One reason for the obscurity of Kant's three Critiques is that the German language was only beginning to become a vehicle for philosophical expression, and Kant felt a need to invent some of its technical vocabulary from scratch. Another reason is that the three works works were intended for academic, rather than popular, audiences. Kant noted in the Preface to the Prolegomena that metaphysics is not for everyone, even those gifted in other areas of thought (Ak 4:263-4). (Aside from Reid, Kant was the only one in our series of philosophers to serve as a university professor.) Kant recognized that his Critique of Pure Reason "is dry, obscure, opposed to all ordinary notions, and moreover long-winded" (Ak 4:261). His own stated reason for the obscurity of the Critique was that his plan was very wide in scope, and that as a result, its overall structure is therefore is easily missed (Prolegomena, Preface, Ak 4:261). Moreover, Kant thought that he could have made his exposition popular had he only sketched it out and left it for others to fill in the details.

The Problem of Representation

Before he became a university professor, Kant published a number of short works on topics in metaphysics. He received his professorship in 1770, at the age of 46. As was the custom at the time, he submitted an inaugural dissertation, which he entitled "Concerning the Form and Principles of the Sensible and Intelligible World." This work set the tone for his future research in metaphysics In a letter to Marcus Herz of February 21, 1772, Kant had revealed "the plan for a work that might have such a title as The Bounds of Sensibility and Reason." Already in his investigations, Kant thought he had found "the key to the whole secret of metaphysics that had until then remained hidden to itself." He said that he would publish the first part of "a critique of pure reason" in "approximately three months." It ended up taking him almost ten more years to reveal the whole of that secret--a period sometimes known as the "silent decade," in which he published nothing.

As it was presented to Herz, the key to metaphysics is the discovery of way in which objects are represented by the mind. (In the Ellington translation, the German word 'Vorstellung' is translated as 'representation.' In Werner Pluhar's translation of the Critique of Pure Reason, it is translated as 'presentation.') The fundamental question was this: "on what grounds rests the reference of what in us is called representation to the object?"

Kant thought that there are two easy cases. In the first, the object causes the existence of the presentation. This is what occurs with the representations of sense. A "sensuous representation" is a "determination of our mind" which is the effect of an object, say a tree. The "content" of the representation is the way in which the tree affects me, and the representation refers to the object because my mind has been affected. "The passive or sensuous presentations thus have a graspable reference to objects." Kant called the capacity of the mind to be affected by objects passively "receptivity."

The point Kant is making here is not profound. If something really does affect the human mind so as to produce a representation, there is a clear sense in which it is the "object" of that representation, and that the representation makes "reference" to it. Kant goes further than this, however, adding that "the principles that are derived from the nature of our soul have a graspable validity for all things insofar as they might be objects of the senses." The meaning and plausibility of this claim will be discussed in future lectures.

The second easy case of reference is that in which the presentation is a component of the cause of the existence of the object. This is not a case that is familiar from our experience. Far from it--we can only conceive of the possibility of a being whose representations actively bring forth objects themselves. This might be the case in the mind of God, whose representations would be the models for the creation of objects which must conform to them. Thus Kant called this kind of intellect "archetypal," as opposed to the "ectypal" human intellect which receives its representations from objects. It is obvious why any principles in God's mind would apply to created objects.

An important bit of Kant's terminology must be introduced here. The kind of representation that results from the influence of objects on the mind, or the influence of a divine mind on objects, is called "intuition" ("Anschauung"). This is a key term in the Critique. For humans, intuitions refer directly to objects. That is to say, they refer to objects because they are caused by the object. This might lead you to ask how a representation could refer to an object indirectly. The answer is that it might refer to an object through the use of general concepts.

You might have a representation of a tree because you see it. But you can refer to all trees if you have a general concept of a tree. You might say, for example, that trees are plants. In that case, your representation of any individual tree would be indirect, through a concept which refers to all other trees as well. Indirect reference to objects through concepts requires a spontaneous activity of the mind, which Kant attributed to the understanding. So the understanding is the faculty of the mind which spontaneously produces concepts, which is contrasted with "sensibility," which is the receptive faculty.

Now we are ready to turn to the difficult case of representation, the one that presents a problem for metaphysics. We might say that the general concept of a tree is derived from representations of individual trees, by some process of "abstraction." So a concept of this sort gets its reference to objects through the intuitions which give rise to it in the first place. But there are some concepts, Kant believed, that do not have their origin in sense-perception. Kant called them "pure concepts of the understanding," which are produced by the human mind itself, and are not derived from sensation (which is what makes them "pure"). The pure use of the understanding (or "pure understanding") occurs when the understanding generates the pure concepts and operates with them.

In the Inaugural Dissertation (§8), Kant had claimed that pure concepts are to be found "in the very nature of the pure understanding." Among these are "possibility, existence, necessity, substance, cause, etc., together with their opposites or correlates" (e.g., impossibility as the opposite of possibility, effect as the correlate of cause). These concepts cannot be abstracted from sensory presentations because they "never enter into any sensory presentations as parts." (Hume earlier had made the point that there is no "impression" of substance or cause. See, for example, A Treatise of Human Nature, Book I, Part 3, Section 14, "Of the Idea of a Necessary Connection.") Nor are these pure concepts innate; instead, they are "abstracted from the laws inherent in the mind (by attending to its actions on the occasion of experience)." This claim lies at the heart of Kant's metaphysical system.

In the letter to Herz two years later, Kant again claimed that pure concepts are not abstracted from sensuous representations and hence are not produced by the objects which cause them. Nor are these concepts responsible for bringing about the existence of the objects to which they are applied.

But neither is our understanding by means of its representations the cause of the object . . . nor is the object the cause of the representations of the understanding in the real sense. . . . The pure concepts of the understanding must, therefore, not be abstracted from the sensation of the senses, nor must those concepts express the receptivity of representations through sense; but they must, to be sure, have their sources in the nature of the soul, though not insofar as they are produced by the object nor insofar as they bring forth the object itself.

The History of Metaphysics

Kant always began his university lectures on metaphysics with an account of the history of metaphysics. A version of this can be found at the end of the Critique, in a chapter entitled "The History of Pure Reason." A brief account of the history of metaphysics can also be found in the letter to Herz. Kant was concerned not so much with the actual metaphysical principles that had been advocated, but with the way in which the philosophers tried to explain the applicability of pure concepts of the understanding to objects.

One approach is to claim that the human mind has access to the contents of the divine mind. This would solve the problem of the reference of the concepts of the understanding. We have seen that there is no problem of reference for the archetypes of objects, which are spontaneous or "intellectual" intuitions in the mind of God. If we could share in God's intuitions, then we would be able to perform a kind of abstraction from them and derive the pure concepts of the understanding. They would not in any way be based on sensuous presentations.

Kant interpreted Plato as having come to this solution. "Plato assumed a prior spiritual intuition of Divinity as the source of the pure concepts and principles of the understanding." (This interpretation is more reminiscent of the neo-Platonist Augustine than Plato himself.) Nicolas Malebranche in the seventeenth century had explicitly claimed that humans have continuous access to the contents of the divine mind. Kant called this kind of system one of "hyperphysical influx." That is, the human mind is influenced by something more than physical objects--something completely beyond the realm of physical things.

Another sort of system was advocated by Kant's contemporary Crusius, and it can be found in one form or another in rationalists such as Descartes and Leibniz. On the system of "preestablished intellectual harmony," the pure concepts of the understanding have reference to objects because they were placed in the human mind by God for just this purpose. In his metaphysics lectures, Kant sometimes called this kind of pure concepts "innate."

Both of these types of systems, which rely on our relation to God to solve a problem for the human understanding, suffer from several common flaws. First, "the deus ex machina is the most absurd thing one can choose in determining the origin and validity of our cognitions." It was always Kant's conviction that the only plausible explanation for the origin of pure concepts of the understanding is that the understanding itself produces them. Everything else smacks of desperation or looks like some kind of cheap trick.

Second, there is "vicious circle in the series of inferences from our cognition." What Kant seems to have had in mind here is something like the Cartesian circle. We could only postulate that God is the source of the validity of our pure concepts if we could prove that God exists. But such a proof would have to rely on the validity of use of the pure concepts themselves. Finally, if we allow this kind of solution to the present problem, we should allow it for others as well. Such a solution "encourages, on a whim, any pious or melancholy chimera." Kant was strongly opposed to any "mystical" tendencies in philosophy, as he had already shown in his 1766 treatise "Dreams of a Spirit-Seer Elucidated by Dreams of Metaphysics."

There is another approach that has been taken by philosophers in the past, although it is not mentioned in the letter to Herz. One could simply deny that there are pure concepts of the understanding and hold that all concepts are abstracted from sensuous presentations. This is the position Kant in the Critique attributed to Epicurus and Locke ("The History of Pure Reason"). One need not invoke the Deity to explain pure concepts because there is nothing in need of explanation. Kant thought that this empiricist approach is unacceptable because it would be the death of metaphysics. So the history of metaphysics leaves us with a dilemma: either we must accept a bad explanation for the reference of pure concepts of the understanding and the validity of its principles, or we must give up the claim that there are any such concepts. Kant was trying to find a third way.

Common Sense

Kant was aware that Hume had been criticized by his fellow Scotsmen Thomas Reid, James Beattie, James Oswald, and Joseph Priestly. These philosophers maintained that Hume's principles give rise to consequences that are in violation of "common sense." In Kant's view, this criticism is fundamentally misguided.

Hume had, in Kant's eyes, rightly challenged the credentials of pure reason and therefore the basis of all metaphysics. His challenge must be met head-on, if skepticism is to be avoided. The practical effects of any skepticism resulting from a failure to meet the challenge are of no interest to the metaphysician.

Common sense itself cannot meet the challenge because it has nothing to do with pure reason, but only with practical deliberation. As Kant put it, common sense is not an "oracle" to be consulted on pure reason's behalf. To look to common sense for metaphysical guidance is a subterfuge, an attempt to evade the real problem. It is an appeal to the beliefs of the masses, and such an appeal encourages all kinds of superficial ranting.

Hume's Insight

On Kant's view, Hume correctly recognized that the glue that holds the metaphysics together is the principle of sufficient reason. If we cannot prove that this principle holds for the objects of the system, there would be no way to establish any connection between beings. Wolff himself tried to derive the principle of sufficient reason from the principle of non-contradiction, but Hume effectively blocked this move. As Hume recognized, there is no contradiction in supposing the presence of a cause without its regular effect.

So the question becomes whether the principle of sufficient reason has any other justification. Here, Hume was pessimistic. Since he rejected the doctrine of innate ideas, Hume denied that it is an inborn principle implanted in the mind by God. And he argued persuasively that no causal principle can be the product of reason applied to experience. In the end, the principle is the product of the imagination, under the guidance of custom. This is why Kant described Humean causality as "a bastard of the imagination, impregnated by experience," rather than a child of reason. True purely rational principles are necessarily true, and experience can only establish contingent truths.

If Hume were right, Kant went on, metaphysics would lose its basis in reason. As it would no longer fall in the domain of human knowledge, it would have to be abandoned to skepticism. The erstwhile "queen of the sciences" would lose her entire domain. Kant thought such a situation was intolerable, not only because it would leave the sciences without a foundation, but because reason has certain vital interests that must be served by metaphysics. Specifically, we count on reason to establish the existence of God and human freedom and immortality. Kant made it his goal to restore metaphysics to her rightful place by massively reforming her.

Hume's Oversight

Hume did not seem particularly bothered by his skeptical conclusion. As far as he was concerned, metaphysics as practiced up to his time was primarily a source of error. Consider the closing statement of the Enquiry Concerning Human Understanding.

When we run over our libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume--of divinity or school metaphysics, for instance--let us ask: Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matters of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion. (Section XII)

This passage is of note not only because of its explicit condemnation of school metaphysics, but also because it exempts "abstract reasoning concerning quantity or number" from destruction. The reason mathematics keeps its place in the library is that it is not subject to the principle of sufficient reason, which applies only to "matters of fact and existence." Because its object is only "relations of ideas," it can proceed without the use of any causal inferences.

As Kant saw it, the only remaining principle Hume left as a basis for mathematics is the principle of non-contradiction. What Hume failed to recognize, on Kant's interpretation, was that this principle is too weak to establish by itself any but the most trivial mathematical truths. Here is one way to look at the matter. The principle does establish which concepts can be combined, it establishes logical possibilites, but it says nothing about how concepts must be combined, as mathematics requires. Though Leibniz had argued otherwise, Kant maintained that there is no contradiction in supposing that the sum of two and two is a number other than four.

Given the (questionable) assumption that Hume really was trying to establish mathematics upon the principle of non-contradiction alone, and given the further (disputed) assumption that this principle an insufficient basis for mathematics, Hume has no basis for any science of quantity. Given the (unquestionable) assumption that Hume thought that a science of quantity is possible, Kant concluded that Hume had overlooked the need of some further principle to establish the truths of mathematics. And had he done so, Kant went on, he might have seen that this or some related principle could be used to save metaphysics as well.

Jugments A Priori

Hume had exempted mathematics from his critique of the idea of a necessary connection because it only deals with "relations of ideas." The relevant feature of relations of ideas is that they can be established without appeal to any existing thing (besides the ideas themselves), which requires experience. So we can draw a distinction between judgments a posteriori, which can be justified only on the basis of experience, and judgments a priori, which can be justified independently of experience. Judgments of pure mathematics (that is mathematics not applied to any existing thing) are one and all a priori.

Now we have a connection between mathematics and metaphysics, because metaphysical judgments are a priori as well. They must be, because they are supposed to be necessary, and necessity cannot be established a posteriori. For Hume, that is exactly what is wrong with them. Even if one were to succeed in inventing a concept of causality without appealing to experience (which Hume thought was impossible), we would have no reason to believe that it applies to any existing thing. At the least, it would be the concept of a necessary connection, but such a connection would be of value only if there are objects which are connected by it. But this could never be established, on Hume's view.

So Kant's challenge is to come up with a priori justifications for the judgments of metaphysics. To do so, he will at least have to reject Hume's demand that an impression be produced for every idea. Kant would agree with Hume that there are no impressions of which the ideas of causality is a copy. The source must be elsewhere.

Analytic and Synthetic Judgments

On Kant's interpretation, Hume could not look to mathematics as the source of a priori judgments in metaphysics because he thought that all mathematical judgments express relations of ideas. For Kant, this means that mathematical judgments proceed through the analysis of the mathematical concept which serves as the subject of a judgment. If we say, for example, that any two straight lines drawn from any two points on the circumference of a circle to the center are equal, we can appeal to the definition of the concept of a circle. Euclid defined a circle as "a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another" (Elements, Book I, Definition 15).

From this alone we can extract the judgment, which Kant called "analytic." As Kant put it, "All analytic judgments express nothing in the predicate but what has already been thought in the concept of the subject, though not so clearly and with the same consciousness" (Preamble). The basis for all analytic judgments is the principle of non-contradiction (which Kant called the "principle of contradiction.") Assuming that two straight lines from the circumference to the center of a circle are not equal would entail a contradiction, given the definition. The use of the principle of non-contradiction is entirely a priori, so all analytic judgments are made a priori.

Kant's own example of an analytic judgment, taken from what he called "pure natural science," is, "All bodies are extended." But this kind of judgment is of no real value in metaphysics, since it does not say anything about the existence of bodies or about any of the properties of bodies that can be discovered through experience. The latter kind of judgment Kant called "synthetic." It would appear that synthetic judgments are one and all made a posteriori, that they are all "judgments of experience." It is experience which brings the concepts in judgments together.

But here is where Kant broke from Hume (at least as Kant understood Hume). Judgments of mathematics are not in general analytic, but rather are synthetic. Kant's argument for this claim is negative. He gives two examples of mathematical judgments that he claims cannot be known to be true through mere analysis of concepts. From arithmetic, there is the proposition that 7+5=12. We may think the union of 7 and 5, but we do not thereby think the number 12. From geometry we have the example that a straight line is the shortest distance between two points. In this case, "my concept of straight contains nothing of quantity, but only of quality" (Preamble).

We are led to think that mathematical judgments are analytic because of the necessary connection between their concepts. But the connection is not found in the concepts themselves: something else is needed to bring them together. Kant found this something in the representation of individual mathematical objects. In the case of addition, it is the numbers themselves. In the geometrical case, it is the line itself.

Here Kant seems to be taking Euclid's geometry as a model. Euclid began his Elements with a series of definitions, postulates, and common notions. The common notions would seem to be analytic for Kant. He explicitly mentions one of the common notions (although in algebraic form), that the whole is greater than its parts. And example of a definition (which as such is not a judgment at all) is that of a circle: "Def. 15. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another."

The proofs of propositions (theorems) require the use of postulates. The first threee postulates are assumptions that a certain figure can be constructed in a certain way. An example is Postulate 3, "To describe a circle with any center and radius." In Kant's terms, the role of the postulates is to produce a geometrical object about which one reasons in a general way. The key to the proofs is that the manner of construction, or synthesis, of the object dictates what its properties are. See, for example, Euclid's first proposition, "to construct an equilateral triangle on a given finite straight line." Because of the essential role of construction in their proofs, geometrical judgments are synthetic.

For Kant, an individual object, such as an equilateral triangle, is represented by an intuition. So Kant concludes that, because in mathematical judgments our reasoning "must proceed beyond the concept to that which its corresponding intuition contains, these judgments, neither can, nor ought to arise analytically, by dissecting the concept, but are all synthetic" (Preamble). The role of the intuition is to provide a paradigm case which exhibits the the characteristics of the concept. Kant puts this point most clearly in the Critique of Pure Reason:

Mathematics can accomplish nothing with the mere concept but hastens at once to intuition, in which it contemplates the concept in concreto, but yet not empirically; rather, mathematics contemplates the concept only in an intuition that it exhibits a priori--i.e., an intuition that it has constructed--and wherein what follows from the construction's universal conditions must also hold universally for the object of the constructed concept. (Doctrine of Method, Section I, "Pure Reason in its Dogmatic Use, A715-16/B743-4)

Metaphysical judgments are synthetic as well, for Kant. As we have seen, they must be a priori. But metaphysical judgments cannot be based entirely on intuitions. Intuition can account for some of the properties of objects, but not all of them. For example, the judgment that bodies are enduring substances, or that every event has a cause, could never be established through intuitive constructions. So Kant will have to find for metaphysical judgments an X which combines its elements a priori. This, he believed, was the most difficult task philosophy has ever faced, a task which cost him "years of work."

Intuition

Mathematical judgments are synthetic in their structure and a priori in their justification. This is possible through the mediation of intuition. Because the judgment is a priori, however, the intuition cannot be drawn from experience. The intuition itself must be a priori or "pure." (Note that for Kant, human intuition is always tied to what he called "sensibility." God might have an intellectual intuition, but human beings do not.)

The claim that an intuition is pure presents us with a paradox. It seems that to be an intuition, an object must be given through the senses. And yet pure intuition is supposed to be a product of the mind itself, independent of what objects are given to me.

An intuition is such a representation as would immediately depend on the presence of an object. Hence it seems impossible to intuit anything a priori originally, because intuition would in that event have to take place without either a former or a present object to refer to, and hence could not be intuition. (First Part, Section 8)

Space and Time

The a priori character of geometrical judgments is due to the mind's contribution of the form of sensible intuition. The form itself is space. It is in space that we construct geometrical shapes, and we can do so a priori because space itself is given by the mind a priori. What Locke called the primary qualities of bodies, extension, figure, bulk, solidity (impenetrability for Kant), and motion, all depend on space. Because space is a mind-dependent form of intuition, the properties of objects intuited in space are mind-dependent as well. If you try to think of spatio-temporal objects as they are in themselves, you are left with nothing to think about. A thing considered in itself is wholly unknown.

Time is a second form of intuition, which applies to all intuited objects, even the mind itself. It is only through time that we are able to represent objects as changing, so properties such as motion depend on time. Kant also held that arithmetic is a pure science of time. The objects of arithmetic, the numbers, are generated by the temporal process of counting. So just as we can know geometrical figures a priori because we construct them in pure space, we can know numbers a priori because we construct them in pure time.

Appearances and Things in Themselves

The application of the a priori judgments of pure mathematics to objects of sense is now secure. They have "objective reality" because the objects of sense are in space and time, and space are a priori forms of sensibility. In fact, Kant held, this is the only way in which pure mathematics can obtain objective reality, as opposed to being "determinations of a mere creation of our poetic imagination" (First Part, Remark I). This solves a problem for Locke and Hume, for whom the properties of objects are given through sense-perception.

They showed much concern whether a line in nature might not consist of physical points, and consequently that true space in the object might consist of simple parts, while the space which the geometer has in mind cannot be such. They did not recognize that this thought space renders possible the physical space. i.e., the extension of matter itself, and that this pure space is not at all a quality of things in themselves but a form of our sensuous faculty of representation, and that furthermore all objects in space are mere appearances, i.e., not things in themselves but representations of our sensuous intuition. (First Part, Remark I).

Kant wished to distinguish "ideality" from "idealism." An idealist believes that only thinking things and their representations exist. Kant maintained, on the contrary, that there are existing things which are not the same as representations, but which are only known through representations. We call the representations "bodies," to be sure, but bodies correspond to existing beings.

Consequently, I grant by all means that there are bodies without us, that is, things which, though quite unknown to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us, and which we call bodies. (First Part, Remark II)

The fact that the residue remains means that Kant has not turned the world of the senses into illusion. We can distinguish between "truth and dreaming" by appeal to coherence, which is the basis of our judgments. This ability is independent of the way in which we understand bodies. On the other hand, to claim that things in themselves are like bodies engenders a real illusion, "in which I proclaim to be universally valid what is merely a subjective condition of the intuition of things and certain only for all objects of sense" (First Part, Remark III). So the ideality of space and time actually prevents illusion, rather than fostering it.

Kant held that Descartes and Berkeley were the true idealists. That Descartes should be called an idealist is puzzling, since he held that bodies exist independently of the mind. But Kant thought that Descartes also acknowledged that this could not be proved, and so he was an "empirical" idealist. (Kant also calls it "dreaming" idealism here, because it makes representations, dreams, into things, at least possibly. In the Critique of Pure Reason he calls it "problematic" or "skeptical" idealism.) Berkeley flat-out denied the existence of anything but spirits. Kant called his idealism "mystical and visionary." He converts things into representations, by denying that mind-independent things exist at all. Both these types of idealism are refuted by Kant's own "transcendental" or "critical" idealism, or so he claimed.

The Understanding

Thus far, we have been concerned with sensibility, the faculty of the human mind whose objects are intuitions. Intuitions, in turn, are representations of concrete objects, whether constructed in pure space and time or given in sense-perception. We have seen how cognition a priori is possible in sensibility. We are now ready to move on to the second major cognitive faculty of the mind, the understanding. This faculty represents objects abstractly through general concepts.

Through sensibility we represent extended, figured, impenetrable bodies. But we do not thereby represent them as extended, figured, and impenetrable. To say of a body, "This is a sphere," is to bring it under the concept of a sphere in a judgment. Judging through concepts is the main business of the understanding. The judgment just given brings an intuition under a concept, while judgments such as "Bodies have weight," relate concepts to one another.

The two judgments just used as examples have something in common. All the concepts involved in them are derived from experience. They are, as we say, empirical concepts. There are other concepts which are not derived from experience, what Kant calls "pure" or "a priori" concepts. An example of such a concept is that of substance. A substance is something enduring over a period of time. Another example is that of causality. A cause is a prior event which is necessary and sufficent to produce a subsequent event.

Hume had argued that concepts such as these are the product of the imagination. We have no impressions of which these concepts are copies, so they are not empirical. In this he agrees with Kant. But Hume argued as well that they are not produced by reason. Kant held that if these concepts are indeed the product of imagination, they do not apply to objects with necessity. As Hume recognized, it is quite conceivable for an event to occur without a cause, or for what has always been a cause not to be followed by the usual event. The heart of Kant's mission was to prove that concepts such as substance and causality apply to objects with necessity.

An example Kant gives involves two judgments, the first a judgment of "perception" and the second a judgment of "experience."

• When the sun shines, the stone becomes warm.
• The sun warms the stone.

Nature

Before deciding on the source of the validity of the laws of nature, Kant points out an ambiguity in the word 'nature.' In the "material" sense, nature is the "totality of all objects of experience" (§ 16). It has already been established that these objects are intuited as in space and time, and that objects in space and time are appearances. So the a priori study of nature will be confined to appearances and will not extend to things in themselves.

There is another sense of nature, though, according to which it is viewed not just as a collection of objects, but as a system of connected objects. This is nature in the "formal" sense. According to this sense of nature, the existence of any object (or any state of an object) is determined by laws of nature that apply to all objects. Kant's goal is to show how an a priori science of nature (in the formal sense) is possible. He takes as a starting-point the claim that there are principles which govern all objects in all spaces and at all times. This claim is argued for in the Critique of Pure Reason and in the Metaphysical Foundations of Natrual Science, but not in the Prolegomena.

Judgments

All principles, according to Kant, are stated in judgments. Kant thought that an examination of the various ways iin which judgments can be made, the "forms" of judgment, would reveal the basis for the principles that are stated by them. Forms of judgment are known a priori, so they are a suitable starting-point for the investigation the origin of the first principles of pure natural science.

Kant isolated twelve forms of judgment, in four groups of three each. These forms are distinguished in part as follows:

• Quantity: how many things the judgment is about
• Quality: whether the judgment is affirmative or negative
• Relation: whether the judgment relates a subject to a predicate, or two judgments
• Modality: whether the judgment expresses what is possible, actual, or necessary

Categories

All judgments apply concepts to something, either to an intuition of a single object or to another concept. Kant held that there is a group of very general concepts, which he called "categories" of the understanding, that can be derived from the forms of judgment. The two most important categories are substance/accident and cause/effect, both of which are relational. Each is the key element in a principle of pure natural science. They have their origin in a priori cognition, and so they are themselves a priori concepts.

The central question in Kant's metaphysics was how it is that such concepts, generated from the understanding, apply to objects which are found in experience. In the Critique of Pure Reason, the answer is given in the "Transcendental Deduction," one of the most imposing chapters of any philosophy book. Very little of the argument of the Transcendental Deduction can be found in the Prolegomena, however.

The basic idea is that for us to intuit an object of exerience, we must unify what is presented to our senses. If we have only an unconnected mass of sense-perception, we do not represent objects. Hume had claimed that the unity of single objects is the product of the imagination, which detects constancy and coherence in some of our sense-perceptions and fictitiously connects them in the guise of a single thing. The unity of nature as a whole is another fiction of the imagination, whereby observed regular connections are projected onto all changes.

Kant gave a role to what he called the "productive" imagination in unifying sense-perceptions. He thought that on all other accounts of perception, it is the senses that "not only supply us with impressions, but indeed also assemble these impressions and thus bring about images of objects" (Critique of Pure Reason, first edition, "Deduction of the Pure Concepts of Understanding," Section III). It does so according to rules derived from the pure understanding. It is the categories which guide the unification or "synthesis" of perceptions, functioning, as it were, as recipes for building representations of unified objects. Thus, if we are to intuit an object, we must represent it as a substance which endures while its accidents change. And if we are to intuit an object, we must represent changes in its accidents as the effects of prior states of the universe.

Causality

To see how this works in the case of the category of cause/effect, we return to one of Kant's examples. "When the sun shines upon the stone, it becomes warm" is a judgment of perception and "The sun warms the stone" is a judgment of experience. The first is made a posteriori, based on observation of the behavior of the sun and the stone. (Of course, these intuitions must have been unified to some extent already in order to be related.) The second cannot be made a posteriori, as Hume had demonstrated. It expresses a relation of cause and effect, which is generated a priori by the understanding. The judgment of experience arises when the category is "superadded" to the judgment of perception.

If true, the judgment of experience is valid "objectively," while the judgment of perception has only "subjective" validity. Hume and Kant were in agreement about the subjectivity of what Kant called judgments of perception. Where they differed was over judgments of experience. On Hume's view, to say that the sun warms the stone is only to say that there has been a constant conjunction between the sun's shining on the stone and the stone's becoming warm. It is really no different from the judgment of perception, except for the fact that there is an easy transition from the first representation to the second. But this feature of the imagination does not confer objective validity.

Kant would say that although the imagination must be involved in the unification process, the fact that it is under the guidance of a pure concept of the understanding makes all the difference. What makes objects of experience possible is an intellectual function of the mind. Clearly, this claim will have to be backed up by argument, but the argument is not to be found in the Prolegomena. There, Kant simply assumes that there are objectively valid judgments of pure natural science, and he invokes the category to explain how such a judgment is possible.

One argument to fill the gap can be found in the section of the Critique entitled the "Second Analogy of Experience." (The Transcendental Deduction contains a more general argument.) It begins with the premise that we can determine the position of objects in time. A boat floating down the Sacramento River was first at Knights Landing, then at Sacramento, and later at Clarksburg. If there were no causal principle to unite my various perceptions of the boat, I could not infer from the boat's initial position at Knights Landing that it will get to Sacramento before it gets to Clarksburg. My imagination could represent it as floating to Clarksburg first, then arriving at Sacramento. But the laws of nature do not permit this order. In general, I would not be able to place any unobserved event in at a definite point of time without invoking causal laws.

Hume might well grant this whole argument. It describes what he called "coherence" in the Treatise, Book I, Part IV, Section 2. We could not make sense of our experience unless we suppose that objects exist when not perceived and behave according to observed patterns. But, Hume might insist, the fact that we must assume that there is regularity in nature in order to make sense of it does not mean that nature must follow a regular course. Things might go haywire: the boat might first float to Clarksburg before arriving at a city it should first have passed. Then we would be at a loss when trying to determine the time when anything happened, but why must we be able to determine it? Hume might further object that there is no need to turn to the understanding to describe the way we make determinations of time. The operations of the imagination will do perfectly well in this regard, so long as things remain orderly. That Kant insisted that they must remain so surely would have been seen by Hume as pure dogmatism.

Reason

Thus far, Kant has been trying to show how established sciences, the sciences of number and the pure science of nature, are possible. He has traced their possibility to the human faculties of sensibility (which yields space and time) and the understanding (which yields pure concepts). Space, time, and the categories apply necessarily to the objects of human experience, but this is also where their domain ends. In Kant's terminology, they have only an 'immanent' use, a use internal to experience. They do not allow of "transcendent" use, application to objects beyond the limits of experience.

A third faculty of the human mind, reason, attempts to establish a science of transcendent objects. This is the would-be science of metaphysics. Its establishment has been the Holy Grail of philosophy since its very beginnings. Particularly prominent in modern philosophy is the role in metaphysics played by God, a being said to be so removed from human experience as to be nearly incomprehensible. But the quest has not been an easy one. Many a metaphysical system has been launched with great hopes, but none has been universally, or even generally, accepted.

Taken in its most basic sense, reason is the faculty of inference, in contrast to the understanding, which is a faculty of judgment. In its purely logical use, drawing conclusions from given premises, reason does not establish anything on its own. But Kant thought that reason has a theoretical use. Theoretical reason postulates the existence of special objects of reason, which Kant sometimes called "noumena." These objects are transcendent, and they are the special subject-matter of metaphysics.

Ideas

Reason is said by Kant to represent its object through "ideas." He did not mean by this what Descartes or Locke meant, i.e., whatever the mind is concerned with in thinking. Rather, he took ideas to be a special form of representation which is directed exclusively at transcendent objects. Kant tried to show, somewhat artificially, that the ideas of reason are derived from the basic forms of deductive inference. Although he put great weight on this connection, it seems to most critics to be an inessential contrivance. Still, we will respect Kant's view of the matter and say a little about how the transition is supposed to take place.

The categorical syllogism has the following form:

A is B B is C Therefore A is C

The hypothetical syllogism has the following form:

If p, then q If q, then r Therefore if p, then r

The disjunctive syllogism has the following form:

a is B or C a is not B Therefore A is C

The Soul

The psychological idea is supposed to represent a soul, which is a being which is not the property of any other being. This conception is purely negative. Metaphysicians have tried to derive from this meager conception the conclusion that the soul is immortal. For example, they might argue that the soul is a simple being, and simple beings cannot be dissolved or otherwise broken up.

According to Kant, the immortality of this kind of soul, if there even is such a thing, cannot be demonstrated. If we are to prove that the soul has some feature, such as immortality, we must appeal to its properties. Now the soul, taken as an object of experience, is a being that continues to exist, even when its properties change. But continuation is a temporal concept--it is persistence over a period of time, yet the soul is taken here as a transcendent being, beyond the limits of time. And outside of time, we have no basis for predicating anything of the soul. At best, we can say that the soul continues to exist so long as it continues to think. But how are we to say that it will continue to think?

It might be responded that there is a property of the soul, taken as a transcendent object, from which immortality can be demonstrated. Since it is a pure subject of predicates without being a predicate itself, it is simple. But Kant argued in the Critique of Pure Reason ("Paralogisms") that this simplicity is not the simplicity of an object that cannot be divided. Rather, it is a purely conceptual simplicity which really only means that we can say nothing positive about what the soul is.

The Cosmos

The second type of idea is applied in metaphysics to the world as a whole, the cosmos or universe. Because all the objects in the universe are in time and some are in space and time, they make up various series. Kant considers two types of series, one homogeneous and one heterogenious. These produce somewhat different problems when reason inquires into how the series is completed. In every case, the cosmological ideas are in conflict with each other. On the side of the "thesis," the series is considered to be completed in a finite progression or regression. On the side of the "antithesis," the series is considered to be an infinite complete whole.

The first conflicting pair of homogeneous ideas of the cosmos concerns its extent in space and time. Is it of a finite size, with a limit beyond which there are no more bodies? Or does the universe occupy infinite space? Was there a beginning of the universe in time? Or does it stretch back infinitely? The second pair concerns the divisibility of bodies. Are there simple bodies which are absolutely indivisible as held by the atomists, or are bodies infinitely divided, as Leibniz had maintained? In all these cases, what makes up the series is the same kind of thing, which is why Kant called such series "homogeneous."

The peculiar thing about these conflicts is that each side has compelling reasons in its favor. On the side of the thesis is the fact that reason demands satisfaction in tracing the series one way or another. If there is no stopping-point, reason will be frustrated in its goal of attaining a complete idea of the whole. On the side of the antithesis is the fact that any choice of a stopping-point would be utterly arbitrary. Reason would purchase its satisfaction by only at the price of proceeding irrationally, since no reason can be given for any particular stopping-point. It should be noted that experience could not be a reason, as the idea of the whole universe is transcendent.

Kant's solution to these conflicts is to declare both the thesis and antithesis to be false. There is no stopping point to be found in the world. For example, any body may be divided, and its parts divided further, etc. On the other hand, there can be no infinite series of the universe, because the series itself is a construct of the human mind. The only thing that can be said of these series is that they are indefinite. Division of objects may continue indefinitely--a stopping point will never be reached--but the bodies are not actually divided infinitely.

The heterogeneous series are very closely related to each other. The first concerns causality in the world, the second the contingency of the world. The first question, then, is whether the series of causes of any event begins with a first ("spontaneous") cause or continues in a chain with no first beginning. The second question is whether there is a necessary being, a being on whom all other beings depend for their existence, or whether there is no such being, so that everything depends for its existence (is "contingent on") something else. Since the spontaneous cause or the necessary being could be entirely different in kind from the effect or contingent beings, respectively, the series may in this case be heterogeneous.

The arguments for the theses and the anthitheses in these conflicts are basically the same as with the first group. Either reason remains dissatisfied, or it violates its own principles in the effort to gain satisfaction. Which side a metaphysician comes down on depends on which conclusion he finds most favorable, since there is no other reason to embrace one of these unpalatable alternatives.

The solution, however, is quite different when the series allows for heterogeneous members. The thesis and antithesis could then both be true. The homogeneous series of immanent causes, that is, the series of causes confined to objects of experience, has no spontaneous first beginning. The principle of causality, which Kant thought he had shown to hold universally, applies to all causation within the experienced world On the other hand, there could be a transcendent spontaneous cause, perhaps the human will. Reason could find satisfaction in such a cause without violating its principle of causality. And the postulation of such a cause need not be arbitrary. We may have some reason for such a postulation--a reason not to be found in the series of causes in the experienced world. The same would hold for the postulation of a necessary being.

The satisfaction reason can find in the idea of a spontaneous cause is more than theoretical. Reason has a vital practical nterest in at least the possibility of such a cause. It is only if they have what Kant called "transcendental freedom" that human beings can be considered as moral agents. So the possibility that humans (viewed as noumena) are spontaneous is what makes morality possible at all.

God

The idea of God is the paradigmatic transcendent idea--that of a "most real" being that exists necessarily. The object of such an idea could never be found in experience, nor could it have its origins in experience, in Kant's view. It is entirely a being of reason, a noumenon. Kant does not state in the Prolegomena the exact ways in which attempts to prove God's existence fail. In the Critique, Kant rejects the ontological argument. The claim that the idea of God requires God's existence would have to be analytic, and so God's existence would have to be a "real predicate" found among the predicates making up the idea of God. But Kant held that existence is not a real predicate.

Other arguments for God's existence involve synthetic judgments, since they begin with the premise of the existence of the universe. Kant's basic criticism of such arguments is that no amount of evidence about the nature of the objects of human experience can justify any conclusion about the existence of a transcendent being. In his works on ethics, Kant proposed an alternative way of proving God's existence, namely that we must assume that God exists in order to for the highest good to be possible.

In the "Conclusion" of the Prolegomena, Kant discusses the positive role the idea of God can play in metaphysics. First he grants "as a necessary hypothesis, the deistic concept of the First Being, in which this Being is thought by the mere ontological predicates of substance, of cause, etc." This is necessary in order to give satisfaction to reason, and there is nothing to prevent our so doing. He grants that Hume was correct in his contention that the abstract characterization of God as omnipotent or omniscient is of no meaning to us unless we understand God as having something like human will and understanding. But this is anthropomorphism, which is an illegitmate transferral of predicates of experience to the idea of a transcendent being..

The solution to this problem is to distinguish between the idea of God as a thing in itself and the idea of God in relation to the universe. Thus, because of its mode of organization, we conceive of the universe as if it were the product of reason. (The use of analogy to portrary the properties of God was made most famously by Thomas Aquinas.) Kant describes his solution as a middle ground between the dogmatism of those who understand God's properties anthropomorphically and the skepticism of those who find God's properties utterly unknowable. Looking in this way beyond the boundary of experience allows reason to be guided by principles that would be otherwise unavailable. These principles are described in an appendix of the Critique of Pure Reason entitled "On the Regulative Use of the Ideas of Pure Reason." They are, "manifoldness, kinship, and unity." As an example of their use, Kant cited the Leibnizian principle that there is a continuous scale of creatures, from the most complex to the simplest.

Naturalism

Kant believed that his investigations had decisively refuted philosophical naturalism. This is the view that the natural universe exhausts all of reality, and that philosophical conceptions must one and all be drawn from the study of nature. One of its variants is materialism, that the natural universe, including the human mind, is entirely material. Kant thought that he had shown that the human mind exists in time but not in space, which is sufficient to refute materialism. Naturalism more generally fails to satisfy the aspirations of reason for a complete notion of the whole universe, which is impossible to maintain. It also frustrates our practical reason, in that it leaves no room for freedom. And it cannot explain the existence of the universe as a whole, since that existence is contingent. This frees us, Kant maintained, from "fatalism," which again helps clear the way for morality.

Kantian Metaphysics

We have finally reached a solution to the main question of both the Prolegomena and the Critique of Pure Reason: how can metaphysics be placed on a sound, scientific, footing? How can it overcome the endless disputes in which it has been engaged since its inception? The solution is for metaphysics to fill out the details of principles of the understanding which Kant thought he had established. Kant himself attempted to do this in Metaphysical Foundations of Natural Science, which he published in 1786, three years after he proposed the task in the Prolegomena. Unfortunately, Kant's rosy prediction that following the path he laid out would lead to "affording permanent satisfaction to reason" ("Solution") was not borne out by the subsequent course of philosophy.

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