54 ideas
| 21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
| Full Idea: I freely admit that remembrance of David Hume was the very thing that many years ago first interrupted my dogmatic slumber. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 4:260), quoted by A.W. Moore - The Evolution of Modern Metaphysics 5.2 | |
| A reaction: A famous declaration. He realised that he had the answer the many scepticisms of Hume, and accept his emphasis on the need for experience. |
| 16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
| Full Idea: The generation of knowledge a priori, both according to intuition and according to concepts, and finally the generation of synthetic propositions a priori in philosophical knowledge, constitutes the essential content of metaphysics. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 274) | |
| A reaction: By 'concepts' he implies mere analytic thought, so 'intuition' is where the exciting bit is, and that is rather vague. |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
| Full Idea: Mathematics cannot proceed analytically, namely by analysis of concepts, but only synthetically. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284) | |
| A reaction: I'm with Kant insofar as I take mathematics to be about the world, no matter how rarefied and 'abstract' it may become. |
| 16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
| Full Idea: No principle of pure geometry is analytic. That the straight line beween two points is the shortest is a synthetic proposition. For my concept of straight contains nothing of quantity but only of quality. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 269) | |
| A reaction: I'm not sure what his authority is for calling straightness a quality rather than a quantity, given that it can be expressed quantitatively. It is a very nice example for focusing our questions about the nature of geometry. I can't decide. |
| 16919 | Geometry rests on our intuition of space [Kant] |
| Full Idea: Geometry is grounded on the pure intuition of space. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284) | |
| A reaction: I have the impression that recent thinkers are coming round to this idea, having attempted purely algebraic or logical accounts of geometry. |
| 16920 | Numbers are formed by addition of units in time [Kant] |
| Full Idea: Arithmetic forms its own concepts of numbers by successive addition of units in time. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284) | |
| A reaction: It is hard to imagine any modern philosopher of mathematics embracing this idea. It sounds as if Kant thinks counting is the foundation of arithmetic, which I quite like. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| Full Idea: The concept of twelve is in no way already thought by merely thinking the unification of seven and five, and though I analyse my concept of such a possible sum as long as I please, I shall never find twelve in it. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 269) | |
| A reaction: It might be more plausible to claim that an analysis of 12 would reveal the concept of 7+5. Doesn't the concept of two collections of objects contain the concept of their combined cardinality? |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
| Full Idea: We find that all mathematical knowledge has this peculiarity, that it must first exhibit its concept in intuition, and do so a priori, in an intuition that is not empirical but pure. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 281) | |
| A reaction: Later thinkers had grave doubts about this Kantian 'intuition', even if they though maths was known a priori. Personally I am increasing fan of rational intuition, even if I am not sure how to discern whether it is rational on any occasion. |
| 16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
| Full Idea: Space and time are the two intuitions on which pure mathematics grounds all its cognitions and judgements that present themselves as at once apodictic and necessary. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284) | |
| A reaction: This unlikely proposal seems to be based on the idea that mathematics must arise from the basic categories of our intuition, and these two are the best candidates he can find. I would say that high-level generality is the basis of mathematics. |
| 16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
| Full Idea: Mathematical propositions are always judgements a priori, and not empirical, because they carry with them necessity, which cannot be taken from experience. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 268) | |
| A reaction: Presumably there are necessities in the physical world, and we might discern them by generalising about that world, so that mathematics is (by a tortuous abstract route) a posteriori necessary? Just a thought… |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
| Full Idea: It has long since been noticed that in all substances the subject proper, namely what is left over after all the accidents (as predicates) have been taken away and hence the 'substantial' itself, is unknown to us. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 333) | |
| A reaction: This is the terminus of the process of abstraction (though Wiggins says such removal of predicates is a myth). Kant is facing the problem of the bare substratum, or haecceity. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 21957 | 'Transcendental' concerns how we know, rather than what we know [Kant] |
| Full Idea: The word 'transcendental' signifies not a relation of our cognition to things, but only to the faculty of cognition. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 4:293), quoted by A.W. Moore - The Evolution of Modern Metaphysics 5.4 | |
| A reaction: This is the annoying abduction of a word which is very useful in metaphysical contexts. |
| 16923 | I admit there are bodies outside us [Kant] |
| Full Idea: I do indeed admit that there are bodies outside us. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 289 n.II) | |
| A reaction: This is the end of a passage in which Kant very explicitly denies being an idealist. Of course, he says we can only know the representations of things, and not how they are in themselves. |
| 21441 | 'Transcendental' is not beyond experience, but a prerequisite of experience [Kant] |
| Full Idea: The word 'transcendental' does not mean something that goes beyond all experience, but something which, though it precedes (a priori) all experience, is destined only to make knowledge by experience possible. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 373 n) | |
| A reaction: One of two explanations by Kant of 'transcendental', picked out by Sebastian Gardner. I think the word 'prerequisite' covers the idea nicely, using a normal English word. Or am I missing something? |
| 16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
| Full Idea: Through intuition we can only know objects as they appear to us (to our senses), not as they may be in themselves; and this presupposition is absolutely necessary if synthetic propositions a priori are to be granted as possible. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 283) | |
| A reaction: This idea is basic to understanding Kant, and especially his claim that arithmetic is a priori synthetic. |
| 16915 | A priori intuitions can only concern the objects of our senses [Kant] |
| Full Idea: Intuitions which are possible a priori can never concern any other things than objects of our senses. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 283) | |
| A reaction: Given the Kantian idea that what is known a priori will also be necessary, we might have had great hopes for big-time metaphysics, but this idea cuts it down to size. Personally, I don't think we are totally imprisoned in the phenomena. |
| 16914 | A priori intuition of objects is only possible by containing the form of my sensibility [Kant] |
| Full Idea: The only way for my intuition to precede the reality of the object and take place as knowledge a priori is if it contains nothing else than the form of sensibility which in me as subject precedes all real impressions through which I'm affected by objects. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 283) | |
| A reaction: This may be the single most famous idea in Kant. I'm not really a Kantian, but this is a powerful idea, the culmination of Descartes' proposal to start philosophy by looking at ourselves. No subsequent thinking can ignore the idea. |
| 21447 | I can make no sense of the red experience being similar to the quality in the object [Kant] |
| Full Idea: I can make little sense of the assertion that the sensation of red is similar to the property of the vermilion [cinnabar] which excites this sensation in me. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 290) | |
| A reaction: A sensible remark. In Kant's case it is probably a part of his scepticism that his intuitions reveal anything directly about reality. Locke seems to have thought (reasonably enough) that the experience contains some sort of valid information. |
| 16924 | I count the primary features of things (as well as the secondary ones) as mere appearances [Kant] |
| Full Idea: I also count as mere appearances, in addition to [heat, colour, taste], the remaining qualities of bodies which are called primariae, extension, place, and space in general, with all that depends on it (impenetrability or materiality, shape etc.). | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 289 n.II) | |
| A reaction: He sides with Berkeley and Hume against Locke and Boyle. He denies being an idealist (Idea 16923), so it seems to me that Kant might be described as a 'phenomenalist'. |
| 16913 | I can't intuit a present thing in itself, because the properties can't enter my representations [Kant] |
| Full Idea: It seems inconceivable how the intuition of a thing that is present should make me know it as it is in itself, for its properties cannot migrate into my faculty of representation. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 282) | |
| A reaction: One might compare this with Locke's distinction of primary and secondary, where the primary properties seem to 'migrate into my faculty of representation', but the secondary ones fail to do so. I think I prefer Locke. This idea threatens idealism. |
| 16925 | Appearance gives truth, as long as it is only used within experience [Kant] |
| Full Idea: Appearance brings forth truth so long as it is used in experience, but as soon as it goes beyond the boundary of experience and becomes transcendent, it brings forth nothing but illusion. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 292 n.III) | |
| A reaction: This is the nearest I have found to Kant declaring for empiricism. It sounds something like direct realism, if experience itself can bring forth truth. |
| 16911 | Intuition is a representation that depends on the presence of the object [Kant] |
| Full Idea: Intuition is a representation, such as would depend on the presence of the object. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 282) | |
| A reaction: This is a distinctively Kantian view of intuition, which arises through particulars, rather than the direct apprehension of generalities. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
| Full Idea: Concepts are of such a nature that we can make some of them ourselves a priori, without standing in any immediate relation to the object; namely concepts that contain the thought of an object in general, such as quantity or cause. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 282) | |
| A reaction: 'Quantity' seems to be the scholastic idea, of something having a magnitude (a big pebble, not six pebbles). |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 16926 | Analytic judgements say clearly what was in the concept of the subject [Kant] |
| Full Idea: Analytic judgements say nothing in the predicate that was not already thought in the concept of the subject, though not so clearly and with the same consciousness. If I say all bodies are extended, I have not amplified my concept of body in the least. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 266) | |
| A reaction: If I say all bodies are made of atoms, have I extended my concept of 'body'? It would come as a sensational revelation for Aristotle, but it now seems analytic. |
| 16927 | Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant] |
| Full Idea: Analytic judgements rest wholly on the principle of contradiction, …because the predicate cannot be denied of the subject without contradiction. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 267) | |
| A reaction: So if I say 'gold has atomic number 79', that is a (Kantian) analytic statement? This is the view of sceptics about Kripke's a posteriori necessity. …a few lines later Kant gives 'gold is a yellow metal' as an example. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
| Full Idea: That complete space …has three dimensions, and that space in general cannot have more, is built on the proposition that not more than three lines can intersect at right angles in a point. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 285) | |
| A reaction: Modern geometry seems to move, via the algebra, to more than three dimensions, and then battles for an intuition of how that can be. I don't know how they would respond to Kant's challenge here. |
| 16921 | If all empirical sensation of bodies is removed, space and time are still left [Kant] |
| Full Idea: If everything empirical, namely what belongs to sensation, is taken away from the empirical intuition of bodies and their changes (motion), space and time are still left. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284) | |
| A reaction: This is an exercise in psychological abstraction, which doesn't sound like good evidence, though it is an interesting claim. Physicists want to hijack this debate, but I like Kant's idea. |