134 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) |
| 5486 | Essentialism says metaphysics can't be done by analysing unreliable language [Ellis] |
| Full Idea: The new essentialism leads to a turning away from semantic analysis as a fundamental tool for the pursuit of metaphysical aims, ..since there is no reason to think that the language we speak accurately reflects the kind of world we live in. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: The last part of that strikes me as false. We have every reason to think that a lot of our language very accurately reflects reality. It had better, because we have no plan B. We should analyse our best concepts, but not outdated, culture-laden ones. |
| 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) |
| 9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
| Full Idea: An argument is 'premise-circular' if it aims to establish a conclusion that is assumed as a premise of that very argument. An argument is 'rule-circular' if it aims to establish a conclusion that asserts the goodness of the rule used in that argument. | |
| From: report of R.B. Braithwaite (Scientific Explanation [1953], p.274-8) by Michael Devitt - There is no a Priori §2 | |
| A reaction: Rule circularity is the sort of thing Quine is always objecting to, but such circularities may be unavoidable, and even totally benign. All the good things in life form a mutually supporting team. |
| 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. |
| 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. |
| 5468 | Properties are 'dispositional', or 'categorical' (the latter as 'block' or 'intrinsic' structures) [Ellis, by PG] |
| Full Idea: 'Dispositional' properties involve behaviour, and 'categorical properties' are structures in two or more dimensions. 'Block' structures (e.g. molecules) depend on other things, and 'instrinsic' structures (e.g. fields) involve no separate parts. | |
| From: report of Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.4) by PG - Db (ideas) | |
| A reaction: This is an essentialist approach to properties, and sounds correct to me. The crucial preliminary step to understanding properties is to eliminate secondary qualities (e.g. colour), which are not properties at all, and cause confusion. |
| 5469 | The passive view of nature says categorical properties are basic, but others say dispositions [Ellis] |
| Full Idea: 'Categorical realism' is the most widely accepted theory of dispositional properties, because passivists can accept it, ..that is, that dispositions supervene on categorical properties; ..the opposite would imply nature is active and reactive. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.4) | |
| A reaction: Essentialists believe 'the opposite' - i.e. that dispositions are fundamental, and hence that the essence of nature is active. See 5468 for explanations of the distinctions. I am with the essentialists on this one. |
| 5456 | Redness is not a property as it is not mind-independent [Ellis] |
| Full Idea: Redness is not a property, because it has no mind-independent existence. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: Well said. Secondary qualities are routinely cited in discussions of properties, and they shouldn't be. Redness causes nothing to happen in the physical world, unless a consciousness experiences it. |
| 5481 | Properties have powers; they aren't just ways for logicians to classify objects [Ellis] |
| Full Idea: One cannot think of a property as just a set of objects in a domain (as Fregean logicians do), as though the property has no powers, but is just a way of classifying objects. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: I agree. It is sometimes suggested that properties are what 'individuate' objects, but how could they do that if they didn't have some power? If properties are known by their causal role, why do they have that causal role? |
| 5458 | Nearly all fundamental properties of physics are dispositional [Ellis] |
| Full Idea: With few, if any, exceptions, the fundamental properties of physical theory are dispositional properties of the things that have them. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: He is denying that they are passive (as Locke saw primary qualities), and says they are actively causal, or else capacities or propensities. Sounds right to me. |
| 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. |
| 5443 | Kripke and others have made essentialism once again respectable [Ellis] |
| Full Idea: The revival of essentialism owes much to the work of Saul Kripke and Hilary Putnam, who made belief in essences once again respectable, with Harré and Madden arguing that there were real causal powers in nature. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Intro) | |
| A reaction: It seems to me important to separate two stages of this: 1) causation results from essences, and 2) essences can never change. The first seems persuasive to me. For the second, see METAPHYSICS/IDENTITY/COUNTERPARTS. |
| 5444 | 'Individual essences' fix a particular individual, and 'kind essences' fix the kind it belongs to [Ellis] |
| Full Idea: The new essentialism retains Aristotelian ideas about essential properties, but it distinguishes more clearly between 'individual essences' and 'kind essences'; the former define a particular individual, the latter what kind it belongs to. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.1) | |
| A reaction: This might actually come into conflict with Aristotle, who seems to think that my personal essence is largely a human nature I share with everyone else. The new distinction is trying to keep the Kantian individual on the stage. |
| 5462 | Essential properties are usually quantitatively determinate [Ellis] |
| Full Idea: Most of the essential properties of things are quantitatively determinate properties. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: This makes the essential nature of the world very much the province of science, which deals in quantities and equations. Essentialists must deal with mental events, as well as basic physics. |
| 5448 | 'Real essence' makes it what it is; 'nominal essence' makes us categorise it a certain way [Ellis] |
| Full Idea: The 'real essence' of a thing is that set of its properties or structures in virtue of which it is a thing of that kind; its 'nominal essence' is the properties or structures in virtue of which it is described as a thing of that kind. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.1) | |
| A reaction: I like this distinction, because it is the kind made by realists like me who are fighting to make philosophers keep their epistemology and their ontology separate. |
| 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? |
| 5477 | One thing can look like something else, without being the something else [Ellis] |
| Full Idea: In considering questions of real possibility, it is important to keep the distinction between what a thing is and what it looks like clearly in mind. There is a possible world containing a horse that could then look like a cow, but it wouldn't BE a horse. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) | |
| A reaction: This is an interesting test assertion of the notion that there are essences (although Ellis does not allow that animals actually have essences - how could you, given evolution?). His point is a good one. |
| 5479 | Scientific essentialists say science should define the limits of the possible [Ellis] |
| Full Idea: Scientific essentialists hold that one of the primary aims of science is to define the limits of the possible. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) | |
| A reaction: I'm not sure working scientists will go along with that, but I like the claim that philosophy is very much part of the same enterprise as practical science (and NOT subservient to it!). I think of metaphysics as very high level physics. |
| 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)? |
| 5483 | Essentialists deny possible worlds, and say possibilities are what is compatible with the actual world [Ellis] |
| Full Idea: Essentialists are modal realists; ..what is really possible, they say, is what is compatible with the natures of things in this world (and this does not commit them to the existence of any world other than the actual world). | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: This introduces something like 'compatibilities' into our ontology. That must rest on some kind of idea of a 'natural contradiction'. We can discuss the possibilities resulting from essences, but what are the possible variations in the essences? |
| 5447 | Metaphysical necessities are true in virtue of the essences of things [Ellis] |
| Full Idea: Metaphysical necessities are propositions that are true in virtue of the essences of things. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.1) | |
| A reaction: I am cautious about this. It sounds like huge Leibnizian metaphysical claims riding in on the back of a rather sensible new view of the laws of science. How can we justify equating natural necessity with metaphysical necessity? |
| 5476 | Essentialists say natural laws are in a new category: necessary a posteriori [Ellis] |
| Full Idea: Essentialists do not accept the standard position, which says necessity is a priori, and contingency is a posteriori. They have a radically new category: the necessary a posteriori. The laws of nature are, for example, both necessary and a posteriori. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) | |
| A reaction: Based on Kripke. I'm cautious about this. Presumably God, who would know the essences, could therefore infer the laws a priori. The laws may follow of necessity from the essences, but the essences can't be known a posteriori to be necessary. |
| 5478 | Imagination tests what is possible for all we know, not true possibility [Ellis] |
| Full Idea: The imaginability test of possibility confuses what is really or metaphysically possible with what is only epistemically possible. ..The latter is just what is possible for all we know. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) |
| 5482 | Possible worlds realism is only needed to give truth conditions for modals and conditionals [Ellis] |
| Full Idea: The main trouble with possible worlds realism is that the only reason anyone has, or ever could have, to believe in other possible worlds (other than this one) is that they are needed, apparently, to provide truth conditions for modals and conditionals. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: This attacks Lewis. Ellis makes this sound like a trivial technicality, but if our metaphysics is going to make sense it must cover modals and conditionals. What do they actually mean? Lewis has a theory, at least. |
| 5453 | Essentialists mostly accept the primary/secondary qualities distinction [Ellis] |
| Full Idea: Essentialists mostly accept the distinction between primary and secondary qualities, ..where the primary qualities of things are those that are intrinsic to the objects that have them. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: One reason I favour essentialism is because I have always thought that the primary/secondary distinction was a key to understanding the world. 'Primary' gets at the ontology, 'secondary' shows us the epistemology. |
| 5466 | Primary qualities are number, figure, size, texture, motion, configuration, impenetrability and (?) mass [Ellis] |
| Full Idea: For Boyle, Locke and Newton, the qualities inherent in bodies were just the primary qualities, namely number, figure, size, texture, motion and configuration of parts, impenetrability and, perhaps, body (or mass). | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.4) | |
| A reaction: It is nice to have a list. Ellis goes on to say these are too passive, and urges dispositions as primary. Even so, the original seventeenth century insight seems to me a brilliant step forward in our understanding of the world. |
| 5485 | Emeralds are naturally green, and only an external force could turn them blue [Ellis] |
| Full Idea: Emeralds cannot all turn blue in 2050 (as Nelson Goodman envisaged), because to do so they would have to have an extrinsically variable nature. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: I was never very impressed by the 'grue' problem, probably for this reason, but also because Goodman probably thought predicates and properties are the same thing, which they aren't (Idea 5457). |
| 5484 | Essentialists don't infer from some to all, but from essences to necessary behaviour [Ellis] |
| Full Idea: For essentialists the problem of induction reduces to discovering what natural kinds there are, and identifying their essential problems and structures. We then know how they must behave in any world, and there is no inference from some to all. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: The obvious question is how you would determine the essences if you are not allowed to infer 'from some to all'. Personally I don't see induction as a problem, because it is self-evidently rational in a stable world. Hume was right to recommend caution. |
| 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. |
| 5457 | Predicates assert properties, values, denials, relations, conventions, existence and fabrications [Ellis, by PG] |
| Full Idea: As well as properties, predicates can assert evaluation, denial, relations, conventions, existence or fabrication. | |
| From: report of Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) by PG - Db (ideas) | |
| A reaction: This seems important, in order to disentangle our ontological commitments from our language, which was a confusion that ran throughout twentieth-century philosophy. A property is a real thing in the world, not a linguistic convention. |
| 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. |
| 5488 | Regularity theories of causation cannot give an account of human agency [Ellis] |
| Full Idea: A Humean theory of causation (as observed regularities) makes it very difficult for anyone even to suggest a plausible theory of human agency. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: I'm not quite sure what a 'theory' of human agency would look like. Hume himself said we only get to understand our mental powers from repeated experience (Idea 2220). How do we learn about the essence of our own will? |
| 5489 | Humans have variable dispositions, and also power to change their dispositions [Ellis] |
| Full Idea: It seems that human beings not only have variable dispositional properties, as most complex systems have, but also meta-powers: powers to change their own dispositional properties. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: This seems to me a key to how we act, and also to morality. 'What dispositions do you want to have?' is the central question of virtue theory. Humans are essentially multi-level thinkers. Irony is the window into the soul. |
| 5490 | Essentialism fits in with Darwinism, but not with extreme politics of left or right [Ellis] |
| Full Idea: The extremes of left and right in politics have much more reason than Darwinists to be threatened by the 'new essentialism', because it must reinstate the concept of human nature. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: The point being that political extremes go against the grain of our nature. Personally I am favour of essentialism, and human nature. I notice that Steven Pinker is now defending human nature, from a background of linguistics and psychology. |
| 5472 | Natural kinds are of objects/substances, or events/processes, or intrinsic natures [Ellis] |
| Full Idea: Natural kinds appear to be of objects or substances, or of events or processes, or of the intrinsic nature of things; hence there should be laws of nature specific to each of these categories. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.5) | |
| A reaction: It is nice to see someone actually discussing what sort of natural kinds there are, instead of getting bogged down in how natural kinds terms get their meaning or reference. Ellis recognises that 'intrinsic nature' needs some discussion. |
| 5471 | Essentialism says natural kinds are fundamental to nature, and determine the laws [Ellis] |
| Full Idea: According to essentialists, the world is wholly structured at the most fundamental level into natural kinds, and the laws of nature are all determined by those kinds. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.5) | |
| A reaction: I am a fan of this view, despite being cautious about claims that natural kinds have necessary identity. Why are the essences active? That is the old Greek puzzle about the origin of movement. And why are natural kinds stable? |
| 5446 | For essentialists two members of a natural kind must be identical [Ellis] |
| Full Idea: Modern essentialists would insist that any two members of the same natural kind must be identical in all essential respects. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.1) | |
| A reaction: For this reason, animals no longer qualify as natural kinds, but electrons, gold atoms, and water molecules do. My sticking point is when anyone asserts that an electron necessarily has (say) its mass. Why no close counterpart of electrons? |
| 5480 | The whole of our world is a natural kind, so all worlds like it necessarily have the same laws [Ellis] |
| Full Idea: It is plausible to suppose that the world is an instance of a natural kind, ..and what is naturally necessary in our world is what must be true in any world of the same natural kind. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) | |
| A reaction: This is putting an awful lot of metaphysical weight on the concept of a 'natural kind', so it had better be a secure one. If we accept that natural laws necessarily follow from essences, why shouldn't the whole of our world have an essence, as water does? |
| 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. |
| 5445 | Essentialists regard inanimate objects as genuine causal agents [Ellis] |
| Full Idea: Essentialist suppose that the inanimate objects of nature are genuine causal agents: things capable of acting or interacting. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Intro) | |
| A reaction: I have no idea how one might demonstrate such a fact, even though it seems to stare us in the face. This is where science bumps into philosophy. I find myself intuitively taking the essentialist side quite strongly. |
| 5463 | Essentialists believe causation is necessary, resulting from dispositions and circumstances [Ellis] |
| Full Idea: Essentialists believe elementary causal relations involve necessary connections between events, namely between the displays of dispositional properties and the circumstances that give rise to them. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.4) | |
| A reaction: I like essentialism, but I feel a Humean caution about talk of 'natural necessity'. Let's just say that causation seems to be entirely the result of the nature of how things are. How things could be is a large topic for little mites like us. |
| 5491 | A general theory of causation is only possible in an area if natural kinds are involved [Ellis] |
| Full Idea: A general theory of causation in an area is possible only if the kinds of entities under investigation can reasonably be assumed to belong to natural kinds. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: Human beings will be a problem, and also different levels of natural kinds (e.g. a chemical and an organism). 'Natural kind' is a very loose concept. He is referring to scientific, rather than philosophical, theories, I presume. |
| 5442 | For 'passivists' behaviour is imposed on things from outside [Ellis] |
| Full Idea: A 'passivist' believes that the tendencies of things to behave as they do can never be inherent in the things themselves; they must always be imposed on them from the outside. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Intro) | |
| A reaction: This is the medieval view, inherited by Newton and Hume, which makes miracles a possibility, and makes the laws of nature contingent. Essentialism disagree. I think I am with the essentialists. |
| 5473 | The laws of nature imitate the hierarchy of natural kinds [Ellis] |
| Full Idea: If the natural kinds are divided into hierarchical categories, then essentialists would expect the laws of nature also to divide up into these categories, with the same hierarchy. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.5) | |
| A reaction: This seems to me a real step forwards in our understanding of nature, and hence a nice example of the contribution which philosophy can make, instead of just physics. |
| 5474 | Laws of nature tend to describe ideal things, or ideal circumstances [Ellis] |
| Full Idea: Most of the propositions we think of as being (or as expressing) genuine laws of nature seem to describe only the behaviour of ideal kinds of things, or of things in ideal circumstances. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.5) | |
| A reaction: Ellis this suggests that this phenomenon is because science aims at broad understanding instead of strict prediction. Do we simplify because we are a bit dim? Or is it because generalisation wouldn't exist without idealisation and abstraction? |
| 5475 | We must explain the necessity, idealisation, ontology and structure of natural laws [Ellis] |
| Full Idea: There are four major problems about the laws of nature: a necessity problem (must they be true?), an idealisation problem (why is this preferable?), an ontological problem (their grounds), and a structural problem (their relationships). | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.5) | |
| A reaction: One might also ask why the laws (or their underlying essences) are the way they are, and not some other way, though the prospects of answering that don't look good. I don't think we should be satisfied with saying all of these questions are hopeless. |
| 5460 | Causal relations cannot be reduced to regularities, as they could occur just once [Ellis] |
| Full Idea: Causal relations cannot be reduced to mere regularities, as Hume supposed, as they could exist as a singular case, even if it never happened on more than one occasions. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: This seems to be the key reason for modern views moving away from Hume. The suspicion is that regularity is a test for or symptom of causation, but we are deeply committed to the real nature of causation being whatever creates the regularities. |
| 5459 | Essentialists say dispositions are basic, rather than supervenient on matter and natural laws [Ellis] |
| Full Idea: Essentialists say that dispositional properties may be fundamental, whereas for a passivist such qualities are not primary, but supervene on the primary qualities of matter, and on the laws of nature. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: I am strongly in favour of this view of nature. Without essentialism, we have laws of nature arising out of a total void (or God), and arbitrarily imposing themselves on matter. What are the 'primary qualities of matter', if not dispositions? |
| 5461 | The essence of uranium is its atomic number and its electron shell [Ellis] |
| Full Idea: The essential properties of uranium are its atomic number, and the common electron shell structure for all uranium atoms. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.3) | |
| A reaction: For those who deny essences (e.g. Quineans) this is a nice challenge. You might have to add accounts of the essences of the various particles that make up the atoms. There is nothing arbitrary or conventional about what makes something uranium. |
| 5464 | For essentialists, laws of nature are metaphysically necessary, being based on essences of natural kinds [Ellis] |
| Full Idea: Essentialist believe the laws of nature are metaphysically necessary, because anything that belongs to a natural kind is logically required (or is necessarily disposed) to behave as its essential properties dictate. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.4) | |
| A reaction: What a thrillingly large claim. Best approached with caution.. If we say 'essences make laws, and essences are necessary', we might wonder whether a natural kind essence could be SLIGHTLY different (a counterpart) in another world. |
| 5487 | Essentialism requires a clear separation of semantics, epistemology and ontology [Ellis] |
| Full Idea: Scientific essentialism requires that philosophers distinguish clearly between semantic issues, epistemological issues, and ontological issues. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.7) | |
| A reaction: Music to my ears - but then I think everyone should require that of philosophers, because it where they get themselves most confused. The trouble is that ontology is only obtainable epistemologically, and only expressible semantically. |
| 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) |