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| 21955 | My dogmatic slumber was first interrupted by David Hume |
| 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 |
| 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. |
| 16918 | Mathematics cannot proceed just by the analysis of concepts |
| 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. |
| 16919 | Geometry rests on our intuition of space |
| 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. |
| 16930 | Geometry is not analytic, because a line's being 'straight' is a quality |
| 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. |
| 16920 | Numbers are formed by addition of units in time |
| 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. |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 |
| 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? |
| 16910 | Mathematics can only start from an a priori intuition which is not empirical but pure |
| 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 |
| 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 |
| 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… |
| 11833 | The substance, once the predicates are removed, remains unknown to us |
| 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. |
| 21957 | 'Transcendental' concerns how we know, rather than what we know |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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. |
| 16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause |
| 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). |
| 16926 | Analytic judgements say clearly what was in the concept of the subject |
| 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 |
| 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. |
| 16922 | Space must have three dimensions, because only three lines can meet at right angles |
| 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 |
| 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. |