151 ideas
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
Full Idea: Though analysis gives us the truth, and nothing but the truth, yet it can never give us the whole truth | |
From: Bertrand Russell (The Principles of Mathematics [1903], §138) |
14109 | The study of grammar is underestimated in philosophy [Russell] |
Full Idea: The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers. | |
From: Bertrand Russell (The Principles of Mathematics [1903], §046) | |
A reaction: This is a dangerous tendency, which has led to some daft linguistic philosophy, but Russell himself was never guilty of losing the correct perspective on the matter. |
7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
Full Idea: If you start with language and try to work your way outwards, you will never get outside language. | |
From: John Heil (From an Ontological Point of View [2003], Pref) | |
A reaction: This voices my pessimism about the linguistic approach to philosophy (and I don't just mean analysis of ordinary language), though I wonder if the career of (say) John Searle is a counterexample. |
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. |
7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
Full Idea: A commitment to parsimony is not a commitment to a conception of the world as simple. The idea, rather, is that we should not complicate our theories about the world unnecessarily. | |
From: John Heil (From an Ontological Point of View [2003], 13.6) | |
A reaction: In other words, Ockham's Razor is about us, not about the world. It would be absurd to make the a priori assumption that the world has to be simple. Are we, though, creating bad theories by insisting that they should be simple? |
7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
Full Idea: It could well turn out that a simpler theory - a theory with fewer fundamental principles - posits more entities than a more complex competitor. | |
From: John Heil (From an Ontological Point of View [2003], 13.6) | |
A reaction: See also Idea 4036. The point here is that you can't simply translate Ockham as 'keep it simple', as there are different types of simplicity. The best theory will negotiate a balance between entities and principles. |
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'. |
7004 | The view that truth making is entailment is misguided and misleading [Heil] |
Full Idea: I argue that the widely held view that truth making is to be understood as entailment is misguided in principle and potentially misleading. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: If reality was just one particle, what would entail the truths about it? Suppose something appears to be self-evident true about reality, but no one can think of any entailments to derive it? Do we assume a priori that they are possible? |
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) |
7035 | God does not create the world, and then add the classes [Heil] |
Full Idea: It is hard to see classes as an 'addition of being'; God does not create the world, and then add the classes. | |
From: John Heil (From an Ontological Point of View [2003], 13.4 n6) | |
A reaction: This seems right. We may be tempted into believing in the reality of classes when considering maths, but it seems utterly implausible when considering trees or cows. |
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. |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
A reaction: [see Hart 73-74 for an explication of this] |
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. |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
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. |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
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. |
7017 | The reductionist programme dispenses with levels of reality [Heil] |
Full Idea: The reductionist programme dispenses with levels of reality. | |
From: John Heil (From an Ontological Point of View [2003], 04.3) | |
A reaction: Fodor, for example, claims that certain causal laws only operate at high levels of reality. I agree with Heil's idea - the notion that there are different realities around here that don't connect properly to one another is philosopher's madness. |
7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
Full Idea: We should accept levels of organisation, levels of complexity, levels of description, and levels of explanation, but not the levels of reality favoured by many anti-reductionists. The world is then ontologically, but not analytically, reductive. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: This sounds right to me. The crunch questions seem to be whether the boundaries at higher levels of organisation exist lower down, and whether the causal laws of the higher levels can be translated without remainder into lower level laws. |
7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
Full Idea: Realism is sometimes said to involve a commitment to the idea that certain of our concepts, those with respect to which we are realists, 'carve reality at the joints'. | |
From: John Heil (From an Ontological Point of View [2003], 14.11) | |
A reaction: Clearly not all concepts cut nature at the joints (e.g. we have concepts of things we know to be imaginary). Personally I am committed to this view of realism. I try very hard to use concepts that cut accurately; why shouldn't I sometimes succeed? |
7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
Full Idea: Anti-realist philosophers, and those who hope to reduce metaphysics to (or replace it with) the philosophy of language, owe the rest of us an account of the ontology of language. | |
From: John Heil (From an Ontological Point of View [2003], 20.6) | |
A reaction: A nice turning-the-tables question. In all accounts of relativism, x is usually said to be relative to y. You haven't got proper relativism if you haven't relativised both x and y. But relativised them to what? Nietzsche's 'perspectivism' (Idea 4420)? |
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. |
7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
Full Idea: Concepts do not 'carve up' the world; the world already contains endless divisions, most of which we remain oblivious to or ignore. | |
From: John Heil (From an Ontological Point of View [2003], 05.3) | |
A reaction: Concepts could still carve up the world, without ever aspiring to do a complete job. We carve up the aspects that interest us, but the majority of the carving is in response to natural divisions, not whimsical conventions. |
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. |
7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
Full Idea: Some philosophers who accept that properties are intrinsic features of objects regard them as pure powers, pure dispositionalities; I prefer to think of properties as simultaneously dispositional and qualitative. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: I am uneasy about 'qualitative' as a category, and am inclined to reduce it to being a dispositional power to cause primary and secondary qualities in observers. Roughness is only a power, not a quality, if there are no observers. |
7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
Full Idea: When a predicate applies truly to an object, it does so in virtue of designating a property possessed by that object and by every object to which the predicate truly applies (or would apply). | |
From: John Heil (From an Ontological Point of View [2003], 03.3) | |
A reaction: I am sympathetic to Heil's aim of shifting our attention from arbitrary predicates to natural properties, but it won't avoid Fodor's problem (Idea 7014) that all kinds of whimsical predicates will apply 'truly', but fail to pick out anything significant. |
7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
Full Idea: The friend of universals has an account of similarity relations as relations of identity and partial identity; the friend of modes must regard similarity relations as primitive and irreducible. | |
From: John Heil (From an Ontological Point of View [2003], 14.5) | |
A reaction: We always seem to be able to ask 'in what respect' a similarity occurs. If similarity is 'primitive and irreducible', we should not be able to analyse and explain a similarity, yet we seem able to. I conclude that Heil is wrong. |
7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
Full Idea: The modern default position on dispositionality is that powers or dispositions are higher-level properties objects possess by virtue of those objects' possession of lower-level qualitative (categorical) properties. | |
From: John Heil (From an Ontological Point of View [2003], 09.2) | |
A reaction: The new idea which is being floated by Heil, and which I prefer, is that dispositions or powers are basic. A 'quality' is a much more dubious entity than a power. |
7025 | Are a property's dispositions built in, or contingently added? [Heil] |
Full Idea: There is a dispute over whether a property's dispositionality is built into the property or whether it is a contingent add-on. | |
From: John Heil (From an Ontological Point of View [2003], 09.4) | |
A reaction: Put that way, the idea that it is built in seems much more plausible. If it is an add-on, an explanation of why that disposition is added to that particular property seems required. If it is built in, it seems legitimate to accept it as a brute fact. |
7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
Full Idea: Universals can explain the one-over-many problem, and easily explain similarity relations between objects, and explain the similar behaviour of similar objects. | |
From: John Heil (From an Ontological Point of View [2003], 13.1) | |
A reaction: A useful summary. If you accept it, you seem to be faced with a choice between Plato (who has universals existing independently of particulars) and Armstrong (who makes them real, but existing only in particulars). |
7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
Full Idea: Imagine a pair of worlds, one in which there are the universals and their instances and one in which there are just the instances (a world of modes). How would the absence of universals make itself felt? | |
From: John Heil (From an Ontological Point of View [2003], 13.7) | |
A reaction: A nice question for Plato, very much in the spirit of Aristotle's string of questions. Compare 'suppose the physics remained, but someone removed the laws'. Either chaos ensues, or you realise they were redundant. Same with Forms. |
7009 | Similarity among modes will explain everthing universals were for [Heil] |
Full Idea: My contention is that similarity among modes can do the job universals are conventionally postulated to do. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: See Idea 4441 for Russell's nice objection to this view. The very process by which we observes similarities (as assess their degrees) needs to be explained by any adequate theory of properties or universals. |
7041 | Similar objects have similar properties; properties are directly similar [Heil] |
Full Idea: Objects are similar by virtue of possessing similar properties; properties, in contrast, are not similar in virtue of anything. | |
From: John Heil (From an Ontological Point of View [2003], 14.2) | |
A reaction: I am not sure if I can understand the concept of similarity if there is no answer to the question 'In what respect?' I suppose David Hume is happy to take resemblance as given and basic, but it could be defined as 'sharing identical properties'. |
7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
Full Idea: The set of red objects is the set of objects possessing a property: being red. Objects are members of the set in virtue of possessing this property; they do not possess the property in virtue of belonging to the set. | |
From: John Heil (From an Ontological Point of View [2003], 12.2) | |
A reaction: This seems to be a very effective denial of the claim that universals are sets. However, if 'being a Londoner' counts as a property, you can only have it by joining the London set. Being tall is more fundamental than being a Londoner. |
7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
Full Idea: Philosophers identifying themselves as trope theorists have, by and large, accepted some form of the 'bundle theory' of objects: an object is a bundle of compresent tropes. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: This view eliminates anything called 'matter' or 'substance' or a 'bare particular'. I think I agree with Heil that this doesn't give a coherent picture, as properties seem to be 'of' something, and bundles always raise the question of what unites them. |
7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
Full Idea: I think of objects as substances, and a substance is an object considered as a bearer of properties. | |
From: John Heil (From an Ontological Point of View [2003], 04.2) | |
A reaction: This is an area of philosophy I always find disconcerting, where an account of how we should see objects seems to have no connection at all to what physicists report about objects. 'Considered as' seems to make substances entirely conventional. |
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. |
7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
Full Idea: It would seem distinctly possible that there is but a single substance: space-time or some all-encompassing quantum field. | |
From: John Heil (From an Ontological Point of View [2003], 05.2) | |
A reaction: This would at least meet my concern that philosophers' 'substances' don't seem to connect to what physicists talk about. I wonder if anyone knows what a 'quantum field' is? The clash between relativity and quantum theory is being alluded to. |
7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
Full Idea: I prefer the more colloquial 'object' to the traditional term 'substance'. An object can be regarded as a possessor of properties: as something that is red, spherical and pungent, for instance. | |
From: John Heil (From an Ontological Point of View [2003], 15.3) | |
A reaction: A nice move, but it seems to beg the question of 'what is it that has the properties?' Objects and substances do two different jobs in our ontology. Heil is just refusing to discuss what it is that has properties. |
7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
Full Idea: Applications of the principle of the indiscernibility of identicals apparently obliges us to distinguish the statue and the lump of bronze making it up. | |
From: John Heil (From an Ontological Point of View [2003], 16.3) | |
A reaction: In other words, statues and lumps of bronze have different properties. It is a moot point, though, whether there are any discernible differences between that statue at time t and its constituting lump of bronze at time t. |
7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
Full Idea: Must we choose between reductionism (the statue is the lump of bronze), eliminativism (there are no statues, only statue-shaped lumps of bronze), and a commitment to coincident objects? | |
From: John Heil (From an Ontological Point of View [2003], 16.5) | |
A reaction: (Heil goes on to offer his own view). Coincident objects sounds the least plausible view. Modern statues are only statues if we see them that way, but a tree is definitely a tree. Trenton Merricks is good on eliminativism. |
14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
Full Idea: The notion of change is obscured by the doctrine of substance, by a thing's nature versus its external relations, and by subject-predicate form, so that things can be different and the same. Hence the useless distinction between essential and accidental. | |
From: Bertrand Russell (The Principles of Mathematics [1903], §443) | |
A reaction: He goes on to object to vague unconscious usage of 'essence' by modern thinkers, but allows (teasingly) that medieval thinkers may have been precise about it. It is a fact, in common life, that things can change and be the same. Explain it! |
14107 | Terms are identical if they belong to all the same classes [Russell] |
Full Idea: Two terms are identical when the second belongs to every class to which the first belongs. | |
From: Bertrand Russell (The Principles of Mathematics [1903], §026) |
11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
Full Idea: Russell's definition of '=' is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has a sense). | |
From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Tractatus Logico-Philosophicus 5.5302 | |
A reaction: This is what now seems to be a standard denial of the bizarre Leibniz claim that there never could be two things with identical properties, even, it seems, in principle. What would Leibniz made of two electrons? |
22303 | It makes no sense to say that a true proposition could have been false [Russell] |
Full Idea: There seems to be no true proposition of which it makes sense to say that it might have been false. One might as well say that redness might have been a taste and not a colour. | |
From: Bertrand Russell (The Principles of Mathematics [1903], §430), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 29 'Analy' | |
A reaction: Few thinkers agree with this rejection of counterfactuals. It seems to rely on Moore's idea that true propositions are facts. It also sounds deterministic. Does 'he is standing' mean he couldn't have been sitting (at t)? |
7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
Full Idea: A pure quality, a property altogether lacking in dispositionality, would be undetectable and would, in one obvious sense, make no difference to its possessor. | |
From: John Heil (From an Ontological Point of View [2003], 11.4) | |
A reaction: This seems to be a very forceful and simple reason why we cannot view properties simply as qualities of things. Heil wants properties to be dispositions and qualities; personally I would vote for them just being dispositions or powers. |
7029 | Can we distinguish the way a property is from the property? [Heil] |
Full Idea: It is not clear to me that we easily distinguish ways a property is from the property itself. | |
From: John Heil (From an Ontological Point of View [2003], 11.6) | |
A reaction: To defend properties as qualities, he is confusing ontology and epistemology. Presumably he means by 'ways a property is' what I would prefer to call 'ways a property seems to be'. I don't believe a smell is simply what it seems to be. |
7030 | Properties don't possess ways they are, because that just is the property [Heil] |
Full Idea: Objects possess properties, but I am sceptical of the idea that properties possess properties; just as a property is a way some object is, a property of a property would be a way a property is, but that is just the property itself. | |
From: John Heil (From an Ontological Point of View [2003], 12.1) | |
A reaction: This is quite a good defence of the idea that properties are qualities as well as dispositions. However, if we make the qualities of properties into secondary qualities, and the dispositions into primary qualities, the absurdity melts away. |
7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
Full Idea: Secondary qualities are not distinct from primary qualities: an object's possession of a given secondary quality is a matter of its possession of certain complex primary qualities. | |
From: John Heil (From an Ontological Point of View [2003], 17.3) | |
A reaction: The bottom line here is that, if essentialism is right, colours are not properties at all (see Idea 5456). Heil wants to subsume secondary properties within primary properties. I think we should sharply distinguish them. |
7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
Full Idea: Secondary qualities are just ordinary properties - roughly, Locke's primary qualities - considered in the light of their effects on us. | |
From: John Heil (From an Ontological Point of View [2003], 14.10) | |
A reaction: Unconvincing. If they only acquire their ontological status as primary qualities if they have to be considered in relation to something (us), then that is not a primary quality. |
7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
Full Idea: Theories that take colours to be properties of the surfaces of objects have difficulty accounting for a host of phenomena including coloured light emitted by radiant sources and so-called film colours (the colour of the sky, for instance). | |
From: John Heil (From an Ontological Point of View [2003], 17.4) | |
A reaction: Personally I never thought that colours might be actual properties of surfaces, but it is nice to have spelled out a couple of instances that make it very implausible. Neon and sodium lights I take to be examples of the first case. |
7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
Full Idea: Theories that tie colours to features of light radiation deal with radiant and diffused colours, but yield implausible results for objects; tomatoes are not red, on such a view, but merely reflect red light. | |
From: John Heil (From an Ontological Point of View [2003], 17.4) | |
A reaction: I see absolutely no problem with the philosophical denial that tomatoes are actually red, while continuing to use 'red' of tomatoes in the normal way. When we analyse our processes of knowledge acquisition, we must give up 'common sense'. |
7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
Full Idea: For those who regard the world as text or a social construct, are texts and social constructs real entities? If they are, what are they? | |
From: John Heil (From an Ontological Point of View [2003], 20.6) | |
A reaction: A nice turn-the-tables question. The oldest attacks of all on scepticism and relativism consist of showing that the positions themselves rest on knowledge or truth. Nietzsche may be the best model for relativists. E.g. Idea 4420. |
7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
Full Idea: If the world is somehow theory-dependent, this implies, on pain of a regress, that theories are not theory-dependent. | |
From: John Heil (From an Ontological Point of View [2003], 06.4) | |
A reaction: I am not sure where this puts the ontology of theories, but this is a nice question, of a type which never seems to occur to your more simple-minded relativist. |
7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
Full Idea: The sciences are sometimes said to be in the business of identifying and classifying powers; the mass of an electron, its spin and charge, could be regarded as powers possessed by the electron; science is silent on an electron's qualities. | |
From: John Heil (From an Ontological Point of View [2003], 11.2) | |
A reaction: Heil raises the possibility that qualities are real, despite the silence of science; he wants colour to be a real quality. I like the simpler version of science. Qualities are the mental effects of powers; there exist substances, powers and effects. |
7060 | One form of explanation is by decomposition [Heil] |
Full Idea: One form of explanation is by decomposition. | |
From: John Heil (From an Ontological Point of View [2003], 19.8) | |
A reaction: This is a fancy word for taking it apart, presumably to see how it works, which implies a functional explanation, rather than to see what it is made of, which seeks an ontological explanation. Simply 'decomposing' something wouldn't in itself explain. |
7010 | Dispositionality provides the grounding for intentionality [Heil] |
Full Idea: Dispositionality provides the grounding for intentionality. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: This is a view with which I am sympathetic, though I am not sure if it explains anything. It would be necessary to identify a disposition of basic matter that could be built up into the disposition of a brain to think about things. |
7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
Full Idea: Nowadays philosophers concerned with intentionality divide into two camps. Internalists epitomise a traditional approach to thought, as intrinsic features of thinkers; externalists say it depends on contextual factors (environment or community). | |
From: John Heil (From an Ontological Point of View [2003], 18.2) | |
A reaction: This is basic to understanding modern debates (those that grow out of Putnam's Twin Earth). Externalism is fashionable, but I am reluctant to shake off my quaint internalism. Start by separating strict and literal meaning from speaker's meaning. |
7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
Full Idea: Properties of conscious experience, the so-called qualia, are not dangling appendages to material states and processes but intrinsic ingredients of those states and processes. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: Personally I am inclined to the view that qualia are intrinsic to the processes and NOT to the 'states'. Heil must be right, though. I am sure qualia are not just epiphenomena - they are too useful. |
7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
Full Idea: Philosophers' zombies (invented by Robert Kirk) differ from the zombies of folklore; they are intended to make clear the idea that consciousness is an addition of being, something 'over and above' the physical world. | |
From: John Heil (From an Ontological Point of View [2003], 20.1 n1) | |
A reaction: The famous defender of zombies is David Chalmers. You can't believe in zombies if you believe (as I do) that 'the physical entails the mental'. Could there be redness without something that is red? If consciousness is extra, what is conscious? |
7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
Full Idea: The possibility of zombies is founded on the idea that consciousness is related contingently to physical states and processes. | |
From: John Heil (From an Ontological Point of View [2003], 20.3) | |
A reaction: The question is, how do you decide whether the relationship is contingent or necessary? Hence the interest in whether conceivability entails possibility. Kripke attacks the idea of contingent identity, pointing towards necessity, and away from zombies. |
7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
Full Idea: Functionalists deny that zombies are possible since states of mind (including conscious states) are purely functional states. If two agents are in the same functional state, regardless of qualitative difference, they are in the same mental state. | |
From: John Heil (From an Ontological Point of View [2003], 20.5) | |
A reaction: In its 'brief' form this idea begins to smell of tautology. Only the right sort of functional state would entail a mental state, and how else can that functional state be defined, apart from its leading to a mental state? |
7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
Full Idea: A central tenet of functionalism is that objects can be dispositionally indiscernible but differ qualitatively as much as you please. | |
From: John Heil (From an Ontological Point of View [2003], 11.3) | |
A reaction: This refers to the multiple realisability of functions. Presumably we reconcile essentialism with the functionalist view by saying that dispositions result from combinations of qualities. A unique combination of qualities will necessitate a disposition. |
7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
Full Idea: Functionalism has been widely criticized on the grounds that it is implausible to think that functional organization alone could suffice for conscious experience. | |
From: John Heil (From an Ontological Point of View [2003], 20.2) | |
A reaction: He cites Block's 'Chinese Mind' as an example. The obvious reply is that you can't explain consciousness with a lump of meat, or with behaviour, or with an anomalous property, or even with a non-physical substance. |
7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
Full Idea: The expression 'explanatory gap' was coined by Joseph Levine in 1983. McGinn and Chalmers have invoked it in defence of the view that consciousness is physically inexplicable, and Nagel that it is inexplicable given existing conceptual resources. | |
From: John Heil (From an Ontological Point of View [2003], 19.8 n14) | |
A reaction: Coining a few concepts isn't going to help, but discovering more about the brain might. With computer simulations we will 'see' more of the physical end of thought. Psychologists may break thought down into physically more manageable components. |
7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
Full Idea: If we regard a Volvo car as a higher-level entity with its own independent reality, something distinct from its constituents (arranged in particular ways and variously connected to other things), we render mysterious how Volvos could do anything at all. | |
From: John Heil (From an Ontological Point of View [2003], 02.3) | |
A reaction: This seems to me perhaps the key reason why we have to be reductionists. The so-called 'bridge laws' from mind to brain are not just needed to explain the mind, they are also essential to show how a mind would cause behaviour. |
7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
Full Idea: Cases of multiple realisability are typically cases in which some predicate ('is red', 'is in pain') applies to an object in virtue of that object's possession of any of a diverse range of properties. | |
From: John Heil (From an Ontological Point of View [2003], 14.8) | |
A reaction: If the properties are diverse, why does one predicate apply to them? I take it that in the case of the pain, the predicate is ambiguous in applying to the behaviour or the phenomenal property. Same behaviour is possible with many qualia. |
7058 | Externalism is causal-historical, or social, or biological [Heil] |
Full Idea: Some externalists focus on causal-historical connections, others emphasise social matters (especially thinkers' linguistic communities), still others focus on biological function. | |
From: John Heil (From an Ontological Point of View [2003], 18.5 n6) | |
A reaction: Helpful. The social view strikes me as the one to take most seriously (allowing for contextual views of justification, and for the social role of experts). The problem is to combine the social view with realism and a robust view of truth. |
7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
Full Idea: I suggest that intentionality is grounded in the dispositionalities of agents. Dispositions are intrinsic to agents, so this places me on the side of the internalists and against the externalists. | |
From: John Heil (From an Ontological Point of View [2003], 18.4) | |
A reaction: I think this is a key idea, and the right view. The key question is whether we see intentionality as active or passive. The externalist view seems to see the brain as a passive organ which the world manipulates. If the brain is active, what is it doing? |
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. |
7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
Full Idea: The theory of language which I designate the 'Picture Theory' says that language pictures reality in roughly the sense that we can 'read off' features of reality from our ways of speaking about it. | |
From: John Heil (From an Ontological Point of View [2003], 03.2) | |
A reaction: Heil, quite rightly, attacks this view very strongly. I think of it as the great twentieth century philosophical heresy, that leads to shocking views like relativism and anti-realism. |
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. |
7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
Full Idea: When pressed, philosophers will describe propositions as states of affairs or sets of possible worlds. But wait! Neither sets of possible worlds nor states of affairs - electrons being negatively charged, for instance - have truth values. | |
From: John Heil (From an Ontological Point of View [2003], Intro) | |
A reaction: I'm not sure that I see a problem. A pure proposition, expressed as, say "there is a giraffe on the roof" only acquires a truth value at the point where you assert it or believe it. There IS a possible world where there is a giraffe on the roof. |
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. |
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. |
7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
Full Idea: The notion that every causal sequence if backed by a law, like the idea that causation is a relation among particular events, forms a part of philosophy's Humean heritage. | |
From: John Heil (From an Ontological Point of View [2003], 04.3) | |
A reaction: This nicely pinpoints a view that needs to come under attack. I take the view that there are no 'laws' - other than the regularities in behaviour that result from the interaction of essential dispositional properties. Essences don't need laws. |
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) |
7036 | The real natural properties are sparse, but there are many complex properties [Heil] |
Full Idea: I am sympathetic to the idea that the real properties are 'sparse'; ...but if, in counting kinds of property, we include complex properties as well as simple properties, the image of sparseness evaporates. | |
From: John Heil (From an Ontological Point of View [2003], 13.4) | |
A reaction: This seems right to me, and invites the obvious question of which are the sparse real properties. Presumably we let the physicists tell us that, though Heil wants to include qualities like phenomenal colour, which physicists ignore. |