Kant's Seminar on The Power of Judgment

1. Philosophy 190: Seminar on Kant Spring, 2015 Prof. Peter Hadreas Course website: http://oucampus.sjsu.edu/people/peter.hadreas/courses/Kant/index.html

2. The Analytic of Principles (pp. 267-295).

4. The Power of Judgment -- as opposed to Reason and Understanding Thus this [the power of judgment] is also what is specific to so-called mother-wit, the lack of which cannot be made good by any school; for, although such a school can provide a limited understanding with plenty of rules borrowed from the insight of others and as it were graft these onto it, nevertheless the faculty for making use of them correctly must belong to the student himself, and in the absence of such a natural gift no rule that one might prescribe to him for this aim is safe from misuse.* (p. 268)

5. The Power of Judgment -- as opposed to Reason and Understanding [continued from previous slide] “A physician therefore, a judge, or a statesman, can have many fine pathological, juridical, or political rules in his head, of which he can even be a thorough teacher, and yet can easily stumble in their application, either because he is lacking in natural power of judgment (though not in understanding), and to be sure understands the universal in abstracto but cannot distinguish whether a case in concreto belongs under it, or also because he has not received adequate training for this judgment through examples and actual business. This is also the sole and great utility of examples: that they sharpen the power of judgment.” (p. 269)

6. The Power of Judgment -- as opposed to Reason and Understanding Footnote to p. 268: * The lack of the power of judgment is that which is properly called stupidity, and such a failing is not to be helped. A dull or limited head, which is lacking nothing but the appropriate degree of understanding and its proper concepts, may well be trained through instruction, even to the point of becoming learned. But since it would usually still lack the power of judgment (the secunda Petri),1 it is not at all uncommon to encounter very learned men who in the use of their science frequently give glimpses of that lack, which is never to be ameliorated. 1. the companion of Peter.

7. Reading Between the Lines: What is Kant Alluding to with the Phrase “the companion of Peter?” “Clement of Alexandria says that those who heard St. Peter were so enlightened by his teaching, ‘that it was not sufficient to for them to hear once only, nor to receive the unwritten doctrine of the Gospel of God but they persevered with many entreaties in their solicitation of Mark, as the companion of Peter, and whose Gospel we have, that he should leave them in writing a memorial of the doctrine thus orally communicated to the’ [Eusebius, Eccl. Hist. ii. 15; vi. 14] . . . Eusebius also quotes Origen as saying that ‘the second Gospel is according to Mark, who composed it as Peter explained it to him, who the Apostle also acknowledges as his son in his general Epistle.’”1 I Peter 5.13 1. Blunt, John Henry, A Companion to the New Testament, Google eBook, 1881, p. 383

8. Kant’s Plan Twofold Approach to Present the Relation of Concepts to Particulars This transcendental doctrine of the power of judgment will contain two chapters: the first, which deals with the sensible condition under which alone pure concepts of the understanding can be employed, i.e., with the schematism of the pure understanding; and the second, which deals with those synthetic judgments that flow a priori from pure concepts of the understanding under these conditions and ground all other cognitions a priori, i.e., with the principles of pure understanding. (p. 270)

9. Transcendental Doctrine of the Power Judgment (or Analytic of Principles) First Chapter: The Schematism of the Pure Concepts of Understanding (pp. 271-77) “In all subsumptions of an object under a concept the representations of the former must be homogeneous with the latter, i.e., the concept must contain that which is represented in the object that is to be subsumed under it, for that is just what is meant by the expression ‘an object is contained under a concept.’ Thus the empirical concept of a plate has homogeneity with the pure geometrical concept of a circle, for the roundness that is thought in the former can be intuited in the latter.” (p. 271

10. Time as the Connecting Link Between Concepts and Intuitions) “Now it is clear that there must be a third thing, which must stand in homogeneity with the category on the one hand and the appearance on the other, and makes possible the application of the former to the latter. This mediating representation must be pure (without anything empirical) and yet intellectual on the one hand and sensible on the other. Such a representation is the transcendental schema. The concept of the understanding contains pure synthetic unity of the manifold in general. Time, as the formal condition of the manifold of inner sense, thus of the connection of all representations, contains an a priori manifold in pure intuition. (p. 272)

11. Time as the Connecting Link Between Concepts and Intuitions) “Now a transcendental time-determination is homogeneous with the category (which constitutes its insofar as it is universal and rests on a rule a priori. But it is on the other hand homogeneous with the appearance insofar as time is contained in every empirical representation of the manifold. Hence an application of the category to appearances becomes possible by means of the transcendental time-determination which, as the schema of the concept of the understanding, mediates the subsumption of the latter under the former. (p. 272)

12. Some New Nomenclature “We will call this formal and pure condition of the sensibility, to which the use of the concept of the understanding is restricted, the schema of this concept of the understanding, and we will call the procedure of the understanding with these schemata the schematism of the pure understanding.” (p. 273)

13. Umberto Eco, (1932- ) Italian semiotician, essayist, philosopher, literary critic, and novelist.

14. Umberto Eco on Kantian Schematism “In order to gain a better understanding of the concept of schema, perhaps we need to consider what computer operators call a flowchart . . . . The chart has something that can be intuited in spatial terms, but at the same time it is substantially based on a temporal course (the flow), in the same way as Kant observes that the schemata are fundamentally based on time.” 1. Eco, Umberto, Kant and The Platypus, Essays on Language and Cognition, McEwen trans. (New York: Harcourt, 1999). p. 82.

15. An Example of Schema and Schematism The schema is in itself always only a product of the imagination; but since the synthesis of the latter has as its aim no individual intuition but rather only the unity in the determination of sensibility, the schema is to be distinguished from an image. Thus, if I place five points in a row, ..... , this is an image of the number five. On the contrary, if I only think a number in general, which could be five or a hundred, this thinking is more the representation of a method for representing a multitude (e.g., a thousand) in accordance with a certain concept than the image itself, which in this case I could survey and compare with the concept only with difficulty. Now this representation of a general procedure of the imagination for providing a concept with its image is what I call the schema for this concept. (p. 273)

16. Schematism is “A Hidden Art in the Depths of the Human Soul” “This schematism of our understanding with regard to appearances and their mere form is a hidden art in the depths of the human soul, whose true operations we can divine from nature and lay unveiled before our eyes only with difficulty. We can say only this much: the image is a product of the empirical faculty of productive imagination, the schema of sensible concepts (such as figures in space) is a product and as it were a monogram of pure a priori imagination, through which and in accordance with which the images first become possible, but which must be connected with the concept, to which they are in themselves never fully congruent, always only by means of the schema that they designate. )(p. 274)

17. Schematism is “A Hidden Art in the Depths of the Human Soul” [continued from previous slide] “The schema of a pure concept of the understanding, on the contrary, is something that can never be brought to an image at all, but is rather only the pure synthesis, in accord with a rule of unity according to concepts in general, which the category expresses, and is a transcendental product of the imagination, which concerns the determination of the inner sense in general, in accordance with conditions of its form (time) in regard to all representations, insofar as these are to be connected together a priori in one concept in accord with the unity of apperception.” (p. 274)

18. Robert Hanna on Transcendental Schemata All the transcendental schemata, according to Kant, express various formal properties of time: properties of “the time-series, the content of time, the order of time, and the sum total of time” (A145/B184–185). What this means then is that every objectively valid judgment, whether empirical or a priori, and in particular synthetic a priori, must implicitly include a schematic a priori formal temporal component that functions as an intermediate structure for interpreting the purely logical elements of judgments and thereby securing their applicability to objects of actual or possible experience. 1 1. Hanna, Robert, "Kant's Theory of Judgment", The Stanford Encyclopedia of Philosophy (Summer 2014 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2014/entries/kant-judgment/>.

19. And it is not only Time which links concepts and intuitions. Space can also be an a priori connector. “If we take, e.g., the pure concept of relation, we find that i) in order to give something that persists in intuition, corresponding to the concept of substance (and thereby to establish the objective reality of this concept), we need an intuition in space (of matter), since space alone persistently determines, while time, however, and thus everything that is in inner sense, constantly flows.” (p. 335)

20. Variations on the Same Monogram

21. Examples of Kantian Schematism “According to the diversity of the subject one will be affected by the same things in diverse manners, e.g., the raven is agreeably affected by spoiled Carrion, and we run from it. Every subject has its own manner of being affected. Its representation thus rests not on the object, but on the particular manner of intuition. Our human nature is of the manner that, when we are affected by external things, they are represented to us in space; this form of intuition can be considered only a priori because it is the basis of every representation, thus precedes them. Likewise time can be considered a priori, i.e., the form which we cognize of our inner state through the inner sense. ― That is all possible because our intuition is sensible. ― It rests on the receptivity of being affected by things’.1 1. Kant, Immanuel, Lectures on Metaphysics, (1782-83) trans. Karl Ameriks and Steve Naragon, (Cambridge: Cambridge University Press, 1997), p. 154.

22. Illustrations of Kantian Schematism: A Dog “The concept of a dog signifies a rule in accordance with which my imagination can specify the shape of a four-footed animal in general, without being restricted to any single particular shape that experience offers me or any possible image that I can exhibit in concreto.”p. 273

23. They have the same schematism Possible features of the dog schematism: its four legged, its tongue hangs out; it barks; it moves spiritedly; it can wag its tail if it has one; it can crouch. . . .

24. The Dog Schematism Finds Application?

25. Illustrations of Kantian Schematism 'No image whatever of a triangle would ever be adequate to the concept of it’ p. 273, A140-41/B180)

26. Illustrations of Kantian Schematism 'No image whatever of a triangle would ever be adequate to the concept of it’ p. 273, A140-41/B180)

27. Illustrations of Kantian Schematism Light and Shade and Y, T, Ψ, X and L junctures. Neckar Cube Adelson, Edward H. “Lightness Perception and Lightness Illusions,” Chapter 24 in M. Gazzaniga, ed., The New Cognitive Neurosciences, 2nd ed. Cambridge, MA: MIT Press, 339-351, 2000.

28. The Transcendental Schemata of the Categories of Understanding “Rather than pausing now for a dry and boring analysis of what is required or transcendental schemata of pure concepts of the understanding in general, we would rather present them according to the order of the categories and in connection with these.  The pure image of all magnitudes (quantorum) for outer sense is space; for all objects of the senses in general, it is time. The pure schema of magnitude (quantitatis), however, as a concept of the understanding, is number, which is a representation that summarizes the successive addition of one (homogeneous) unit to another. Thus number is nothing other than the unity of the synthesis of the manifold of a homogeneous intuition in general, because I generate time itself in the apprehension of the intuition. (p. 274)

29. The Transcendental Schemata of the Categories of Understanding “Reality is in the pure concept of the understanding that to which a sensation in general corresponds, that, therefore, the concept of which in itself indicates a being (in time). Negation is that the concept of which represents a non-being (in time). The opposition of the two thus takes place in the distinction of one and the same time as either a filled or an empty time. Since time is only the form of intuition, thus of objects as appearances, that which corresponds to the sensation in these is the transcendental matter of all objects, as things in themselves (thinghood,a reality). Now every sensation has a degree or magnitude, through which it can more or less fill the same time, i.e., the inner sense in regard to the same representation of an object, until it ceases in nothingness (= 0 = negatio). (p. 274-5)

30. The Transcendental Schemata of the Categories of Understanding “The schema of substance is the persistence of the real in time, i.e., the representation of the real as a substratum of empirical time-determination in general, which therefore endures while everything else changes. . . .  The schema of the cause and of the causality of a thing in general is the real upon which, whenever it is posited, something else always follows. It therefore consists in the succession of the manifold insofar as it is subject to a rule. The schema of community (reciprocity), or of the reciprocal causality of substances with regard to their accidents, is the simultaneity of the determinations of the one with those of the other, in accordance with a general rule.” (p. 274-5)

31. The Transcendental Schemata of the Categories of Understanding “The schema of possibility is the agreement of the synthesis of various representations with the conditions of time in general (e.g., since opposites cannot exist in one thing at the same time, they can only exist one after another), thus the determination of the representation of a thing to some time. The schema of actuality is existence at a determinate time. A The schema of necessity is the existence of an object at all times.” (p. 275)

32. The system of all principles of pure understanding (pp. 278-295, A148–235/B187–294)

33. §1 The System of the Principles of Pure Understanding. First Section. On the Supreme Principle of all analytic judgments (p. 279-81). Aristotle held it is not possible for something to be A and not-A at one and the same time. But Aristotle’s principle, according to Kant, is a blur of analytic and synthetic. A bachelor cannot be a married male. This is an analytic truth. But it is not a judgment, that is, applies a concept to a particular, and thereby relevant to experience. Kant’s revision: “If I say "A person who is unlearned is not learned," the condition at the same time must hold; for one who is unlearned at one time can very well be learned at another time. But if I say that "No unlearned person is learned," then the proposition is analytic, since the mark (of unlearnedness) is now comprised in the concept of the subject, . . .” (p. 281)

34. § 2 Of the System of the Principles of Pure Understanding. Second Section. On the Supreme Principle of All Synthetic Judgments (pp. 281-3). “If a cognition is to have objective reality, i.e., to be related to an object, and is to have significance and sense in that object, the object must be able to be given in some way. Without that the concepts are empty, and through them one has, to be sure, thought but not in fact cognized anything through this thinking, but rather merely played with representations.” (p. 282)

35. Some Etymologies of Word for Experience German for ‘experience’Erfahrung. Cassell's German Dictionary has for erfahren, to come to know, learn, hear, be told, discover, experience, suffer, undergo and for fahren, to travel, drive, ride, sail, fare, get on. Latin experientia from the verb experior from perior (try, attempt). The English term "empirical" derives from the Greek word ἐμπειρία, which is cognate with the Latin experientia. The Greek, ἐμπειρία, is built upon πεῖρα (a test, an attempt)

36. § 3 Of the System of the Principles of Pure Understanding. Third Section. Systematic representation of all Synthetic Principles of Pure Understanding (283-6) Table of Categories Categories of Quantity: Unity, Plurality, Totality Categories of Quality: Reality, Negation, Limitation Categories of Relation: Inherence and Subsistence (substantia et accidens), Causality and Dependence (cause and effect), Community (reciprocity between agent and patient) Categories of Modality: Possibility--Impossibility, Existence--Non-existence, Necessity--Contingency (CPR A80/B106) System of Principles Axioms of Intuition Anticipations of Perception Analogies of Experience Postulates of Empirical Thinking in General (CPR A161/B200)

37. § 3 Of the System of the Principles of Pure Understanding. Third Section. Systematic representation of all Synthetic Principles of Pure Understanding (283-6) * [Note added in the second edition:] All combination (conjunctio) is either composition' (compositio) or connection (nexus). The former is the synthesis of a manifold of what does not necessarily belong to each other, as e.g., the two triangles into which a square is divided by the diagonal do not of themselves necessarily belong to each other, and of such a sort is the synthesis of the homogeneous in everything that can be considered mathematically . . . The second combination (nexus) is the synthesis of that which is manifold insofar as they necessarily belong to one another, as e.g., an accident belongs to some substance, or the effect to the cause -- thus also as represented as unhomogeneous but yet as combined a priori, which combination, since it is not arbitrary, I call dynamical, . . . p. 286

38. § 3 Of the System of the Principles of Pure Understanding. 1. Axioms of Intuition Their principle is: All intuitions are extensive magnitudes Proof. <B> “All appearances contain, as regards their form, an intuition in space and time, which grounds all of them a priori. They cannot be apprehended, therefore, i.e., taken up into empirical consciousness, except through the synthesis of the manifold through which the representations of a determinate space or time are generated, i.e., through the composition of that which is homogeneous a and the consciousness of the synthetic unity of this manifold (of the homogeneous). . . the appearances are all magnitudes, and indeed extensive magnitudes, since as intuitions in space or time they must be represented through the same synthesis as that through which space and time in general are determined.” p. 287

39. § 3 Of the System of the Principles of Pure Understanding. 2. Anticipations of Perception Its principle is: In all appearance the real, which is an object of the sensation, has intensive magnitude, i. e. a degree Proof. <B> “If all reality in perception has a degree, between which and negation there is an infinite gradation of ever lesser degrees, and if likewise every sense must have a determinate degree of receptivity for the sensations, then no perception, hence also no experience, is possible that, whether immediately or mediately (through whatever detour in inference one might want), would prove an entire absence of everything real in appearance, i.e., a proof of empty space or of empty time can never be drawn from experience.” (p. 293)

40. § 3 Of the System of the Principles of Pure Understanding. 2. Anticipations of Perception Its principle is: In all appearance the real, which is an object of the sensation, has intensive magnitude, i. e. a degree Proof. <B> “For, first, the entire absence of the real in sensible intuition cannot itself be perceived, and, second, it cannot be deduced from any single appearance and the difference in the degree of its reality, nor may it ever be assumed for the explanation of that. For even if the entire intuition of a determinate space or time is real through and through, i.e., no part of it is empty, yet, since every reality has its degree that can decrease to nothing (emptiness) through infinite steps while the extensive magnitude of the appearance remains unaltered, it must yield infinitely different degrees with which space or time is filled, and the intensive magnitude in different appearances can be smaller or greater even though the extensive magnitude of the intuition remains identical. (p. 293)

41. Umberto Eco on Anticipations of Perception1 “We can see how schematism works in the anticipations of perception. A really fundamental principle because it implies that observable reality is a segmentable continuum. Now can we anticipate what we have not yet sensibly intuited? We must work as if degrees might be inserted into experience (as if one could digitize the continuous) without this causing our digitization to exclude infinite other intermediate degrees. Cassirer points out that if we were to admit that in the instant a a body manifests itself in the state x and in the instant b it manifests itself in the state x, without having passed through the intermediate values between these two, then we would conclude that we were not dealing with the same body: we would assert that the body that was in the state x in the moment a, had disappeared, and that in the moment b another body appeared in state x. The upshot is that the assumption of the continuity of physical changes is not a singular result of observation but a presupposition of knowledge of nature in general, and therefore it is one of those principles that govern the construction of the schemata. (Cassirer, 1918, III,3). 1. Eco, Umberto, Kant and The Platypus, Essays on Language and Cognition, McEwen trans.(New York: Harcourt, 1999). p. 84

42. Slides #1 and following, Portrait of Immanuel Kant in mid-life: http://www.lancaster.ac.uk/users/philosophy/courses/100/Kant003.jpg Slide #13, photograph of Umbberto Eco: http://en.wikipedia.org/wiki/Umberto_Eco#/media/File:Umberto_Eco_04.jpg Slide #16, variations on same monograms: http://microscopist.net/BramhallJ.html Slide #17, schematism of triangle: https://www.google.com/search?q=pictures+of+Kant%27s+schematism&biw Slide #18, scatter4ed drawing in which one may see a dog sniffing the ground: https://www.google.com/search?q=schema+of+a+dog&biw