55 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 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. |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 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. |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 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? |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 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… |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 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. |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 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. |
| 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). |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 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. |
| 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. |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 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. |