counting always comes first. |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| Full Idea: It is possible, without the notion of unity, to define what is meant by one-to-one. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: This is the trick which enables the Greek account of numbers, based on units, to be abandoned. But when you have arranged the boys and the girls one-to-one, you have not yet got a concept of number. |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| Full Idea: It is not at present known whether, of two different infinite numbers, one must be greater and the other less. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §118) | |
| A reaction: This must refer to cardinal numbers, as ordinal numbers have an order. The point is that the proper subset is equal to the set (according to Dedekind). |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| Full Idea: The theory of infinity has two forms, cardinal and ordinal, of which the former springs from the logical theory of numbers; the theory of continuity is purely ordinal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §249) |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| Full Idea: There are two differences of infinite numbers from finite: that they do not obey mathematical induction (both cardinals and ordinals), and that the whole contains a part consisting of the same number of terms (applying only to ordinals). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §250) |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| Full Idea: The ordinal representing the whole series must be different from what represents a segment of itself, with no immediate predecessor, since the series has no last term. ω names the class progression, or generating relation of series of this class. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §291) | |
| A reaction: He is paraphrasing Cantor's original account of ω. |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| Full Idea: It must not be supposed that we can obtain a new transfinite cardinal by merely adding one to it, or even by adding any finite number, or aleph-0. On the contrary, such puny weapons cannot disturb the transfinite cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §288) | |
| A reaction: If you add one, the original cardinal would be a subset of the new one, and infinite numbers have their subsets equal to the whole, so you have gone nowhere. You begin to wonder whether transfinite cardinals are numbers at all. |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| Full Idea: For every transfinite cardinal there is an infinite collection of transfinite ordinals, although the cardinal number of all ordinals is the same as or less than that of all cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Sort that one out, and you are beginning to get to grips with the world of the transfinite! Sounds like there are more ordinals than cardinals, and more cardinals than ordinals. |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| Full Idea: The Axiom of Archimedes asserts that, given any two magnitudes of a kind, some finite multiple of the lesser exceeds the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §168 n*) |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| Full Idea: What Russell tried to show [at this time] was that Peano's Postulates (based on 'zero', 'number' and 'successor') could in turn be dispensed with, and the whole edifice built upon nothing more than the notion of 'class'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: (See Idea 5897 for Peano) Presumably you can't afford to lose the notion of 'successor' in the account. If you build any theory on the idea of classes, you are still required to explain why a particular is a member of that class, and not another. |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| Full Idea: Dedekind's demonstrations nowhere - not even where he comes to cardinals - involve any property distinguishing numbers from other progressions. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903], p.249) by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Shapiro notes that his sounds like Frege's Julius Caesar problem, of ensuring that your definition really does capture a number. Russell is objecting to mathematical structuralism. |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| Full Idea: The transfinite was obtained by denying mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §310) | |
| A reaction: This refers to the work of Dedekind and Cantor. This raises the question (about which thinkers have ceased to care, it seems), of whether it is rational to deny mathematical induction. |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| Full Idea: Finite numbers obey the law of mathematical induction: infinite numbers do not. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §183) |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| Full Idea: It used to be common to define numbers by means of 1, with 2 being 1+1 and so on. But this method was only applicable to finite numbers, made a tiresome different between 1 and the other numbers, and left + unexplained. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: Am I alone in hankering after the old approach? The idea of a 'unit' is what connected numbers to the patterns of the world. Russell's approach invites unneeded platonism. + is just 'and', and infinities are fictional extrapolations. Sounds fine to me. |
| 14117 | Numbers are properties of classes [Russell] |
| Full Idea: Numbers are to be regarded as properties of classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: If properties are then defined extensionally as classes, you end up with numbers as classes of classes. |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| Full Idea: It is impossible that the ordinals should be, as Dedekind suggests, nothing but the terms of such relations as constitute a progression. If they are anything at all, they must be intrinsically something. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §242) | |
| A reaction: This is the obvious platonist response to the incipient doctrine of structuralism. We have a chicken-and-egg problem. Bricks need intrinsic properties to make a structure. A structure isomorphic to numbers is not thereby the numbers. |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| Full Idea: Mathematics is throughout indifferent to the question whether its entities exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §434) | |
| A reaction: There is an 'if-thenist' attitude in this book, since he is trying to reduce mathematics to logic. Total indifference leaves the problem of why mathematics is applicable to the real world. |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| Full Idea: Pure mathematics is the class of all propositions of the form 'p implies q', where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §001) | |
| A reaction: Linnebo calls Russell's view here 'deductive structuralism'. Russell gives (§5) as an example that Euclid is just whatever is deduced from his axioms. |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| Full Idea: In his 1903 theory of types he distinguished between individuals, ranges of individuals, ranges of ranges of individuals, and so on. Each level was a type, and it was stipulated that for 'x is a u' to be meaningful, u must be one type higher than x. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App) | |
| A reaction: Russell was dissatisfied because this theory could not deal with Cantor's Paradox. Is this the first time in modern philosophy that someone has offered a criterion for whether a proposition is 'meaningful'? |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| Full Idea: Russell argues that in a statement of the form 'x is a u' (and correspondingly, 'x is a not-u'), 'x must be of different types', and hence that ''x is an x' must in general be meaningless'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], App B:524) by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: " 'Word' is a word " comes to mind, but this would be the sort of ascent to a metalanguage (to distinguish the types) which Tarski exploited. It is the simple point that a classification can't be the same as a member of the classification. |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| Full Idea: Being is that which belongs to every conceivable, to every possible object of thought. | |
| From: Bertrand Russell (The Principles of Mathematics [1903]), quoted by Stephen Read - Thinking About Logic Ch.5 | |
| A reaction: I take Russell's (or anyone's) attempt to distinguish two different senses of the word 'being' or 'exist' to be an umitigated metaphysical disaster. |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| Full Idea: Numbers, the Homeric gods, relations, chimeras and four-dimensional space all have being, for if they were not entities of a kind, we could not make propositions about them. Existence, on the contrary, is the prerogative of some only amongst the beings. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §427) | |
| A reaction: This is the analytic philosophy account of being (a long way from Heidegger). Contemporary philosophy seems to be full of confusions on this, with many writers claiming existence for things which should only be awarded 'being' status. |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| Full Idea: It would seem that whatever exists at any part of time has causal relations. This is not a distinguishing characteristic of what exists, since we have seen that two non-existent terms may be cause and effect. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Presumably he means that the non-existence of something (such as a safety rail) might the cause of an event. This is a problem for Alexander's Principle, in Idea 3534. I think we could redescribe his problem cases, to save Alexander. |
| 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. |
| 15554 | A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis] |
| Full Idea: I take for granted that a disposition requires a causal basis: one has the disposition iff one has a property that occupies a certain causal role. Shall we then identify the disposition with its basis? That makes the disposition cause its manifestations. | |
| From: David Lewis (Causal Explanation [1986], III) | |
| A reaction: Introduce the concept of a 'power' and I see no problem with his proposal. Fundamental dispositions are powerful, and provide the causal basis for complex dispositions. Something had better be powerful. |
| 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? |
| 15560 | We can explain a chance event, but can never show why some other outcome did not occur [Lewis] |
| Full Idea: I think we are right to explain chance events, yet we are right also to deny that we can ever explain why a chance process yields one outcome rather than another. We cannot explain why one event happened rather than the other. | |
| From: David Lewis (Causal Explanation [1986], VI) | |
| A reaction: This misses out an investigation which slowly reveals that a 'chance' event wasn't so chancey after all. Failure to explain confirms chance, so the judgement of chance shouldn't block attempts to explain. |
| 20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
| Full Idea: 'Luck' is loose shorthand. It stands for various causal chains that intersect and whose intersection we can neither predict nor explain, because we lack the relevant knowledge. | |
| From: John Kekes (The Human Condition [2010], 01.2) | |
| A reaction: Aristotle's example is a chance meeting in the market place. The point about 'intersection' seems good, since luck doesn't seem to arise for an event in isolation. |
| 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)? |
| 15559 | Does a good explanation produce understanding? That claim is just empty [Lewis] |
| Full Idea: It is said that a good explanation ought to produce understanding, ...but this just says that a good explanation produces possession of that which it provide, so this desideratum is empty. It adds nothing to our understanding of explanation. | |
| From: David Lewis (Causal Explanation [1986], V) | |
| A reaction: I am not convinced by this dismissal. If you are looking for a test of whether an explanation is good, the announcement that the participants feel they have achieved a good understanding sounds like success. |
| 15556 | Science may well pursue generalised explanation, rather than laws [Lewis] |
| Full Idea: The pursuit of general explanations may be very much more widespread in science than the pursuit of general laws. | |
| From: David Lewis (Causal Explanation [1986], IV) | |
| A reaction: Nice. I increasingly think that the main target of all enquiry is ever-widening generality, with no need to aspire to universality. |
| 15558 | A good explanation is supposed to show that the event had to happen [Lewis] |
| Full Idea: It is said that a good explanation ought to show that the explanandum event had to happen, given the laws and circumstances. | |
| From: David Lewis (Causal Explanation [1986], V) | |
| A reaction: I cautiously go along with this view. Given that there are necessities in nature (a long story), we should aim to reveal them. There is no higher aspiration open to us than successful explanation. Lewis says good explanations can reveal falsehoods. |
| 4809 | Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos] |
| Full Idea: Lewis endorses the thesis that all explanation of singular events is causal explanation. | |
| From: report of David Lewis (Causal Explanation [1986]) by Stathis Psillos - Causation and Explanation p.237 | |
| A reaction: It is hard to challenge this. The assumption is that only nomological and causal explanations are possible, and the former are unobtainable for singular events. |
| 14321 | To explain an event is to provide some information about its causal history [Lewis] |
| Full Idea: Here is my main thesis: to explain an event is to provide some information about its causal history. | |
| From: David Lewis (Causal Explanation [1986], II) | |
| A reaction: The obvious thought is that you might provide some tiny and barely relevant part of that causal history, such as a bird perched on the Titanic's iceberg. So how do we distinguish the 'important' causal information? |
| 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. |
| 20169 | An action may be intended under one description, but not under another [Kekes] |
| Full Idea: People can usually be described as intending an action under one description, but not under another. ...Consequently the same action may reasonably be said to be both intentional and unintentional. | |
| From: John Kekes (The Human Condition [2010], 07.2) | |
| A reaction: This is the terrorist/freedom fighter problem. The problem seems to arise with long-term intentions, rather than immediate ones. Maybe it is the significance of the intention, rather than the intention itself? |
| 20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
| Full Idea: We increase our control by making our actions more and more the effects of our attitudes, and less and less the effects of external forces acting on us independently of our attitudes. | |
| From: John Kekes (The Human Condition [2010], 02.4) | |
| A reaction: He says that the attitudes should be focused on our well-being. Attitudes may also, however, serve some exernal ideal, such as altruism or patriotism. He has built a case for 'control' being a much more important value than 'free will'. |
| 19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
| Full Idea: Our system of values should be understood, among other things, as our attempt to cope with contingencies by making the connection between our well-being and actions less contingent and more within our control. | |
| From: John Kekes (The Human Condition [2010], Intro) | |
| A reaction: He gives an account in which every aspect of morality focuses on human well-being. Of course, the values will dictate what constitutes that well-being, as well as good means of attaining it. |
| 20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
| Full Idea: Values are ...an attempt to cope with contingencies by making the connection between our well-being and actions less contingent and more within our control. | |
| From: John Kekes (The Human Condition [2010], Intro) | |
| A reaction: This sounds more like principles than values, since the former tell you what to do, but a value in itself is just a picture of possibilities. |
| 20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
| Full Idea: Full responsibility is when evil-doers can fully foresee the harm that results, their victims have not provoked it, it violates the requirements of physical protection in a society, the action reflects character, and it is viciously motivated. | |
| From: John Kekes (The Human Condition [2010], 07.4) | |
| A reaction: [compressed] The point of this is to omit any reference to an explicit intention to perform an evil act. The Nazi Franz Stangl claimed that he never intended evil, but Kekes says that if true he is innocent, but the above definition makes him guilty. |
| 20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
| Full Idea: A central assumption of Western moral thought is mistaken: the requirements of reason and morality do not coincide. Immorality need not be unreasonable. ...Malevolent motives in combination with ideologies supply reasons for doing evil. | |
| From: John Kekes (The Human Condition [2010], 06.5) | |
| A reaction: I presume that Kant would say the malevolent motives are irrational. If I perform an evil act because someone gives me a stupid reason for doing it, I am not thereby rational because I am acting for a reason. Wrong. |
| 20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
| Full Idea: The assumption that the requirements of reason are universal and impersonal ...is false of practical reason that aims at successful action. Whether a belief is true depends on the facts. Whether an action is successful depends on what success consists in. | |
| From: John Kekes (The Human Condition [2010], 08.5) | |
| A reaction: Kekes is trying to eliminate the Kantian idea that reason can lead us to the 'right' thing to do. He rightly points to the complex demands of human, cultural and personal values. |
| 20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
| Full Idea: The absurdity follows [from Kant's categorical imperative] that in the case of moral conflicts reason and morality require us to act irrationally and immorally. | |
| From: John Kekes (The Human Condition [2010], 10.4) | |
| A reaction: We can't pick one from two equals if we must have a reason for the preference, but that does not make it 'irrational' to choose one of them, when it doesn't matter which one is chosen. Taking one of the cheese sandwiches is not irrational. |
| 20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
| Full Idea: We must distinguish between pluralism and relativism about values. Pluralists accept that the validity of cultural and personal values is relative to societies and individuals. But they also hold that human values are objectively valid. | |
| From: John Kekes (The Human Condition [2010], 09.4) | |
| A reaction: This is a very attractive response to global moral relativism. I see a problem in the neat division into three distinct forms of value. Each of the three sets of values ought to be sensitive to the other two areas. Humans are cultured individuals. |
| 20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
| Full Idea: I distinguish four types of cultural values likely to be found in a particular society: interpretations of human values; forms of expression and conduct; institutions and practices within them; and modes of evaluation. | |
| From: John Kekes (The Human Condition [2010], 05.2) | |
| A reaction: He proceeds to enlarge on these four. This sub-divides the second of his three main areas of value. I like philosophers who do that sort of thing. It gives you the reassuring feeling that you can break a problem down into elements we understand.... |
| 20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
| Full Idea: The major problem for the human dimension of values is the prevalence of evil; for the cultural dimension it is widespread disenchantment; and for the personal dimension it is pervasive boredom. | |
| From: John Kekes (The Human Condition [2010], 05.5) | |
| A reaction: Boldly simple claims, but quite persuasive. Presumably it is the evil in human beings, rather than natural evil (like earthquakes) that is the problem. Disenchantment must come through alienation from social values. Powerlessness, rather than boredom? |
| 20156 | We are bound to regret some values we never aspired to [Kekes] |
| Full Idea: We inevitably feel regret for the many values we could have, but did not, try to realize. | |
| From: John Kekes (The Human Condition [2010], 04.5) | |
| A reaction: He's obviously talking about working harder at our projects. |
| 20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
| Full Idea: A significant feature of our system of values is that it provides many more values than we could pursue. ...We encounter values as possibilities, and we must accept or reject them. | |
| From: John Kekes (The Human Condition [2010], 03.1) | |
| A reaction: This immediately invites the lovely question of what values you are going to invoke when you discriminate among the values available in your culture. Nietzsche says it comes down to 'taste'. |
| 20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
| Full Idea: There is an irreducible plurality of values that follow from the universal requirements of human well-being, from a shared cultural identity, and from individual conceptions of well-being. | |
| From: John Kekes (The Human Condition [2010], 05 Intro) | |
| A reaction: This strikes me as a very helpful division. It seems reasonably obvious, but I have not encountered it elsewhere. It is an obvious foundation for international negotiations. We can criticise another culture by appealing to human values. |
| 20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
| Full Idea: The beliefs, emotions, motives, and desires that form our attitudes ...include not only what possibilities we value, but also the limits we should not transgress. ...The strongest limit is what I call 'the unthinkable'. | |
| From: John Kekes (The Human Condition [2010], 03.2) | |
| A reaction: Another chance to link to my favourite idea from Democritus! Ideally we want a theory which shows how a vision of the possibilities immediately points to the limits, and to what is unthinkable. |
| 20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
| Full Idea: Unconditional commitments are the most basic convictions we have. They tell us what we must not do no matter what, what we regard as outrageous, horrible, beyond the pale, or, in religious language, as sacrilegious. | |
| From: John Kekes (The Human Condition [2010], 03.3) | |
| A reaction: The Aztecs should have made rather different unconditional commitments from the ones they ended up with. How do you persuade someone to make such an unconditional commitment. Abortion seems to involve huge clashes here. |
| 20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
| Full Idea: Doing the unthinkable causes deep, often irreparable, damage to our sense of ourselves. ...That is why the unthinkable indicates a more basic commitment than what we have to any value. | |
| From: John Kekes (The Human Condition [2010], 03.3) | |
| A reaction: Kekes makes the interesting claim that what is unthinkable is so basic that it doesn't even count as a value - it is more like a fact of your own nature, which is prior to your values. Not sure about that. |
| 20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
| Full Idea: Four inadequate explanations of human evil attribute it to natural causes, moral monsters, uncharacteristic actions, and corrupting social conditions. | |
| From: John Kekes (The Human Condition [2010], 06.3) | |
| A reaction: He is addressing the 'secular problem of evil', which arises if you assume that human beings are essentially good, and then look around you. He says evil explains corrupting social conditions, so we can't be circular about it. |
| 20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
| Full Idea: A reasonable conception of well-being requires mistake-free attitudes and well-ordered commitments to some values selected from our society's system of values. | |
| From: John Kekes (The Human Condition [2010], 05 Intro) | |
| A reaction: This summarises where he has got to so far. |
| 20154 | Control is the key to well-being [Kekes] |
| Full Idea: Increasing control is the key to our well-being. | |
| From: John Kekes (The Human Condition [2010], 04 Intro) | |
| A reaction: This slogan emerges from a sustained discussion. Hitler and Stalin increased control rather impressively, so we obviously need a bit more than this to get proper well-being. There's also something to be said for going with the flow. |
| 20172 | Boredom destroys our ability to evaluate [Kekes] |
| Full Idea: The threat of boredom is the dissolution of the evaluative dimension of our life. | |
| From: John Kekes (The Human Condition [2010], 09.1) | |
| A reaction: This seems right. If nothing is interesting, then there is no scale of values left, except perhaps 'of possible interest to other people'. |
| 20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
| Full Idea: Boredom combines apathy and restlessness. ...We crave stimulation, worthwhile activities, and objects that engage our interest. | |
| From: John Kekes (The Human Condition [2010], 09.1) |
| 20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
| Full Idea: We feel estranged from our society if the values we prize are not available, and if we do not want to live by the available values. | |
| From: John Kekes (The Human Condition [2010], 04.4) | |
| A reaction: There are two pictures here, for a monolithic culture, and for pluralism. For example, the values of Islam are fairly available in the Christian/atheist UK - but not sharia law. Pluralism can embrace a huge array of moderate values, but not extremes? |
| 20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
| Full Idea: The ideal in an ideology may be set down in a sacred text, exemplified in an exceptional life, dictated by laws of history, sociology, or psychology, located in a past uncorrupted idyllic past, or in a future Utopia of perfected human nature, and so on. | |
| From: John Kekes (The Human Condition [2010], 06.4) | |
| A reaction: A bit grumpy, but a fair observation about an awful lot of slightly mad social endeavours. |
| 20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
| Full Idea: Ideologies have a set of beliefs about the world, an ideal of life, an explanation of the gap between the ideal and actuality, and a program for closing the gap. | |
| From: John Kekes (The Human Condition [2010], 06.4) | |
| A reaction: [compressed] Kekes emerges as a bit right of centre in his politics. He clearly despises such ideologies, yet his book is an optimistic program for correcting things. Maybe the enemy is dogmatic ideologies. Kekes gives an undogmatic account of values. |
| 20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |
| Full Idea: It is useless to distribute insufficient resources equally, because the equal distribution of insufficient resources may result in the even worse outcome that no one's reasonable expectations are met. | |
| From: John Kekes (The Human Condition [2010], 01.5) | |
| A reaction: He gives a shortage of oxygen tanks as a persuasive example, but that is hardly typical of the sorts of things that we normally want to distribute. |
| 15555 | Explaining match lighting in general is like explaining one lighting of a match [Lewis] |
| Full Idea: Explaining why struck matches light in general is not so very different from explaining why some particular struck match lit. ...We may generalize modestly, without laying claim to universality. | |
| From: David Lewis (Causal Explanation [1986], IV) | |
| A reaction: A suggestive remark, since particular causation and general causation seem far apart, but Lewis suggests that the needs of explanation bring them together. Lawlike and unlawlike explanations? |
| 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. |
| 15551 | Ways of carving causes may be natural, but never 'right' [Lewis] |
| Full Idea: There is no one right way - though there may be more or less natural ways - of carving up a causal history. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: This invites a distinction between the 'natural' causes and the 'real' causes. Presumably if any causes were 'real', they would have a better claim to be 'right'. Is an earthquake the 'real' (correct?) cause of a tsunami? |
| 15552 | We only pick 'the' cause for the purposes of some particular enquiry. [Lewis] |
| Full Idea: Disagreement about 'the' cause is only disagreement about which part of the causal history is most salient for the purposes of some particular inquiry. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: I don't believe this. In the majority of cases I see the cause of an event, without having any interest in any particular enquiry. It is just so obvious that there isn't even a disagreement. Maybe there is only one sensible enquiry. |
| 15553 | Causal dependence is counterfactual dependence between events [Lewis] |
| Full Idea: I take causal dependence to be counterfactual dependence, of a suitably back-tracking sort, between distinct events. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: He quotes Hume in support. 'Counterfactual dependence' strikes me as too vague, or merely descriptive, for the job of explanation. 'If...then' is a logical relationship; what is it in nature that justifies the dependency? |
| 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) |