130 ideas
| 7822 | A neo-Stoic movement began in the late sixteenth century [Lipsius, by Grayling] |
| Full Idea: A neo-Stoic movement began at the end of the sixteenth century, under the inspiration of the Dutch scholar Justus Lipsius. | |
| From: report of Justus Lipsius (works [1584]) by A.C. Grayling - What is Good? Ch.5 | |
| A reaction: I would take this to be just as much a movement against Christianity as the interest in the less theistic Epicurus. They wanted the virtues of Christianity without the theological trappings. |
| 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. |
| 22223 | Being-in-the-world is projection to possibilities, thrownness among them, and fallenness within them [Heidegger, by Caputo] |
| Full Idea: Being-in-the-world is a phenomenon of 'care' with a tripartite structure: a) projection towards its possibilities, b) thrownness among those possibilities, so Dasein is not free, and c) fallenness among worldly possibilities, to neglect of its own. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: Sounds a bit Californian to me. Just living among the world's possibilities is evidently a bad thing, because you could be concentrating on yourself and your own development instead? |
| 22158 | Pheomenology seeks things themselves, without empty theories, problems and concepts [Heidegger] |
| Full Idea: 'Phenomenology' can be formulated as 'To the things themselves!' It is opposed to all free-floating constructions and accidental findings, and to conceptions which only seem to have been demonstrated. It is opposed to traditiona' pseudo-problems. | |
| From: Martin Heidegger (Being and Time [1927], Intro II.07) | |
| A reaction: It sounds as if we are invited to look at the world the way a dog might look at it. I am not at all clear what it to be gained from this approach. |
| 15574 | 'Logos' really means 'making something manifest' [Heidegger, by Polt] |
| Full Idea: Heidegger concludes that 'logos' essentially means 'making something manifest'. | |
| From: report of Martin Heidegger (Being and Time [1927], 56/33) by Richard Polt - Heidegger: an introduction 3.§7 | |
| A reaction: It would at least seem to involve revealing the truth of something, though truth doesn't seem to be central to Heidegger's thought. 'Logos' is often translated as 'an account', as well as a 'reason', so Heidegger may be right. |
| 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'. |
| 15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
| Full Idea: Heidegger is a relentless enemy of ahistorical, absolutist concepts of truth. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Richard Polt - Heidegger: an introduction 1 | |
| A reaction: I presume that if truth is not absolute then it must be relative, but Polt is a little coy about saying so. For me, anyone who says truth is relative doesn't understand the concept, and is talking about something else. |
| 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. |
| 21897 | Reducing being to the study of beings too readily accepts the modern scientific view [Heidegger, by May] |
| Full Idea: Continental philosophers, following Heidegger, see in the attempt to reduce the question of being to that of beings a symptom of an age that is too ready to accept the terms in which science conceives the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Todd May - Gilles Deleuze 1.04 | |
| A reaction: Interesting. I take the idea that this is a failing of the modern age to be ridiculous, since I take it to be the key metaphysical move made by Aristotle. Neverthless, Aristotle is closely in tune with modern science. For 'beings', read 'objects'. |
| 15573 | For us, Being is constituted by awareness of other sorts of Being [Heidegger] |
| Full Idea: We are Dasein - the entity who possesses - as constitutive for its understanding of existence - an understanding of the Being of all entities of a character other than its own. | |
| From: Martin Heidegger (Being and Time [1927], 34/13), quoted by Richard Polt - Heidegger: an introduction 3.§4 | |
| A reaction: This seems to connect to the emerging 'externalist' view of mind that comes with the external view of content coming from Purnam's Twin Earth idea. |
| 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. |
| 8137 | Dasein is ahead of itself in the world, and alongside encountered entities [Heidegger] |
| Full Idea: The formal existential totality of Dasein's ontological structural whole is: the Being of Dasein means ahead-of-itself-Being-already-in-(the-world) as Being-alongside (entities encountered within-the-world). | |
| From: Martin Heidegger (Being and Time [1927], I.6 41) | |
| A reaction: If you find that thought really illuminating, you are probably on the wrong website. However, the thought that we exist 'ahead of ourselves' might be a fruitful line for existentialists to explore. |
| 21951 | In company with others one's Dasein dissolves, and even the others themselves dissolve [Heidegger] |
| Full Idea: This being-with-one-another dissolves one's own Dasein completely into the kind of being of 'the others', in such a way, indeed, that the others, as distinguishable and explicit, vanish more and more. | |
| From: Martin Heidegger (Being and Time [1927], p.164), quoted by Mark Wrathall - Heidegger: how to read 5 | |
| A reaction: He seems to be describing the psychology of someone who joins a small crowd which gradually increases in size. I take this relation to others to be the basic existential dilemma, of retaining individual authenticity within a community. |
| 20745 | 'Dasein' expresses not 'what' the entity is, but its being [Heidegger] |
| Full Idea: When we designate this entity with the term 'Dasein' we are expressing not its 'what' (as if it were a table, house, or tree) but its being. | |
| From: Martin Heidegger (Being and Time [1927], p.297), quoted by Kevin Aho - Existentialism: an introduction 2 'Phenomenology' | |
| A reaction: Presumably analytic discussions of persons try to be too objective. Heidegger is trying to capture the thought at the heart of Kierkegaard's existentialism. Objectivity and subjectivity are never in conflict. Is there really a different mode of existence? |
| 8134 | The word 'dasein' is used to mean 'the manner of Being which man possesses', and also the human creature [Heidegger, by Cooper,DE] |
| Full Idea: Heidegger borrows a common German word 'dasein', meaning 'being' or 'existence', to refer both to 'the manner of Being which... man... possesses', and to the creature which possesses it. | |
| From: report of Martin Heidegger (Being and Time [1927], p.32) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: This just strikes me as an elementary ontological mistake. Because something has startling properties it doesn't follow that we have a different type of Being. Magnets don't have a different type of being from ordinary iron. |
| 8135 | 'Dasein' is Being which is laid claim to, and which matters to its owner [Heidegger, by Cooper,DE] |
| Full Idea: We each of us not only have Dasein (our kind of Being), but we can lay claim to it. Also the Dasein of a thing 'is an issue for it' - we care about the kinds of creatures we can make ourselves into. | |
| From: report of Martin Heidegger (Being and Time [1927], p.67) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: Heidegger says other more puzzling things about Dasein. The second half of the idea is what makes Heidegger an existentialist, and an inspiration for Sartre. |
| 21948 | Dasein is being which can understand itself, and possess itself in a way allowing authenticity [Heidegger] |
| Full Idea: Dasein is an entity which, in its very being, comports itself understandingly towards that being. ...Mineness belongs to an existent Dasein, and belongs to it as the condition which makes authenticity and inauthenticity possible. | |
| From: Martin Heidegger (Being and Time [1927], p.78), quoted by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: He might eventually persuade me that Dasein is so different from mere material being that it deserves a category of its own. But a reductive account of mind is also a reductive account of being. |
| 9273 | Heidegger turns to 'Being' to affirm the uniqueness of humans in the world [Heidegger, by Gray] |
| Full Idea: Heidegger turns to 'Being' for the same reason that Christians turn to God - to affirm the unique place of humans in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John Gray - Straw Dogs 2.4 | |
| A reaction: This is the first remark I have encountered that makes sense of Heidegger's Being to me! It places Heidegger as a modernist philosopher, trying to grapple with the decline of religion. I'll stick with Bertrand Russell on that. |
| 22157 | Dasein is a mode of Being distinguished by concern for its own Being [Heidegger] |
| Full Idea: Dasein is an entity which does not just occur among other entities. Rather it is ontically distinguished by the fact that, in its very Being, that Being is an issue for it. | |
| From: Martin Heidegger (Being and Time [1927], Intro I.04) | |
| A reaction: How do you distinguish the Being of normal humans from the Being of someone in a deep coma, who has no existential issues? Has that Dasein ceased to be? Why does angst create a new mode of Being, but flying doesn't? |
| 7680 | Ontology is possible only as phenomenology [Heidegger] |
| Full Idea: Ontology is possible only as phenomenology. | |
| From: Martin Heidegger (Being and Time [1927], p.31), quoted by Dale Jacquette - Ontology Ch.1 | |
| A reaction: Jacquette argues against this claim. The idea seems to be the ultimate extension of Kant, and it is not a big move to say that the only real phenomenology we can discuss is our semantics. Wrong, wrong, wrong. |
| 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. |
| 22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
| Full Idea: Readiness-to-hand is the way in which entities as they are 'in themselves' are defined ontologico-categorially. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: I assume this is a direct reference to the problem idealists had with the thing-in-itself. It seems that the reality of a thing consists of the strengthened relationship it has with Dasein, which sounds fairly idealist to me. |
| 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. |
| 15576 | Heidegger seeks a non-traditional concept of essence as 'essential unfolding' [Heidegger, by Polt] |
| Full Idea: Heidegger tries to develop a non-traditional concept of essence as 'essential unfolding' ('wesen' as a verb). | |
| From: report of Martin Heidegger (Being and Time [1927], I.4.27) by Richard Polt - Heidegger: an introduction 3.§25-7 |
| 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)? |
| 15578 | Propositions don't provide understanding, because the understanding must come first [Heidegger, by Polt] |
| Full Idea: Propositions are not a good clue to the essence of understanding, because we must already understand things before we formulate propositions about them. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.31) by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: I like this, because I think the most important aspects of our thought and understanding are entirely non-verbal - even in cases where they seem to be highly specific and verbal. We don't understand ourselves at all! |
| 22159 | If we posit 'I' as the starting point, we miss the mind's phenomenal content [Heidegger] |
| Full Idea: One of our first tasks will be to prove that if we posit an 'I' or subject as that which is proximally given, we shall completely miss the phenomenal content of Dasein. | |
| From: Martin Heidegger (Being and Time [1927], I.1.10) | |
| A reaction: Descartes had thrown doubt on the informativeness of the phenomena, so presumably your phenomenologist is not interested in whether they reveal any truth. So why are unreliable phenomena of any interest? |
| 22160 | Our relationship to a hammer strengthens when we use [Heidegger] |
| Full Idea: The less we stare at the hammer-Thing, and the more we seize hold of it and use it, the more primordial does our relationship to it become. ...The kind of Being which equipment possesses... we call 'readiness-to-hand' [Zuhandenheit]. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: This example would be well at home in the writings of the pragmatists. It is also an important example for existentialists. In analytic philosophy we might say the experience combines perception with direct exerience of causation. |
| 15580 | There are no raw sense-data - our experiences are of the sound or colour of something [Heidegger] |
| Full Idea: We always take a noise as the sound of something; we always take a hue as the color of something. We simply do not experience raw, uninterpreted sense-data - these are the inventions of philosophers. | |
| From: Martin Heidegger (Being and Time [1927], 207/163-4), quoted by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: This is something like the modern view of sense-data as promoted by John McDowell, rather than the experiential atoms of Russell and Moore. Experience is holistic, but that doesn't mean we can't analyse it into components. |
| 20749 | Perceived objects always appear in a context [Heidegger] |
| Full Idea: The perceptual 'something' is always in the middle of something else, it always forms part of a 'field'. | |
| From: Martin Heidegger (Being and Time [1927], p.4), quoted by Kevin Aho - Existentialism: an introduction 3 'Perceptual' | |
| A reaction: Sounds like our knowledge of electrons. Nice point. Standard analytic discussions of perceiving a glass always treat it in isolation, when it is on an expensive table near a brandy bottle. Or near a hammer. |
| 22163 | The scandal of philosophy is expecting to prove reality when the prover's Being is vague [Heidegger] |
| Full Idea: The 'scandal of philosophy' is not that this proof [of external things] has yet to be given, but that such proofs are expected and attempted again and again. ...The kind of Being of the entity which does the proving has not been made definite enough. | |
| From: Martin Heidegger (Being and Time [1927], I.6.43a) | |
| A reaction: The 'scandal' was a remark of Kant's. Presumably Heidegger's exploration of Dasein aims to establish the Being of the prover sufficiently to solve this problem (via phenomenology). |
| 21949 | Having thoughts and feelings need engagement in the world [Heidegger, by Wrathall] |
| Full Idea: Heidegger argues that having thoughts and feelings is only possible for entity that is actually engaged in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: This seems to be an a priori exclusion of the possibility of a brain in a vat. I guess the ancestor of this idea is Schopenhauer. |
| 22222 | Dasein finds itself already amongst others [Heidegger, by Caputo] |
| Full Idea: The world is a world shared with others, so that far from being a solipsistic ego ...Dasein finds itself already amongst others. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.226 | |
| A reaction: Phenomenologists don't seem bothered about the problem of knowing other minds. If you take something for granted, it ceases to be a problem to be solved! |
| 8136 | If we work and play with other people, they are bound to be 'Dasein', intelligent agents [Heidegger, by Cooper,DE] |
| Full Idea: How do I know that other people have minds? The question is a bad one. Precisely because I encounter them at work, play and the like, it is guaranteed that they, too, are Dasein, intelligent agents. | |
| From: report of Martin Heidegger (Being and Time [1927], p.153-) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: I've seen film of someone playing peek-a-boo with a bonobo ape, so presumably they have Dasein. It might be easier for the AI community to aim at building a robot with Dasein, than one which was simply conscious. |
| 22164 | When Dasein grasps something it exists externally alongside the thing [Heidegger] |
| Full Idea: When Dasein directs itself towards something and grasps it, it does not somehow first get out of an inner sphere in which it has been proximally encapsulated, but its primary kind of Being is such that it is always 'outside' alongside entities. | |
| From: Martin Heidegger (Being and Time [1927], I.2.13) | |
| A reaction: This is the first plausible fruit of phenomenology I have been able to discover. Analysing the passive mind is not very promising, but seeing what happens when we become more proactive is revealing. |
| 22162 | There is an everyday self, and an authentic self, when it is grasped in its own way [Heidegger] |
| Full Idea: The self of everyday Dasein is the they-self [das Man-selbst], which we distinguish from the authentic self - that is, from the Self which has been taken hold of in its own way. | |
| From: Martin Heidegger (Being and Time [1927], I.4.27) | |
| A reaction: To a novice this sounds like a requirement for increased self-consciousness during daily activity. 'Be a good animal, true to your animal self' said one of Lawrence's characters. |
| 20114 | Everyone is other, and no one is himself [Heidegger] |
| Full Idea: Everyone is other, and no one is himself. | |
| From: Martin Heidegger (Being and Time [1927], p.165), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 09 | |
| A reaction: Safranski describes this as the idea of 'structural self-evasion'. He detects the same idea in Nietzsche's 'Daybreak'. |
| 15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
| Full Idea: For Heidegger moods are disclosive; they show us things in a more fundamental way than theoretical propositions ever can. For example, fear reveals something as a threat. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.30) by Richard Polt - Heidegger: an introduction 3.§30 | |
| A reaction: Most modern students of emotion seem to agree. Even though they may not have specific content, it is always possible to consider the underlying cause of the mood. |
| 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. |
| 20748 | We do not add value to naked things; its involvement is disclosed in understanding it [Heidegger] |
| Full Idea: We do not throw a 'signification' over some naked thing which is present-at-hand, we do not stick a value on it; but when something is encountered as such, the thing in question has an involvement which is disclosed in our understanding of the world. | |
| From: Martin Heidegger (Being and Time [1927], p.190-1), quoted by George Dickie - The Myth of the Aesthetic Attitude 3 'Undoing' | |
| A reaction: Analytic philosophy and science have tried to dismantle experience, and Heidegger wants to put it back together. I would say there is a big difference between encountering a thing (which is a bit facty), and understanding it (which is more valuey). |
| 22166 | Dasein has the potential to be itself, but must be shown this in the midst of ordinariness [Heidegger] |
| Full Idea: Because Dasein is lost in the 'they', it must first find itself. It must be 'shown' to itself in its possible authenticity. In terms of its possibility, Dasein is already a potentiality-for-Being-its-self, but it needs to have this potentiality attested. | |
| From: Martin Heidegger (Being and Time [1927], II.2.54) | |
| A reaction: I wish there was some criterion for knowing when you are being yourself and when you are not. |
| 22165 | Anxiety reveals the possibility and individuality of Dasein [Heidegger] |
| Full Idea: Anxiety discloses Dasein as Being-possible, and indeed as the only kind of thing which it can be of its own accord as something individualised in individualisation. | |
| From: Martin Heidegger (Being and Time [1927], I.6.40) | |
| A reaction: Is sounds like insecurity, as a sort of trauma that shocks one into self-realisation. The idea means very little to me personally. |
| 21952 | Anxiety about death frees me to live my own life [Heidegger, by Wrathall] |
| Full Idea: For Heidegger, as a consequence of my anxiety in the face of death, I am set free to live my life as my own rather than doing things merely because others expect me to do them. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 7 | |
| A reaction: Contrary to Epicurus, Heidegger thinks anxiety about death is a good thing. The point is, I suppose, that we all die alone, and people who are very socially contrained need to face up to death in order to grasp their autonomy. |
| 22224 | Anxiety is the uncanniness felt when constantly fleeing from asserting one's own freedom [Heidegger, by Caputo] |
| Full Idea: Anxiety [angst] is the disturbing sense of uncanniness by which Dasein is overtaken (thrownness) when it discovers there is nothing other than its own freedom to sustain its projects (projection), and from which Dasein constantly takes flight (falling). | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: This seems to be Kierkegaard's idea, unamended. In my experience anxiety only comes when I am forced into making decisions by worldly situations. An 'existential crisis' is a sort of blankness appearing where a future life was supposed to be. |
| 15572 | Being what it is (essentia) must be conceived in terms of Being (existence) [Heidegger] |
| Full Idea: Dasein's Being-what-it-is (essentia) must….be conceived in terms of its Being (existentia). | |
| From: Martin Heidegger (Being and Time [1927], 67/42), quoted by Richard Polt - Heidegger: an introduction 3.§2 | |
| A reaction: This seems to be the origin of Sartre's famous slogan 'existence before essence'. It seems to be a rebellion against Husserl's quest for essences. |
| 20453 | Heidegger says we must either choose an inauthentic hero, or choose yourself as hero [Heidegger, by Critchley] |
| Full Idea: Heidegger says you must choose your hero; either you choose 'das Man', the inauthentic life, or you choose yourself - the point being that you have to choose yourself as your hero in order to be authentic. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Simon Critchley - Impossible Objects: interviews 5 | |
| A reaction: If Nietzsche's 'Ecce Homo' is the model for choosing yourself as hero, I am not too sure about this idea. Needing a hero seems awfully German and romantic. Ein Heldenleben. Be your own anit-hero (like a standup comedian)? |
| 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) |