90 ideas
| 5300 | Philosophers have interpreted the world, but the point is to change it [Marx] |
| Full Idea: The philosophers have only interpreted the world, in various ways; the point is to change it. | |
| From: Karl Marx (Theses on Feuerbach [1846], §XI) | |
| A reaction: The 'point' of what? Personally I am more with Aristotle - that the aim is to create a society in which we can all aspire to contemplate like gods. As an interim statement of aim, though, one must respect Marx. But was he a philosopher? |
| 5297 | Whether human thinking can be 'true' must be decided in practice, not theory [Marx] |
| Full Idea: The question whether objective truth can be attributed to human thinking is not a question of theory but is a practical question; man must prove the truth of his thinking in practice. | |
| From: Karl Marx (Theses on Feuerbach [1846], §II) | |
| A reaction: This would appear to be an assertion of the pragmatic view of truth well before Peirce. The obvious objections arise, such as whether falsehood (Plato's 'noble lie') might not have equal practical success, and whether truth might be disastrous. |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
| Full Idea: Instead of focusing on the individual, Marxism suggested that the authentic self was at the social level in the form of class. | |
| From: report of Karl Marx (Theses on Feuerbach [1846]) by Ian Dunt - How to be a Liberal 6 | |
| A reaction: [not sure of the best source in Marx] This idea is expressed here by a defender of liberal individualism. Dunt persuasively attacks any concept of the self as part of some group, rather than as being an individual. |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 5298 | The human essence is not found in individuals but in social relations [Marx] |
| Full Idea: The human essence is no abstraction inherent in each single individual; in its reality it is the ensemble of the social relations. | |
| From: Karl Marx (Theses on Feuerbach [1846], §VI) | |
| A reaction: This is a key Marxist doctrine, and the central difference from Aristotle. Personally I am more with Aristotle, but the truth obviously lies somewhere in between. Man must be a 'social being', or there wouldn't be any social relations. |
| 23874 | Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil] |
| Full Idea: Marx saw that social groups manufacture moralities for their own use, so their activity is placed outside the reach of evil. Thus the first articles of soldiers and businessmen is to deny that it is possible to do evil while waging war or doing business. | |
| From: report of Karl Marx (works [1860]) by Simone Weil - Fragments: London 1943 p.146 | |
| A reaction: This is especially true of the modern reverence for 'market forces'. It is a key debate in the ethics of warfare - compare Walzer and McMahon. A striking thought, obviously containing a lot of truth. |
| 22001 | The real will of the cooperative will replace the 'will of the people' [Marx] |
| Full Idea: Under collective property, the so called will of the people disappears in order to make way for the real will of the cooperative. | |
| From: Karl Marx (Grundrisse [1876], p.563), quoted by Peter Singer - Marx 10 | |
| A reaction: [from an 1874 note on Bakunin's 'Statism and Anarchy'] So how do you settle on the 'real' will of a cooperative? The travesty is when a ruling elite decide that, without consultation. An institution is needed. This is still a social contract. |
| 21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
| Full Idea: Where the middle class can win freedom for themselves on the basis of rights to property - thus excluding others from their freedom - the working class have nothing but their title as human beings. They only liberate themselves by liberating humanity. | |
| From: report of Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844]) by Peter Singer - Marx 4 | |
| A reaction: Individual workers might gain freedom via education, marriage, or entrepreneurship, or by opting for total simplicity of life, but in general Marx seems to be right about this. But we must ask what sort of 'freedom' is needed. |
| 21990 | Theory is as much a part of a revolution as material force is [Marx] |
| Full Idea: Material force must be overthrown by material force. But theory also becomes a material force once it has gripped the masses. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro p.69), quoted by Peter Singer - Marx 4 | |
| A reaction: A huge problem, I think, is that every theory (even conservatism) has to be simplified in a democracy if it is to grip the imagination of the majority. My current hatred is labels in political philosophy. They give us a cartoon view of the world. |
| 22971 | In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx] |
| Full Idea: Between the capitalist and communist society lies the revolutionary transformation of the one into the other. Corresponding to this is a political transition period in which the state can be nothing but the revolutionary dictatorship of the proletariat. | |
| From: Karl Marx (Critique of the Gotha Program [1875], IV) | |
| A reaction: This hugely influential idea was catastrophic for the twentieth century, because the leaders of the proletarian dictatorship adored and abused the power, and wouldn't give it up for some feeble next stage. |
| 18662 | Liberal freedom is the right to be separate, and ignores the union of man with man [Marx] |
| Full Idea: The liberal right of man to freedom is not based on the union of man with man, but on the separation of man from man; it is the right to this separation. | |
| From: Karl Marx (works [1860]), quoted by Will Kymlicka - Contemporary Political Philosophy (1st edn) 7.2.a | |
| A reaction: [quoted from an anthology] It is interesting that liberal freedom is the right NOT to be involved in politics, and even not to vote in elections. Home counties England (high hedges etc) is the embodiment of the freedom not to be involved in society. |
| 23372 | Liberals want the right to be separate, rather than for people to be united [Marx] |
| Full Idea: The [liberal] right of man to freedom is not based on the union of man with man, but on the separation of man from man. It is the right to this separation. | |
| From: Karl Marx (works [1860], p.53), quoted by Will Kymlicka - Contemporary Political Philosophy (2nd edn) 7 | |
| A reaction: [in collection ed.McLelland p.53] That nicely encapsulates the debate. Modern liberal thinkers regret the loss of community, but people in authoritarian communities yearn for separation. You can have too much 'union'! |
| 20576 | Early Marx anticipates communitarian objections to liberalism [Marx, by Oksala] |
| Full Idea: The early writings of Marx anticipate the communitarian critique of liberalism. | |
| From: report of Karl Marx (works [1860]) by Johanna Oksala - Political Philosophy: all that matters Ch.8 | |
| A reaction: [Oksala says modern writers seem to prefer this to the hardcore later Marx, which is presumably too 'scientific'. He says 'Capital Vol 1' is Marx's most important work] |
| 21989 | Man is dominated by money, which is the essence of his alienation [Marx] |
| Full Idea: Money is the alienated essence of man's labour and life, and this alien essence dominates him as he worships it. | |
| From: Karl Marx (On the Jewish Question [1844], p.60), quoted by Peter Singer - Marx 3 | |
| A reaction: Presumably this is inherit in the very nature of money, rather than in the wickedness of capitalists who control it. But money is not inherently alienting for the rich, or for the comfortable bourgeoisie (is it?). |
| 22000 | From each according to his ability, to each according to his need [Marx] |
| Full Idea: From each according to his ability, to each according to his need. | |
| From: Karl Marx (Critique of the Gotha Program [1875]), quoted by Peter Singer - Marx 9 | |
| A reaction: Singer says this was not original to Marx, and he placed little emphasis on it. The obvious capitalist response is to ask how you will motivate someone who has huge abilities but few needs. It implies huge inequalities of altruism. |
| 22970 | Freedom is making the state subordinate to its society [Marx] |
| Full Idea: Freedom consists in converting the state from an organ superimposed on society into one completely subordinate to it. | |
| From: Karl Marx (Critique of the Gotha Program [1875], IV) | |
| A reaction: The intermediate stage is dictatorship of the proletariat (presumably exercised by the communist leadership). No twentieth century marxist state ever got near the freedom which Marx was seeking. A liberal society might achieve it! |
| 23862 | By saying the material dialectic of history aspires to the best, Marx agreed with capitalism [Weil on Marx] |
| Full Idea: When Marx inverted Hegel's dialectic of history, by substituting matter for mind as the motive, he attributed to matter the essence of mind, an unceasing aspiration towards the best - which was in keeping with the general current of capitalist thought. | |
| From: comment on Karl Marx (works [1860]) by Simone Weil - Reflections on Liberty and Social Oppression p.43 | |
| A reaction: [compressed] A rather nice debating point! Marx seems to share the universal nineteenth century belief in unremitting progress. Without that, it is impossible to believe that a revolution will necessarily improve anything. |
| 21999 | False consciousness results from concealment by the superstructure [Marx, by Singer] |
| Full Idea: False consciousness involves failing to see things as they really are. It comes about because a society's superstructure can conceal the real basis of the society. | |
| From: report of Karl Marx (works [1860]) by Peter Singer - Marx 9 | |
| A reaction: That seems a poor label, probably revealing a Hegelian background. It seems a matter of knowledge rather than consciousness. Can a whole mind be in a state of error? |
| 23875 | Marx says force is everything, and that the weak will become strong, while remaining the weak [Weil on Marx] |
| Full Idea: Marx posits on the one hand that force alone governs social relations to the exclusion of anything else, and on the other hand that one day the weak, while remaining weak, will nevertheless be stronger. He believed in miracles. | |
| From: comment on Karl Marx (works [1860]) by Simone Weil - Fragments: London 1943 p.149 | |
| A reaction: This is close to the obvious contradiction if the working classes despise the middle classes (the dreaded 'bourgeoisie') while their only aspiration is to be like them. It is hard to custom design a new class to which they could both aspire. |
| 21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
| Full Idea: Once the 'interaction' between the superstructure and the productive forces is admitted, is it still possible to maintain that production determines the superstructure, rather than the other way round? | |
| From: comment on Karl Marx (Capital Vol. 1 [1867]) by Peter Singer - Marx 7 | |
| A reaction: It is much harder to defend historical determinism if Singer is right about this. Modern capitalism won't admit of the sort of simple distinctions that mark was looking for. |
| 18653 | Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka] |
| Full Idea: Marx rejected the idea of equal rights, not because he was not a friend to the idea of treating people as equals, but precisely because he thought rights failed to live up to that ideal. | |
| From: report of Karl Marx (works [1860]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 5.1 | |
| A reaction: Presumably because the power to award 'rights' goes to the highest bidder. If equality is to be enshrined in law, it is a bit difficult to see how else to manage it. |
| 20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
| Full Idea: Even if the workers are paid a fair wage, the whole thing still remains the age-old activity of the conqueror, who buys commodities from the conquered with the money has has stolen from them, | |
| From: Karl Marx (Capital Vol. 1 [1867], p.728), quoted by Johanna Oksala - Political Philosophy: all that matters Ch.8 | |
| A reaction: [Penguin edition cited] The word 'stolen' is obviously dubious here. 'Exploitation' is a much more accurate word. One might talk of 'blackmail' or 'extortion' rather than theft. |
| 22969 | People who only have their labour power are the slaves of those permitting them to work [Marx] |
| Full Idea: The man who possesses no other property than his labour power must, in all conditions of society and culture, be the slave of other men who have made themselves the owners of the material conditions of labour. He can only work with their permission. | |
| From: Karl Marx (Critique of the Gotha Program [1875], I) | |
| A reaction: In a world of vast multinationals, the person giving the permission to work is nearly always dependent on some higher level permission. In any sort of society people can only work with the consensus of other people. |
| 21996 | Freedom only comes when labour is no longer necessary [Marx] |
| Full Idea: The realm of freedom actually begins only where labour which is determined by necessity and mundane considerations ceases. | |
| From: Karl Marx (Capital Vol. 3 [1873], p.496), quoted by Peter Singer - Marx 8 | |
| A reaction: This is a bit discouraging fo idealistic dreamers. Modern political thought needs an ecological dimension to this problem. If society always needs a fair degree of labour, there must be a way to maximise freedom in that context. |
| 21994 | The handmill gives feudalism, the steam mill capitalism [Marx] |
| Full Idea: The handmill gives you society with the feudal lord; the steam mill society with the industrial capitalist. | |
| From: Karl Marx (The Poverty of Philosophy [1847], p.202), quoted by Peter Singer - Marx 7 | |
| A reaction: If technology dictates social structure, then feudalism is still with us, in low-tech industries. What if the steam mill had been invented in 1300? |
| 23876 | The essence of capitalism is the subordination of people to things [Marx, by Weil] |
| Full Idea: Marx discovered a formula impossible to surpass when he said that the essence of capitalism lies in the subordination of subject to object, of man to thing. | |
| From: report of Karl Marx (works [1860]) by Simone Weil - Fragments: London 1943 p,155 | |
| A reaction: I find this rather too vague to be a penetrating observation. I would suggest the obliteration of cooperation and community, in favour of competition. Winners and losers. |
| 20958 | Capitalism changes the world, by socialising the idea of a commodity [Marx, by Bowie] |
| Full Idea: In Marx's view the essential factor in capitalism is that the encroachment of the commodity form into society fundamentally changes the world. | |
| From: report of Karl Marx (works [1860]) by Andrew Bowie - Introduction to German Philosophy 6 'Historical' | |
| A reaction: The main point is that people and their labour become commodities. Haven't animals always been treated as commodities? Clearly slave were commodities, long before capitalism. Capitalism universalises it? |
| 20960 | Marx thought capitalism was partly liberating, and could make labour and ownership more humane [Marx, by Bowie] |
| Full Idea: Marx did not disapprove per se of capitalism. New divisions of labour and forms of ownership could transform individuals in modern societies, creating a more humane world with the means capitalism had liberated from feudalism. | |
| From: report of Karl Marx (works [1860]) by Andrew Bowie - Introduction to German Philosophy 11 'Metaphysics' | |
| A reaction: I'm guessing this might be early Marx, which has less to say about the 'scientific' inevitably of deep change, and the necessity for revolution. Nowadays we tinker with humane changes at the poorer end, while the rich run rampant. |
| 22972 | Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx] |
| Full Idea: Bourgeois 'freedom of conscience' is just the toleration of all possible kinds of religious unfreedom of conscience, and the workers' party should endeavour to liberate the conscience from the witchery of religion. | |
| From: Karl Marx (Critique of the Gotha Program [1875], IV) | |
| A reaction: We see this in modern 'faith' schools in the UK, which do not seem to be required to live up to the standards of freedom of belief expected in the rest of a liberal society. |
| 20519 | Marxists say liberal rights are confrontational, and liberal equality is a sham [Marx, by Wolff,J] |
| Full Idea: For Marx liberal rights are egoistic rights of separation: they encourage each individual to view others as limitations to his or her freedom. ....Liberals set up a sham community of 'equal' citizens. | |
| From: report of Karl Marx (On the Jewish Question [1844]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Marxist' | |
| A reaction: The point is that equality in law does not ensure equal treatment in daily life. I suppose a liberal right can be seen as an opt-out clause for some aspect of society. |
| 20624 | Work degrades into heat, but not vice versa [Close] |
| Full Idea: William Thomson, Lord Kelvin, declared (in 1865) the second law of thermodynamics: mechanical work inevitably tends to degrade into heat, but not vice versa. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: The basis of entropy, which makes time an essential part of physics. Might this be the single most important fact about the physical world? |
| 20623 | First Law: energy can change form, but is conserved overall [Close] |
| Full Idea: The first law of thermodynamics : energy can be changed from one form to another, but is always conserved overall. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: So we have no idea what energy is, but we know it's conserved. (Daniel Bernoulli showed the greater the mean energy, the higher the temperature. James Joule showed the quantitative equivalence of heat and work p.26-7) |
| 20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
| Full Idea: The third law of thermodynamics says that a hypothetical state of total order and minimum entropy can be attained only at the absolute zero temperature, minus 273 degrees Celsius. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: If temperature is energetic movement of atoms (or whatever), then obviously zero movement is the coldest it can get. So is absolute zero an energy state, or an absence of energy? I have no idea what 'total order' means. |
| 20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
| Full Idea: Electric and magnetic phenomena are profoundly intertwined; what you interpret as electric or magnetic thus depends on your own motion. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like an earlier version of special relativity. |
| 20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
| Full Idea: There is no absolute state of rest; only relative motions are unambiguous. Contrast this with acceleration, however, which has the same magnitude in all inertial frames. | |
| From: Frank Close (Theories of Everything [2017], 3 'Newton's') | |
| A reaction: It seems important to remember this, before we start trumpeting about the whole of physics being relative. ....But see Idea 20634! |
| 20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
| Full Idea: The essence of general relativity relates 'curvature in space-time' on one side of the equation to the 'density of momentum and energy' on the other. ...In full, Einstein required ten equations of this type. | |
| From: Frank Close (Theories of Everything [2017], 5 'Gravity') | |
| A reaction: Momentum involves mass, and energy is equivalent to mass (e=mc^2). |
| 20627 | Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close] |
| Full Idea: Four basic laws of electric and magnetic fields: Gauss's Law (about the flux produced by a field), Gauss's law of magnets (there can be no monopoles), Ampère's Law (fields on surfaces), and Farday's Law (accelerated magnets produce fields). | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: [Highly compressed, for an overview. Close explains them] |
| 20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
| Full Idea: Planck had assumed that light is emitted in quanta called photons. Einstein went further - light is photons. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: The point is that light travels as entities which are photons, rather than the emissions being quantized packets of some other stuff. |
| 20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
| Full Idea: In Einstein's general theory, gravity acts also on energy and momentum, not simply on mass. For example, massless photons of light feel the gravitational attraction of the Sun and can be deflected. | |
| From: Frank Close (Theories of Everything [2017], 5 'Planck') | |
| A reaction: Ah, a puzzle solved. How come massless photons are bent by gravity? |
| 20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
| Full Idea: Faradays' measurements predicted the speed of electro-magnetic waves, which happened to be the speed of light, so Maxwell made an inspired leap: light is an electromagnetic wave! | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Put that way, it doesn't sound like an 'inspired' leap, because travelling at exactly the same speed seems a pretty good indication that they are the same sort of thing. (But I'm not denying that Maxwell was a special guy!) |
| 20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
| Full Idea: Dirac created quantum electrodynamics (QED): the universal electro-magnetic field can exist in discreet states of energy (with photons appearing and disappearing by energy excitations. This combined classical ideas, quantum theory and special relativity. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Close says this is the theory of everything in atomic structure, but not in nuclei (which needs QCD and QFD). So if there are lots of other 'fields' (e.g. gravitational, weak, strong, Higgs), how do they all fit together? Do they talk to one another? |
| 20642 | Photon exchange drives the electro-magnetic force [Close] |
| Full Idea: The exchange of photons drives the electro-magnetic force. | |
| From: Frank Close (Theories of Everything [2017], 6 'Superstrings') | |
| A reaction: So light, which we just think of as what is visible, is a mere side-effect of the engine room of nature - the core mechanism of the whole electro-magnetic field. |
| 20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
| Full Idea: Quantum field theory implies that the vacuum of space is filled with particles and antiparticles which bubble in and out of existence on faster and faster timescales over shorter and shorter distances. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: Ponder this sentence until you head aches. Existence, but not as we know it, Jim. Close says calculations in QED about the electron confirm this. |
| 20631 | Dirac showed how electrons conform to special relativity [Close] |
| Full Idea: In 1928 Paul Dirac discovered the quantum equation that describes the electron and conforms to the requirements special relativity theory. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like a major step in the unification of physics. Quantum theory and General relativity remain irreconcilable. |
| 20641 | Electrons get their mass by interaction with the Higgs field [Close] |
| Full Idea: The electron gets its mass by interaction with the ubiquitous Higgs field. | |
| From: Frank Close (Theories of Everything [2017], 6 'Hierarchy') | |
| A reaction: I thought I understood mass until I read this. Is it just wrong to say the mass of a table is the 'amount of stuff' in it? |
| 20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
| Full Idea: The link between temperature, heat, work and energy is at the root of our historical ability to construct theories of matter, such as Newton's dynamics, while ignoring, and indeed being ignorant of - atomic dimensions. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: That is, presumably, that even when you fill in the atoms, and the standard model of physics, these aspects of matter do the main explaiining (of the behaviour, rather than of the structure). |
| 20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
| Full Idea: In 2012 it was confirmed that we are immersed in an electroweak plasma - the Higgs field. We curently have no knowledge of what this stuff might consist of. | |
| From: Frank Close (Theories of Everything [2017], 4 'Higgs') | |
| A reaction: The second sentence has my full attention. So we don't understand a field properly until we understand the 'stuff' it is made of? So what are all the familiar fields made of? Tell me more! |
| 20640 | Space-time is indeterminate foam over short distances [Close] |
| Full Idea: At very short distances, space-time itself becomes some indeterminate foam. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: [see Close for a bit more detail of this weird idea] |
| 5299 | Religious feeling is social in origin [Marx] |
| Full Idea: The "religious sentiment" (discussed by Feuerbach) is itself a social product. | |
| From: Karl Marx (Theses on Feuerbach [1846], §VII) | |
| A reaction: Recent brain research has identified a part of the brain which is only active during religious thought and experience. It is easy to produce cynical political accounts of religion, but in its time it was also quite a good scientific account of nature. |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| Full Idea: Religion is the opium of the people. The abolition of religion as the illusory happiness of the people is required for their real happiness. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro) | |
| A reaction: Not being religious myself, I have some sympathy with this ringing clarion-call. However, while opium satisfies an artificial and superficial need, religion certainly seems to speak to something deeper and more central in people. |