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A Brief Sketch of Kant’s Critical Philosophy

A Brief Sketch of Kant’s Critical Philosophy



Jason's Pictures May 2009 - February 2010 283

Jason Zarri

(Based on my notes and paper for a Modern Philosophy class

taken in Spring 2009 at San Francisco State University)


(Also available as a PDF)

Kant’s purpose—


1) In two of his most famous works, the Critique of Pure Reason and the Prolegomena to any Future Metaphysics, Immanuel Kant tried to resolve the issues of whether and how metaphysics was possible, and by extension the issue of how synthetic a priori knowledge was possible. Kant says that his purpose in writing the Prolegomena is to get people who think that metaphysics is worth studying to ask themselves whether it is possible at all (Prolegomena, p. 3). And as Kant makes clear later on, he also wishes to present his ideas in a less obscure manner than he did in the Critique of Pure Reason (Prolegomena, p. 9).


Analytic vs. synthetic judgments, a priori vs. a posteriori knowledge—


1) Kant divided all judgments into two classes: the analytic and the synthetic. An analytic judgment is one in which the predicate is contained in the concept of the subject; as when we say, for example, that a cat is an animal, for the concept of being an animal is included in the concept of being a cat. A synthetic judgment is one in which the predicate is not contained in the concept of the subject, as when we say that a cat is lying on the mat. It is no part of the concept of cats in general that they must lie on mats, nor is lying on mats part of the concept of any particular cat. So if I see that a cat, say Felix, is lying on a mat, I have discovered something that I never could have discovered just by analyzing those of my concepts that apply to Felix or to cats in general. Thus in synthetic judgments something is added to the concept of the subject, and we learn something new instead of merely explicating what we knew before, as we do in analytic judgments (Prolegomena, p. 14).

2) There are, for Kant, three kinds of synthetic knowledge, which belong to judgments of experience, mathematics, and metaphysics (Prolegomena pp. 15-19). Cross-cutting this three-fold division is the distinction between synthetic a priori and synthetic a posteriori knowledge (See again Prolegomena, pp. 15-19). For Kant, a priori knowledge is not derived from experience. It is certain, and holds necessarily of all possible experience. A posteriori knowledge is derived from experience. It is uncertain, and does not hold necessarily for all possible experience. Mathematics and metaphysics are both synthetic a priori, while judgments of experience are synthetic a posteriori. As the definition of ‘synthetic’ specifies, in both synthetic a priori and synthetic a posteriori knowledge something is added to the concept of the subject. In synthetic a priori knowledge, however, we can know what we know independently of experience. We might need experience in order to acquire certain concepts which we must have in order to understand a synthetic a priori knowledge claim, but once we have those concepts we do not need to appeal to experience in order to come to know whether or not the claim is true. By contrast, when it comes to synthetic a posteriori knowledge claims, we must turn to experience if we wish to know whether they are true.

3) Kant finds it necessary to show that synthetic a priori knowledge is possible primarily because he thinks that without it there can be no metaphysics. Metaphysics cannot be analytic a priori, for then it could not give us new knowledge. Neither could it be synthetic a posteriori, for then it its conclusions would not be certain. It is only if metaphysics is synthetic a priori that its conclusions can be both informative and go beyond the sort of knowledge that is acquired through the natural sciences.

4) Mathematical and geometrical knowledge is, according to Kant, a priori and necessary, (Prolegomena, pp. 15-16, and p. 18). However, Kant argues that mathematical and geometrical judgments cannot be analytic (or at any rate not all of them can), on the grounds that they are grounded in our pure intuitions of space and time. Kant gives as an example the proposition 7 + 5 = 12 (Prolegomena, p. 16). By analyzing the concepts of 7, 5 and addition I can only see that 7 and 5 must be combined in a single number, not what specific number this is. It is only by counting things in reality or in my imagination, and thus utilizing my pure intuitions of space and time, that I can come to see that the sum of 7 and 5 must be 12.  If mathematical propositions were synthetic a posteriori we could not know that mathematical and geometrical truths hold necessarily of all possible experience. But we do know this, and consequently they must be synthetic a priori.

5) Because they are synthetic a priori, they cannot rest on the law of non-contradiction alone. They also depend on our pure intuitions of space and time. For example, Kant says, “Arithmetic achieves its concept of number by the successive addition of units in time…” (Prolegomena, p. 30). Now, if space and time were things in themselves, or representations of things in themselves, mathematical knowledge could not be necessary and a priori.  However, anything which appears to us must conform itself to space and time as forms of our sensibility, and so if mathematical and geometrical principles are, so to speak, built into the structure of these forms of sensibility, they must apply to all appearances, and so to all possible experience. Thus for Kant space and time are aspects of the way in which we represent objects, and not inherent in things in themselves, otherwise mathematical and geometrical knowledge would not be possible (Prolegomena, pp. 34-36).


Space and Time—


1) Space and time are our forms of sensibility (Prolegomena, pp. 30-31). Kant calls them such because he believes that anything which we can possibly experience will appear to us as being spatially extended or as persisting through time (or both). Space and time are what all of our perceptions have in common. By contrast, our sensibility itself concerns sensations, or appearances, the “matter” of perception, the things that appear to us as being “in” space and time (Prolegomena, p. 31, p. 54 and p. 56). They may include such things the color of a rose or the sound of a trumpet. Our sensibility is passive, being nothing more than the ability to receive this matter.

2) Kant thinks there are certain aspects of our intuitions of space which cannot be captured by any concept, and which can only be understood through intuition. He gives an example of a hand and its mirror image. Any concept which applies, e.g., to my right hand, will apply just as much to its mirror image; so we cannot distinguish between them merely by thinking (Prolegomena, p. 33). And yet, if the mirror image of my right hand were real, it would be a left hand, and if I were to remove my right hand from some place its mirror image could not subsequently come to occupy the very same space my right hand once did. As Kant says, the hands are not congruent (Prolegomena, p. 33). It is only by reference to our intuition of space that they can be distinguished. From this Kant concludes that space is not inherent in things in themselves, because a part of space is possible only through the whole, something which is not true of things in themselves (Prolegomena, p.34).


Judgments of perception and judgments of experience—


1) We often observe that one appearance regularly succeeds another. For example, we may take notice of the fact that whenever a metal is heated, it expands. If we affirm that this is so, we have made a judgment of perception. But we don’t stop there; usually, we go on to conclude that heating a metal causes it to expand. Now we have a judgment of experience, in which two or more appearances are linked through a pure concept of the understanding, in this case the concept of causation. The faculty of understanding is active. It is the source of pure concepts, which are used to organize our perceptions and bind them together into experience. And though the function of pure concepts is to turn perception into experience, they are not derived from experience. On the contrary, experience is derived from them (Prolegomena, p. 60).

2) Returning to the above example, the judgment that whenever a metal is heated it expands is a judgment of perception, as it involves no pure concepts of the understanding. However, if I judge that heating a metal causes it to expand, I subsume the concepts of the metal’s being heated and its expanding under the pure concept of cause and effect. In the judgment of perception we have subjective validity, for it asserts only a constant conjunction, which does not carry with it any hint of necessity or universality. But in the judgment of experience we have both, for it asserts a necessary relation between two concepts, and for that reason it must always hold, not only for oneself but for everyone.  Thus judgments of experience are objectively valid (Prolegomena, pp. 45-47).

3) Kant agrees with David Hume that the concept of causation cannot be derived from experience. But unlike Hume, Kant does not think causation is merely a habitual association of concepts that we project onto external objects. Instead, he regards it as being a pure concept of the understanding, which the mind imposes on experience in order to make sense of it (Prolegomena, pp. 57-60). As such, it cannot have any application beyond the bounds of possible experience—or, at any rate, we cannot know whether it does.

Metaphysical knowledge—


1) Metaphysical knowledge can be either dogmatic or critical. Dogmatic metaphysics seeks to know things as they are in themselves. Critical metaphysics, which Kant calls “Critique”, only gives us knowledge of things as they must appear to us, and hence of the necessary features of all possible experience. Dogmatic metaphysics would have to meet two requirements which are inconsistent in Kant’s system. First, it would have to be synthetic a priori. It could not be analytic a priori, for then it could not give us new knowledge. Neither could it be synthetic a posteriori, for then it could tell us no more than natural science does. Second, it would have to go beyond the bounds of all possible experience; otherwise, it would not be distinct from mathematics and geometry, which, while also synthetic a priori, are limited to possible experience. This limitation is what makes them possible, for as we said above, they are “built into” space and time as forms of our sensibility. Anything which can appear to us must be subject to our forms of sensibility, and so mathematics and geometry must hold of all appearances. But since dogmatic metaphysics is supposed to apply to things which cannot appear to us, we cannot know a priori what they are like, for they are not subject to the only conditions under which experience, and hence synthetic a priori knowledge, is possible. In consequence, metaphysical knowledge of a dogmatic sort is impossible. Now we can see the source of Kant’s distaste for dogmatic metaphysics: It poses questions which it cannot answer.

2) However, while dogmatic metaphysics cannot yield knowledge, it is not for that reason useless. For it has ideas of its own: the Psychological, Cosmological and Theological Ideas (Prolegomena, pp. 80-96). The first is that of the soul or self as an absolutely simple subject of experience. The second has to do with the connection of conditioned things with their conditions. It has four sub-divisions, which concern (1) whether the world is limited or unlimited in space and time; (2) whether everything is simple or composite; (3) whether there is freedom or only nature; and (4) whether there is a necessary being. The third is the idea of a perfect being, which grounds the possibility and actuality of all other things. While it is clear that things such as these can never be given in experience, they can serve to unite our experiences into a system (Prolegomena, pp. 97-98). Such a regulative use is the only one possible for these Ideas of Pure Reason.

3) If metaphysics is to be a science, then, it must take the form of Critique, a complete system which contains all a priori concepts along with their analysis and categorization, and which shows how by their means synthetic a priori knowledge is possible (Prolegomena, p. 114). Critique is possible because the knowledge it provides has its source in reason itself, as Kant says on p. 115 of the Prolegomena. For this reason Critique can never give us knowledge that transgresses the bounds of all possible experience, for we cannot extract more from experience than reason has put into it. Kant argues against two other possible grounds for metaphysical knowledge, which are probability and common sense (Prolegomena, pp. 117-120). Metaphysics is supposed to be certain and a priori, being derived from pure reason, so we cannot appeal to probability and conjecture in our metaphysical reasoning. Neither can we appeal to common sense, for that is only valid insofar as is justified by experience. Critique, then, is the only game in town. It might not completely satisfy our thirst for speculative knowledge, but it is all that metaphysics can be.


Kant, Immanuel. Critique of Pure Reason, edited by Paul Guyer and Allen W. Wood, Cambridge University Press, 1998

Kant, Immanuel. Prolegomena to Any Future Metaphysics (A revision of the Carus translation with an introduction by Lewis White Beck). The Library of Liberal Arts. Published by  Prentice Hall, Inc.: Upper Saddle River, New Jersey  1997



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