163 ideas
| 3722 | Metaphysics goes beyond the empirical, so doesn't need examples [Kant] |
| Full Idea: Metaphysics doesn't let itself be held back by anything empirical, and indeed goes right to Ideas, where examples themselves fail. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 412.36) |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| Full Idea: Though analysis gives us the truth, and nothing but the truth, yet it can never give us the whole truth | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §138) |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| Full Idea: The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §046) | |
| A reaction: This is a dangerous tendency, which has led to some daft linguistic philosophy, but Russell himself was never guilty of losing the correct perspective on the matter. |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| Full Idea: It is said that analysis is falsification, that the complex is not equivalent to the sum of its constituents and is changed when analysed into these. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: Not quite Moore's Paradox of Analysis, but close. Russell is articulating the view we now call 'holism' - that the whole is more than the sum of its parts - which I can never quite believe. |
| 3738 | The hallmark of rationality is setting itself an end [Kant] |
| Full Idea: Rational nature separates itself out from all other things by the fact that it sets itself an end. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 437.82) |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| Full Idea: A definition as an analysis of an idea into its constituents is inconvenient and, I think, useless; it overlooks the fact that wholes are not, as a rule, determinate when their constituents are given. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §108) | |
| A reaction: The influence of Leibniz seems rather strong here, since he was obsessed with explaining what creates true unities. |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| Full Idea: The statement that a class is to be represented by a symbol is a definition in mathematics, and says nothing about mathematical entities. Any formula can be stated in terms of primitive ideas, so the definitions are superfluous. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §412) | |
| A reaction: [compressed wording] I'm not sure that everyone would agree with this (e.g. Kit Fine), as certain types of numbers seem to be introduced by stipulative definitions. |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| Full Idea: In the objectionable kind of infinite regress, some propositions join to constitute the meaning of some proposition, but one of them is similarly compounded, and so ad infinitum. This comes from circular definitions, where the term defined reappears. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §329) |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| Full Idea: Every proposition function …has, in addition to its range of truth, a range of significance, i.e. a range within which x must lie if φ(x) is to be a proposition at all, whether true or false. This is the first point of the theory of types. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App B:523), quoted by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: Magidor quotes this as the origin of the idea of a 'category mistake'. It is the basis of the formal theory of types, but is highly influential in philosophy generally, especially as a criterion for ruling many propositions as 'meaningless'. |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| Full Idea: I hold that what is true or false is not in general mental, and requiring a name for the true or false as such, this name can scarcely be other than 'propositions'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], Pref) | |
| A reaction: This is the Fregean and logicians' dream that that there is some fixed eternal realm of the true and the false. I think true and false concern the mental. We can talk about the 'facts' which are independent of minds, but not the 'truth'. |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| Full Idea: "The death of Caesar is true" is not, I think, the same proposition as "Caesar died". | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §478) | |
| A reaction: I suspect that it was this remark which provoked Ramsey into rebellion, because he couldn't see the difference. Nowadays we must talk first of conversational implicature, and then of language and metalanguage. |
| 14113 | The null class is a fiction [Russell] |
| Full Idea: The null class is a fiction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §079) | |
| A reaction: This does not commit him to regarding all classes as fictions - though he seems to have eventually come to believe that. The null class seems to have a role something like 'Once upon a time...' in story-telling. You can then tell truth or fiction. |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| Full Idea: Russell was the inventor of the naïve set theory so often attributed to Cantor. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| Full Idea: The two sources of order are 'between' and 'separation'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §204) |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| Full Idea: All order depends upon transitive asymmetrical relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §208) |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| Full Idea: The relation of whole and part is, it would seem, an indefinable and ultimate relation, or rather several relations, often confounded, of which one at least is indefinable. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §135) | |
| A reaction: This is before anyone had produced a mathematical account of mereology (qv). |
| 14106 | Implication cannot be defined [Russell] |
| Full Idea: A definition of implication is quite impossible. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §016) |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §037) | |
| A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'. |
| 14167 | The only classes are things, predicates and relations [Russell] |
| Full Idea: The only classes appear to be things, predicates and relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §440) | |
| A reaction: This is the first-order logic view of reality, which has begun to look incredibly impoverished in modern times. Processes certainly demand a hearing, as do modal facts. |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| Full Idea: The number of logical constants is not great: it appears, in fact, to be eight or nine. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §012) | |
| A reaction: There is, of course, lots of scope for interdefinability. No one is going to disagree greatly with his claim, so it is an interesting fact, which invites some sort of (non-platonic) explanation. |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3 | |
| A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value? |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| Full Idea: A constant is something absolutely definite, concerning which there is no ambiguity whatever. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §006) |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| Full Idea: A variable is not any term simply, but any term as entering into a propositional function. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §093) | |
| A reaction: So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107). |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| Full Idea: The word 'any' is preferable to the word 'all' where infinite classes are concerned. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §284) | |
| A reaction: The reason must be that it is hard to quantify over 'all' of the infinite members, but it is easier to say what is true of any one of them. |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| Full Idea: When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §321) | |
| A reaction: Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle. |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| Full Idea: Burali-Forti didn't discover any paradoxes, though his work suggested a paradox to Russell. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| Full Idea: The approach to practical geometry of the idealists, and especially of Kant, was that we must be certain of the premisses on their own account. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| Full Idea: Geometry no longer throws any direct light on the nature of actual space. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: This was 1903. Minkowski then contributed a geometry of space which was used in Einstein's General Theory. It looks to me as if geometry reveals the possibilities for actual space. |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| Full Idea: As a branch of pure mathematics, geometry is strictly deductive, indifferent to the choice of its premises, and to the question of whether there strictly exist such entities. It just deals with series of more than one dimension. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §352) | |
| A reaction: This seems to be the culmination of the seventeenth century reduction of geometry to algebra. Russell admits that there is also the 'study of actual space'. |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| Full Idea: The approach to practical geometry of the empiricists, notably Mill, was to show that no other set of premisses would give results consistent with experience. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: The modern phrase might be that geometry just needs to be 'empirically adequate'. The empiricists are faced with the possibility of more than one successful set of premisses, and the idealist don't know how to demonstrate truth. |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| Full Idea: Two points will define the line that joins them ('descriptive' geometry), the distance between them ('metrical' geometry), and the whole of the extended line ('projective' geometry). | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], §362) by PG - Db (ideas) | |
| A reaction: [a summary of Russell's §362] Projective Geometry clearly has the highest generality, and the modern view seems to make it the master subject of geometry. |
| 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. |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| Full Idea: Whatever may be an object of thought, or occur in a true or false proposition, or be counted as one, I call a term. This is the widest word in the philosophical vocabulary, which I use synonymously with unit, individual, entity (being one, and existing). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §047) | |
| A reaction: The claim of existence begs many questions, such as whether the non-existence of the Loch Ness Monster is an 'object' of thought. |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| Full Idea: It is sufficient to observe that all unities are propositions or propositional concepts, and that consequently nothing that exists is a unity. If, therefore, it is maintained that things are unities, we must reply that no things exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: The point, I presume, is that you end up as a nihilist about identities (like van Inwagen and Merricks) by mistakenly thinking (as Aristotle and Leibniz did) that everything that exists needs to have something called 'unity'. |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| Full Idea: The only kind of unity to which I can attach any precise sense - apart from the unity of the absolutely simple - is that of a whole composed of parts. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: This comes from a keen student of Leibniz, who was obsessed with unity. Russell leaves unaddressed the question of what turns some parts into a whole. |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| Full Idea: In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §070) | |
| A reaction: This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes. |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| Full Idea: The notion of change is obscured by the doctrine of substance, by a thing's nature versus its external relations, and by subject-predicate form, so that things can be different and the same. Hence the useless distinction between essential and accidental. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §443) | |
| A reaction: He goes on to object to vague unconscious usage of 'essence' by modern thinkers, but allows (teasingly) that medieval thinkers may have been precise about it. It is a fact, in common life, that things can change and be the same. Explain it! |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| Full Idea: Two terms are identical when the second belongs to every class to which the first belongs. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §026) |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| Full Idea: Russell's definition of '=' is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has a sense). | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Tractatus Logico-Philosophicus 5.5302 | |
| A reaction: This is what now seems to be a standard denial of the bizarre Leibniz claim that there never could be two things with identical properties, even, it seems, in principle. What would Leibniz made of two electrons? |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| Full Idea: There seems to be no true proposition of which it makes sense to say that it might have been false. One might as well say that redness might have been a taste and not a colour. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §430), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 29 'Analy' | |
| A reaction: Few thinkers agree with this rejection of counterfactuals. It seems to rely on Moore's idea that true propositions are facts. It also sounds deterministic. Does 'he is standing' mean he couldn't have been sitting (at t)? |
| 3726 | The categorical imperative is a practical synthetic a priori proposition [Kant] |
| Full Idea: With the categorical imperative or law of morality we have a very serious difficulty, because it is a synthetic a priori practical proposition. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 420.50) |
| 3102 | Why don't we experience or remember going to sleep at night? [Magee] |
| Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?' | |
| From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I) | |
| A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose. |
| 3739 | Free will is a kind of causality which works independently of other causes [Kant] |
| Full Idea: Will is a kind of causality belonging to living beings so far as they are rational. Freedom would then be the property this causality has of being able to work independently of determination by alien causes. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 446.97) |
| 3741 | We shall never be able to comprehend how freedom is possible [Kant] |
| Full Idea: We shall never be able to comprehend how freedom is possible. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 456.115) |
| 3740 | We cannot conceive of reason as being externally controlled [Kant] |
| Full Idea: We cannot possibly conceive of a reason as being consciously directed from outside in regard to its judgements. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 448.101) |
| 5296 | Kant made the political will into a pure self-determined "free" will [Kant, by Marx/Engels] |
| Full Idea: Kant made the materially motivated determinations of the will of the French bourgeois into pure self-determinations of the "free will", of the will in and for itself. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by K Marx / F Engels - The German Ideology §II | |
| A reaction: This is the social determinism of Marx and Engels. Most commentators would say that Kant was taking the idea of "free will" from religion rather than politics, but presumably Marx would merely reply "same thing!" |
| 24011 | Kant thought emotions are too random and passive to be part of morality [Kant, by Williams,B] |
| Full Idea: Kant thinks emotions can't contribute to moral worth because emotions are too capricious, they are too passive, and they are fortuitously distributed by nature. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Bernard Williams - Morality and the emotions p.226 | |
| A reaction: [compressed] If, like Kant, you want morality to be concerned with rational principles, then you will want morality to be clear, stable and consistent - which emotions are not. I'm with Williams on this one. |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| Full Idea: The relations in an abstraction principle are always constituted by possession of a common property (which is imprecise as it relies on 'predicate'), ..so we say a common property of two terms is any third term to which both have the same relation. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: This brings out clearly the linguistic approach of the modern account of abstraction, where the older abstractionism was torn between the ontology and the epistemology (that is, the parts of objects, or the appearances of them in the mind). |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| Full Idea: The principle of Abstraction says that whenever a relation with instances is symmetrical and transitive, then the relation is not primitive, but is analyzable into sameness of relation to some other term. ..This is provable and states a common assumption. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: At last I have found someone who explains the whole thing clearly! Bertrand Russell was wonderful. See other ideas on the subject from this text, for a proper understanding of abstraction by equivalence. |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| Full Idea: The possession of a common property of a certain type always leads to a symmetrical transitive relation. The principle of Abstraction asserts the converse, that such relations only spring from common properties of the above type. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: The type of property is where only one term is applicable to it, such as the magnitude of a quantity, or the time of an event. So symmetrical and transitive relations occur if and only if there is a property of that type. |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| Full Idea: A proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §051) | |
| A reaction: Russell says in his Preface that he took over this view of propositions from G.E. Moore. They are now known as 'Russellian' propositions, which are mainly distinguished by not being mental event, but by being complexes out in the world. |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| Full Idea: Russell often treated propositions as facts, but discovered that correspondence then became useless for explaining truth, since every meaningful expression, true or false, expresses a proposition. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Donald Davidson - Truth and Predication 6 | |
| A reaction: So 'pigs fly' would have to mean pigs actually flying (which they don't). They might correspond to possible situations, but only if pigs might fly. What do you make of 'circles are square'? Russell had many a sleepless night over that. |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| Full Idea: A proposition is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §054) | |
| A reaction: The question of the 'unity of the proposition' led to a prolonged debate. |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| Full Idea: Moore and Russell reacted strongly against the idea that the unity of the proposition depended on human acts of judgement. ...Russell decided that unless the unity is explained in terms of the proposition itself, there can be no objective truth. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], p.42) by Donald Davidson - Truth and Predication 5 | |
| A reaction: Put like this, the Russellian view strikes me as false. Effectively he is saying that a unified proposition is the same as a fact. I take a proposition to be a brain event, best labelled by Frege as a 'thought'. Thoughts may not even have parts. |
| 5074 | Kant united religion and philosophy, by basing obedience to law on reason instead of faith [Taylor,R on Kant] |
| Full Idea: Kant united the two ideas of virtue (as being and as doing) into the idea of a law that is founded not upon faith but upon reason. Thus in one stroke he united the seemingly irreconcilable philosophical and religious ethics, preserving the best of both. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8 | |
| A reaction: An interesting analysis that sounds exactly right. Taylor's point is that Kant subjects himself to an authority, when the underpinnings of the authority are no longer there. There is a religious strand in the altruistic requirements of utilitarianism too. |
| 8024 | The categorical imperative says nothing about what our activities and ends should be [MacIntyre on Kant] |
| Full Idea: As to what activities we ought to engage in, what ends we should pursue, the categorical imperative seems to be silent. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - A Short History of Ethics Ch.14 | |
| A reaction: I think this is the fatal objection to Kant's view. He says, for example, that promise-breaking is inconsistent with a belief that promises are good, but who said promises are good? No ethical system can get started without values. |
| 22390 | Kant thought human nature was pure hedonism, so virtue is only possible via the categorical imperative [Foot on Kant] |
| Full Idea: Kant was a psychological hedonist about all actions except those done for the sake of the moral law, and this faulty theory of human nature prevented him from seeing that moral virtue might be compatible with the rejection of the categorical imperative. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Philippa Foot - Morality as system of hypothetical imperatives p.165 | |
| A reaction: Nice. Kant wasn't unusual in his view, which seems standard in the Renaissance and Enlightenment. Aristotle understood that it is human nature, on the whole, to want to be a good citizen, since we are social beings. |
| 9750 | We must only value what others find acceptable [Kant, by Korsgaard] |
| Full Idea: We are limited to pursuits which are acceptable from the standpoint of others; ..hence we can't value just anything, and there are things which we must value. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Christine M. Korsgaard - Intro to 'Creating the Kingdom of Ends' x | |
| A reaction: This at least moves towards greater objectivity, compared with Idea 9749, but it now seems deeply conservative. Our values become lowest common denominator. We need space for the Nietzschean moral hero, who creates new values. |
| 20160 | Kant focuses exclusively on human values, and neglects cultural and personal values [Kekes on Kant] |
| Full Idea: Kant grossly inflated the importance of the human dimension of value in which moral considerations are indeed overriding. He unjustifiably denied the perfectly reasonable contributions of the cultural and personal dimensions to human well-being. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by John Kekes - The Human Condition 05.5 | |
| A reaction: Excellent to see someone talking about the ultimate values that reside behind Kant's theory. Without such assumptions his theory is, frankly, ridiculous (as Mill explained). |
| 9749 | Our rational choices confer value, arising from the sense that we ourselves are important [Kant, by Korsgaard] |
| Full Idea: According to Kant, we confer value on the objects of our rational choices. ..When we choose things because they are important to us we are taking ourselves to be important. Hence our humanity is a source of value. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Christine M. Korsgaard - Intro to 'Creating the Kingdom of Ends' ix | |
| A reaction: He's trying to filter to out our gormless choices with the word 'rational', but it is common sense that I may choose things despite thinking they have little value, like watching soap opera. A more objective account of value seems needed. See 9750! |
| 7671 | Values are created by human choices, and are not some intrinsic quality, out there [Kant, by Berlin] |
| Full Idea: Kant's fundamental sermon is that a value is made a value (or, at least, a duty) by human choice and not by some intrinsic quality in itself, out there. Values are what humans freely choose to live, fight and die for. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Isaiah Berlin - The Roots of Romanticism Ch.4 | |
| A reaction: If this is right, then it would appear that the great Kant is the father of relativism, which wouldn't please him. However, his whole system rests on what is consistent and rational, and that seems to a value that is above our choices. |
| 3720 | We may claim noble motives, but we cannot penetrate our secret impulses [Kant] |
| Full Idea: We are pleased to flatter ourselves with the false claim to a nobler motive, but in fact we can never, even by the most strenuous self-examination, get to the bottom of our secret impulsions. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 407.26) | |
| A reaction: Sounds more like Nietzsche than Kant. If some impulsions are totally hidden from us, then they are presumably irrelevant to any rational or moral thinking. Look at the deeds. |
| 3717 | Reverence is awareness of a value which demolishes my self-love [Kant] |
| Full Idea: Reverence is awareness of a value which demolishes my self-love. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 401.16 n) | |
| A reaction: Presumably simple love of someone or something could achieve this, without the addition of reverence. I'm suspicious of this idea, because some dreadful people have commanded reverence. |
| 3712 | A good will is not good because of what it achieves [Kant] |
| Full Idea: A good will is not good because of what it effects or accomplishes. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 394.3) | |
| A reaction: This invites the obvious objection of the well-meaning fool, who causes misery despite meaning well. I firmly hold the view that what matters is what we do, not what we intend. |
| 3725 | The good of an action is in the mind of the doer, not the consequences [Kant] |
| Full Idea: What is essentially good in an action consists in the mental disposition, let the consequences be what they may. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 416.43) | |
| A reaction: Dreadful idea. I always claim that consequences are relevant in Kant, in formulating and choosing maxims for action, but this idea seems to refute my view. This is a slogan for the Spanish Inquisition. |
| 3733 | The 'golden rule' cannot be a universal law as it implies no duties [Kant] |
| Full Idea: The 'golden rule' is merely derivative from our principle, but it cannot be a universal law since it isn't the ground of duties to oneself or others (since it implies a breakable contract). | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 430.68 n) |
| 3736 | Virtue lets a rational being make universal law, and share in the kingdom of ends [Kant] |
| Full Idea: A morally good attitude of mind (or virtue) claims the intrinsic value of dignity, because it affords a rational being a share in the making of universal law, which therefore fits him to be a member in a possible kingdom of ends. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 435.79) |
| 3544 | Kant thinks virtue becomes passive, and hence morally unaccountable [Kant, by Annas] |
| Full Idea: Kant thinks that if virtue becomes a stable disposition of the person, then it turns into a rigid mechanical habit, with respect to which the person is passive, and thus not fully morally accountable. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Julia Annas - The Morality of Happiness 2.1 |
| 7674 | Generosity and pity are vices, because they falsely imply one person's superiority to another [Kant, by Berlin] |
| Full Idea: For Kant, generosity is a vice, because it is a form of condescension and patronage, and pity is detestable, because it entails a superiority on the part of the pitier, which Kant stoutly denied. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: An interesting view, but being too proud to receive help from friends strikes me as a greater vice. How can friendship and community be built, if we do not rush to help one another when needed? The virtue is generosity without condescension. |
| 21029 | Kantian respect is for humanity and reason (not from love or sympathy or solidarity) [Kant, by Sandel] |
| Full Idea: Kantian respect is unlike love. It's unlike sympathy. It's unlike solidarity or fellow feeling. ...Kantian respect is for humanity as such, for a rational capacity that resides, undifferentiated, in all of us. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Michael J. Sandel - Justice: What's the right thing to do? 05 | |
| A reaction: Why is it 'undifferentiated'? If reason is the source of the respect, why don't greater powers of reason command greater respect? The nice thing is that the rejected versions involve bias, but Kant's version does not. |
| 7105 | If 'maxims' are deeper underlying intentions, Kant can be read as a virtue theorist [Kant, by Statman] |
| Full Idea: It has been argued that by 'maxim' Kant does not mean a specific intention for some discrete act, but the underlying intention by which the agent orchestrates his numerous more specific intentions, ...which leads to a virtue reading of Kant. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Daniel Statman - Introduction to Virtue Ethics §7 | |
| A reaction: Kant admired virtue of character, and would want to fit it into the framework of his moral duties. Nevertheless a virtue would often seem to be beyond words, and principles seem to crumble in the face of complex cases. |
| 7625 | We can ask how rational goodness is, but also why is rationality good [Putnam on Kant] |
| Full Idea: We can reverse the terms of the comparison and ask not how rational is goodness, but why is it good to be rational? | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Hilary Putnam - Reason, Truth and History | |
| A reaction: [Putnam doesn't mention Kant]. This seems to me to be the biggest question for Kant. See Idea 1403. The main point of tbe romantic movement, I take it, is that purely rational living does not bring happiness or fulfilment. |
| 3710 | The only purely good thing is a good will [Kant] |
| Full Idea: It is impossible to conceive anything at all in the world, or even out of it, which can be taken as good without qualification, except a good will. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 393.1) | |
| A reaction: This is precisely the thought of Epictetus, that the will is the source of goodness, because morality resides in choices (as opposed to character, or states of affairs). |
| 3737 | The will is good if its universalised maxim is never in conflict with itself [Kant] |
| Full Idea: The will is absolutely good if it cannot be evil - that is, if its maxim, when made into a universal law, can never be in conflict with itself. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 437.81) |
| 3715 | Other causes can produce nice results, so morality must consist in the law, found only in rational beings [Kant] |
| Full Idea: Agreeable results could be brought about by other causes;…therefore nothing but the idea of the law in itself, which is present only in a rational being, can constitute that pre-eminent good which we call moral. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 401.15) |
| 20715 | It is basic that moral actions must be done from duty [Kant] |
| Full Idea: The first proposition of morality is that to have moral worth an action must be done from duty. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], p.19), quoted by Brian Davies - Introduction to the Philosophy of Religion 9 'Religion' | |
| A reaction: [p.19 in Beck tr] In Aristotle's account these are 'controlled' actions [enkrateia], which are a step below virtuous actions, which combine reason and pleasure. |
| 4024 | Kant follows Rousseau in defining freedom and morality in terms of each other [Taylor,C on Kant] |
| Full Idea: Kant follows Rousseau in defining freedom and morality essentially in terms of each other. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Charles Taylor - Sources of the Self §20.2 | |
| A reaction: An interesting comment on the modern tendency to overvalue freedom at the expense of the other civic virtues. |
| 3735 | Men are subject to laws which are both self-made and universal [Kant] |
| Full Idea: Man is subject only to laws which are made by himself and yet are universal. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 432.73) |
| 3718 | Telling the truth from duty is quite different from doing so to avoid inconvenience [Kant] |
| Full Idea: To tell the truth for the sake of duty is something entirely different from doing so out of concern for inconvenient results. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 402.18) |
| 3723 | There are no imperatives for a holy will, as the will is in harmony with moral law [Kant] |
| Full Idea: For the divine or holy will there are no imperatives: 'I ought' is here out of place, because 'I will' is already of itself necessarily in harmony with the law. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 414.39) |
| 3724 | A categorical imperative sees an action as necessary purely for its own sake [Kant] |
| Full Idea: A categorical imperative would be one which represented an action as objectively necessary in itself apart from its relation to a further end. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 414.39) |
| 3714 | Dutiful actions are judged not by purpose, but by the maxim followed [Kant] |
| Full Idea: An action done from duty has its moral worth, not in the purpose to be attained by it, but in the maxim according to which it is decided upon. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 399.13) |
| 5295 | Kant was happy with 'good will', even if it had no result [Kant, by Marx/Engels] |
| Full Idea: Kant was satisfied with "good will" alone, even if it remained entirely without result. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by K Marx / F Engels - The German Ideology §II | |
| A reaction: Kant is obviously a million miles away from Marxist pragmatism. And yet the members of the revolutionary class can only be identified and endorsed if they show a particular kind of will. |
| 6695 | Kant has to attribute high moral worth to some deeply unattractive human lives [Kant, by Graham] |
| Full Idea: An implausible and uncomfortable conclusion to be drawn from Kant's conception of morality is that we must attribute high moral worth to deeply unattractive human lives. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Gordon Graham - Eight Theories of Ethics Ch.6 | |
| A reaction: Graham quotes a loathsome character from a Victorian novel, who coldly 'does her duty'. Indeed it might be that a robot could be programmed with the categorical imperative (though it would need a table of values first). Virtue theory is the answer. |
| 8028 | Kantian duty seems to imply conformism with authority [MacIntyre on Kant] |
| Full Idea: Anyone educated into the Kantian notion of duty will (so far) have been educated into easy conformism with authority. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - A Short History of Ethics Ch.14 | |
| A reaction: The Nazi Eichmann cited Kant at his trial for mass murder. I'm not sure the criticism is fair. There are surely times when the categorical imperative will go quite contrary to what the irrational authorities are implementing? |
| 8026 | Almost any precept can be consistently universalized [MacIntyre on Kant] |
| Full Idea: With sufficient ingenuity, almost every precept can be consistently universalized. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - A Short History of Ethics Ch.14 | |
| A reaction: A concise statement of J.S.Mill's point (Idea 3762). The point is that Kant seems to allow burglary, as long as you don't complain when you are burgled. What sort of maxim would a suicidal mass murderer being willing to universalize? |
| 15673 | The intuition behind the categorical imperative is that one ought not to make an exception of oneself [Kant, by Finlayson] |
| Full Idea: Kant's first formulation of the categorical imperative is supposed to capture the widespread intuition that one ought not to make an exception of oneself. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by James Gordon Finlayson - Habermas Ch.6:83 | |
| A reaction: Interesting. I always take the plain English version to be 'what if everybody did that?' Suppose I were to forgive everyone, except myself? |
| 8068 | Universalising a maxim needs to first stipulate the right description for the action [Anscombe on Kant] |
| Full Idea: Kant's rule about universalisable maxims is useless without stipulations as to what shall count as a relevant description of an action with a view to constructing a maxim about it. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by G.E.M. Anscombe - Modern Moral Philosophy p.176 | |
| A reaction: This is one of the key objections to Kant (along with his need for preliminary values). One man's 'terrorist' is another man's 'freedom fighter'. The charge adds up to Nietzsche's view, that Kant could never shake off his very conventional prejudices. |
| 8025 | The categorical imperative will not suggest maxims suitable for testing [MacIntyre on Kant] |
| Full Idea: The doctrine of the categorical imperative provides me with a test for rejecting proposed maxims; it does not tell me whence I am to derive the maxims which first provide the need for a test. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - A Short History of Ethics Ch.14 | |
| A reaction: Nice objection. 'What if we all stood on one leg for an hour (in this crisis)?' Question for Kant: what sort of maxims should we consider, when faced with a dilemma. Mill will obviously suggest happiness as a target. Good of society? My own good? |
| 8027 | I can universalize a selfish maxim, if it is expressed in a way that only applies to me [MacIntyre on Kant] |
| Full Idea: If we enquire whether I can consistently universalize the maxim 'I may break my promises only when.....', the gap can be filled by a description devised so that it will apply to my present circumstances, but to very few others. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - A Short History of Ethics Ch.14 | |
| A reaction: Another good objection to Kant. There is just a huge problem with how you state the maxim under discussion. One man's 'terrorist' is another man's 'freedom fighter'. 'Do everything possible to implement the will of God'. |
| 3728 | Suicide, false promises, neglected talent, and lack of charity all involve contradictions of principle [Kant, by PG] |
| Full Idea: Kant's four illustrations of the Categorical Imperative are: the contradiction of suicide, the contradiction of false promises, the contradiction of neglecting your talents, and the contradiction of neglecting charity. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 422.53) by PG - Db (ideas) |
| 22008 | Always treat yourself and others as an end, and never simply as a means [Kant] |
| Full Idea: Act in such a way that you always treat humanity whether in your own person or in the person of any other, never simply as a means, but always at the same time as an end. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], AA429 p.96), quoted by Terry Pinkard - German Philosophy 1760-1860 02 | |
| A reaction: This sets up the Kingdom of Ends. Note that this does not prohibit using people as a means. It just asks you to respect waiters and shop assistants. It seems to say you should not treat 'your own person' merely as a means. Prostitution? |
| 3719 | If lying were the universal law it would make promises impossible [Kant] |
| Full Idea: I can indeed will to lie, but I can by no means will a universal law of lying; for by such a law there could properly be no promises at all. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 403.19) |
| 3762 | Why couldn't all rational beings accept outrageously immoral rules of conduct? [Mill on Kant] |
| Full Idea: Kant fails, almost grotesquely, to show that there would be any logical or physical impossibility in the adoption by all rational beings of the most outrageously immoral rules of conduct. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by John Stuart Mill - Utilitarianism Ch.1 |
| 22009 | Morality is the creation of the laws that enable a Kingdom of Ends [Kant] |
| Full Idea: Morality consists in the relation of all action to the making of laws whereby alone a kingdom of ends is possible. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], AA434 p.102), quoted by Terry Pinkard - German Philosophy 1760-1860 02 | |
| A reaction: Each individual gives themselves a law in the categorical imperative. Presumably the kingdom of ends is the convergence of these laws, because the categorical imperative has to be rational. |
| 4413 | The categorical imperative smells of cruelty [Nietzsche on Kant] |
| Full Idea: The categorical imperative smells of cruelty. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Friedrich Nietzsche - On the Genealogy of Morals II.§6 | |
| A reaction: I presume this is because it is so pure and impersonal. Seems harsh. Nowadays we don't think pure just has to be cruel, but Nietzsche may have assumed it had to be. |
| 3716 | Act according to a maxim you can will as a universal law [Kant] |
| Full Idea: I ought never to act except in such a way that I can also will that my maxim should become a universal law. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 402.17) |
| 3727 | Act as if your maxim were to become a universal law of nature [Kant] |
| Full Idea: The universal imperative may also run as follows: 'Act as if the maxim of your action were to become through your will a universal law of nature'. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 421.52) |
| 22050 | The maxim of an action is chosen, and not externally imposed [Kant, by Bowie] |
| Full Idea: Kant does not dictate what the maxim (the principle) of my action should be, and this is the crux. The individual has to decide the basis for their actions, rather than have it imposed on them, which differentiates us from the world of nature. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Andrew Bowie - German Philosophy: a very short introduction 1 | |
| A reaction: Apparenty this inspired the Romantic era (the Age of Freedom?) just as much as the French Revolution. It is the chief doctrine of extreme individualism - except that the maxim chosen should be one on which rational beings should agree. |
| 6694 | Always treat humanity as an end and never as a means only [Kant] |
| Full Idea: Act so that you treat humanity, whether in your own person or that of another always as an end and never as a means only. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]), quoted by Gordon Graham - Eight Theories of Ethics Ch.6 | |
| A reaction: Does this really mean that I can't just negligently buy a newspaper without making an effort to respect its seller? How do I ensure that I treat myself as an end, and don't slip into treating myself as a means? What would that be like? Prostitution? |
| 3731 | Rational beings necessarily conceive their own existence as an end in itself [Kant] |
| Full Idea: Rational nature exists as an end in itself; this is the way in which a man necessarily conceives his own existence. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 429.66) |
| 4345 | For Kant, even a person who lacks all sympathy for others still has a motive for benevolence [Kant, by Hursthouse] |
| Full Idea: Kant, we may suppose, would say that if a man were 'cold in temperament and indifferent to the sufferings of others', he would still find in himself a source that would enable him to do what is benevolent. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Rosalind Hursthouse - On Virtue Ethics Ch.4 | |
| A reaction: This identifies a strong appeal of Kant's theory - that whether we are morally good should not be a matter of luck in our upbringing or natural temperament. How is the vicious person to be saved, if not by reason? |
| 4251 | If we are required to give moral thought the highest priority, this gives morality no content [Williams,B on Kant] |
| Full Idea: The Kantian view of what is important is that people should give moral considerations the highest deliberative priority, which Hegel attacked because it gives moral thought no content. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.10 | |
| A reaction: Interesting. This points towards empathy and compassion as motivators, rather than reason, because there is some content to the morality, which calls out to us. |
| 16004 | If Kant lives by self-administered laws, this is as feeble as self-administered punishments [Kierkegaard on Kant] |
| Full Idea: Kant thought that man is his own law - he binds himself under the law which he gives himself. This is how lawlessness or experimentation is established. This is no more rigorously earnest than Sancho Panza's self-administered blows to his own ass. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Søren Kierkegaard - The Journals of Kierkegaard JP-I, 188 | |
| A reaction: It really is tempting to go easy on yourself rather than on others. Kant had the right ideas, but human beings aren't as disciplined as the categorical imperative requires. [SY] |
| 3711 | Only a good will makes us worthy of happiness [Kant] |
| Full Idea: A good will seems to constitute the indispensable condition of our very worthiness to be happy. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 393.2) |
| 3713 | The function of reason is to produce a good will [Kant] |
| Full Idea: Since reason has been imparted to us as a practical power, which thus influences the will, its true function must be to produce a will which is good. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 396.7) |
| 3729 | Our inclinations are not innately desirable; in fact most rational beings would like to be rid of them [Kant] |
| Full Idea: Inclinations, as a source of needs, are so far from having an absolute value to make them desirable for their own sake that it must rather be the universal wish of every rational being to be wholly free from them. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 428.65) |
| 4344 | Actions where people spread happiness because they enjoy it have no genuine moral worth [Kant] |
| Full Idea: There are many spirits of so sympathetic a temper that they find an inner pleasure in spreading happiness around them. ..I maintain that an action of this kind, however right and amiable it may be, has still no genuinely moral worth. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], p.66) | |
| A reaction: We understand what he means (that principle is everything), but this still seems a big hole in his account, one which drives us to Aristotle's sensible views about what a nice person is really like. |
| 3732 | Rational beings have a right to share in the end of an action, not just be part of the means [Kant] |
| Full Idea: A violator of the rights of man intends to use the person of others merely as a means, not considering that they should be used only as beings who must themselves be able to share in the end of the very same action. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 430.68) |
| 7670 | Kant is the father of the notion of exploitation as an evil [Kant, by Berlin] |
| Full Idea: Kant is the father of the notion of exploitation as an evil. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Isaiah Berlin - The Roots of Romanticism Ch.3 | |
| A reaction: This is central to the idea of Kant as the main father of liberalism, the idea that every individual deserves respect, and hence has rights. The idea would also be a crucial element in Europe turning against slavery. |
| 7591 | Kant completed Grotius's project of a non-religious basis for natural law [Scruton on Kant] |
| Full Idea: Kant is often held to have completed a task begun by Grotius, giving a basis for natural law which does not invoke the will of God, but rather commands God himself to obedience. | |
| From: comment on Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Roger Scruton - A Dictionary of Political Thought 'Kant' | |
| A reaction: This project, if successful, would clinch the naturalistic response to the Euthyphro Question (Ideas 336 and 337). It is a key issue for atheists, who generally wish to deny that their lack of religion leads inevitably to amorality. |
| 7673 | Retributive punishment is better than being sent to hospital for your crimes [Kant, by Berlin] |
| Full Idea: Kant believed in retributive punishment, because he thought that a man would prefer being sent to prison to going to hospital. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Isaiah Berlin - The Roots of Romanticism Ch.4 | |
| A reaction: That is, even criminals welcome the dignity of being treated as if they are actually responsible for their deeds, and are not just victims of inner forces. Criminals demand free will! Truth is best, though; many of them are not responsible at all. |
| 3730 | Non-rational beings only have a relative value, as means rather than as ends [Kant] |
| Full Idea: Beings whose existence depends not on our will but on nature have, if they are non-rational beings, only a relative value as means and are consequently called 'things' (rather than 'persons'). | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 428.65) | |
| A reaction: Ugh. Is there nothing in between 'persons' and 'things'? How about a deeply comatose human, or an embryo? It is a gross distortion to think of a chimpanzee as a 'thing'. |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| Full Idea: On the whole it is not worthwhile preserving the word 'cause': it is enough to say, what is far less misleading, that any two configurations allow us to infer any other. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §460) | |
| A reaction: Russell spelled this out fully in a 1912 paper. This sounds like David Hume, but he prefers to talk of 'habit' rather than 'inference', which might contain a sneaky necessity. |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| Full Idea: Some people would hold that two moments of time, or two points of space, imply each other's existence; yet the relation between these cannot be said to be causal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Famously, Russell utterly rejected causation a few years after this. The example seems clearer if you say that two points or moments can imply at least one point or instant between them, without causing them. |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| Full Idea: For us, as pure mathematicians, the laws of motion and the law of gravitation are not properly laws at all, but parts of the definition of a certain kind of matter. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §459) | |
| A reaction: The 'certain kind of matter' is that which has 'mass'. Since these are paradigm cases of supposed laws, this is the beginning of the end for real laws of nature, and good riddance say I. See Mumford on this. |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| Full Idea: The concept of motion is logically subsequent to that of occupying as place at a time, and also to that of change. Motion is the occupation, by one entity, of a continuous series of places at a continuous series of times. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) | |
| A reaction: This is Russell's famous theory of motion, which came to be called the 'At-At' theory (at some place at some time). It seems to mathematically pin down motion all right, but seems a bit short on the poetry of the thing. |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| Full Idea: A force is the supposed cause of acceleration, ...but an acceleration is a mere mathematical fiction, a number, not a physical fact. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §448) | |
| A reaction: This rests on his at-at theory of motion, in Idea 14168. I'm not sure that if I fell off a cliff I could be reassured on the way down that my acceleration was just a mathematical fiction. |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| Full Idea: I won't discuss whether points are unities or simple terms, but whether space is an aggregate of them. ..There is no geometry without points, nothing against them, and logical reasons in their favour. Space is the extension of the concept 'point'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §423) |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| Full Idea: To the mathematician as such there is no relevant distinction between the instants of time and the points on a line. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §387) | |
| A reaction: This is the germ of the modern view of space time, which is dictated by the mathematics, rather than by our intuitions or insights into what is actually going on. |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| Full Idea: The universe is a somewhat ambiguous term: it may mean all the things that exist at a single moment, or all things that ever have existed or will exist, or the common quality of whatever exists. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) |
| 3721 | We judge God to be good by a priori standards of moral perfection [Kant] |
| Full Idea: Where do we get the concept of God as the highest good? Solely from the idea of moral perfection, which reason traces a priori. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 408.29) |
| 8046 | We can only know we should obey God if we already have moral standards for judging God [Kant, by MacIntyre] |
| Full Idea: On Kant's view it never follows that we ought to do what God commands, for we would have to know that we always ought to do what God commands, but that would need a standard of moral judgement independent of God's commands. God's commands are redundant. | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Alasdair MacIntyre - After Virtue: a Study in Moral Theory Ch.4 | |
| A reaction: This strikes me as a very powerful argument, even an undeniable one. How could you accept any authority if you didn't have some standards for accepting it, even if the standard was just to be awestruck by someone's charisma and will-power? |
| 20714 | God is not proved by reason, but is a postulate of moral thinking [Kant, by Davies,B] |
| Full Idea: Kant speaks of God not as something known or proved to exist by virtue of rational argument, but as a postulate of moral reflection (that is, of 'practical reason'). | |
| From: report of Immanuel Kant (Groundwork of the Metaphysic of Morals [1785]) by Brian Davies - Introduction to the Philosophy of Religion 9 'Morality' | |
| A reaction: Presumably it is a necessary postulate, which makes this a transcendental argument, surely? |