1. Introduction
This book completes the two-volume account of Kant and the empiricists begun with Waxman Reference Waxman2006. Both volumes are masterworks from one of the most original philosophers working on the early modern period today. The latest work gives a reading of Kant’s argument in the Critique of Pure Reason through to the end of the Analytic, a reading which understands ‘critique’ as cognitive science. This is a long book, published on large pages each one of which is dense with argument and exposition. It is also in its parts remarkably (for the difficulty of the subject matter) clear and, in its whole, coherent. Still, it is a tough read: the positions developed are very subtle and complex, exposited in great detail and at great length. So Waxman needs his readership to be generous, giving their time and effort to see the book through to its last page, as they should. Yet, unfortunately, Waxman is not generous with his readership – his colleagues in the world of Kant scholarship – for example, once dismissing an entire body of interpretation with a brisk ‘all of this is wrong’.Footnote 1 But these obstacles should not deter anyone from reading this book.
There is much to agree with here. Waxman is right to insist that we profit most – both as interpreters of the historical Kant and as timeless inquirers into the nature of the intelligent mind – when reading Kant as a cognitive psychologist. There is also much to disagree with here. Indeed, my overall assessment of the interpretation is that its four main foundations – the interpretations of the contribution of sensibility to cognition, the nature of pure intuition, the nature of apperception and synthesis speciosa – are not as well supported by the texts as alternative readings. However, I will not argue for that here. My main task will be to present a clear and concise summary of the main lines of Waxman’s interpretation,Footnote 2 but I will also present, in the final section, an alternative to his account of the Second Analogy proof of the causal maxim.
2. Detailed Exposition
Kant and the Empiricists
In Kant and the Empiricists Waxman lays out his general understanding of the empiricists and of what he calls ‘Hume’s Problem’; he also briefly sketches Kant’s solution. In chapter 2 of the present work, Waxman recapitulates the high points of his earlier work – Hume’s problem and Kant’s eventual solution is fully laid out in the present work only in chapter 17 – concentrating initially on the debt that Kant has to Hume.
Hume’s problem is that, while he considers that sense experience consists of a series of instantaneous perceptions occurring as discrete ‘flashes’ at every moment, at every moment experience itself is continuous. The same is true of the elements of our synchronic experience. Waxman’s Kant provides a solution to this problem by proposing a pre-conceptual mechanism of synthesis. Kant’s debt to Hume is not only doctrinal, the explicitly acknowledged disproof of the possibility of natural necessity, but also methodological. For Hume, metaphysical and epistemological ideas are to be assessed primarily by a psychological investigation into the sources of the ideas in light of concept-empiricism: ideas exist only if they arise from impressions of the senses or of reflection. According to Waxman, this is exactly Kant’s method also, right down to the concept-empiricism. The main differences are in the postulation of synthesis as the core psychological process and the addition of a pure element to the account of sensibility.
But Hume himself is in debt to Berkeley for his method of assessing metaphysical doctrines. Waxman sees the idea of existence in general for Berkeley as equivalent to the idea of presence in sensation, thus conceptually inseparable from mind. Because of this, applying existence to objects which are mind-independent by definition (material objects) is conceptually impossible. Waxman’s interest in Berkeley’s argument in the present volume lies in the potential challenge it poses to Kant’s assertion of the existence of things in themselves – the latter, like Berkeley’s matter, is also mind-independent by definition. This would not be a problem, of course, if Kant were not a concept empiricist but, as indicated, that is just what Waxman takes him to be. Fortunately, contends Waxman (in chapter 8, especially pp. 208–15), Kant is able to consistently find room for an an sich form of existence because, unlike Berkeley, he takes imagination to provide essential elements of sense perception.
Waxman’s Kant
SensibilityFootnote 3
Suppose that we approach Kant’s account of sensibility as Berkeley would, equipped with the notion of immediate perceptual awareness and distinguishing between what we believe and what we immediately perceive. An analysis of what we immediately perceive – take visual perception as our example – quickly gets us to appearances. Looking at the penny on the desk from a sharp angle presents us immediately with something that is different from that presented to us when viewing the penny from the top. Ordinary language invites us to call these objects ‘appearances’ and they change with changes in our perspective. Moreover, there are many appearances together in our visual field, and the relations they bear seem best described as spatial. Of course, pace Berkeley, we also believe that the penny in itself does not change with perspective, so the penny and its appearance are distinct entities. Suppose that we now encounter in Kant’s Aesthetic the two notions of appearance –‘the undetermined object of empirical intuition’ (A20/B34) and the form of appearances, i.e. ‘that within which sensations can be ordered and placed in a certain form’ (A20/B34).Footnote 4 Understanding Kant’s appearances as perspectival objects, we naturally understand the form of appearances to be the means by which the spatial arrangement of the appearances in our visual field is accomplished. Lest we be puzzled why a special entity, the form of appearances, should be required to accomplish this, we recall that, for Berkeley, visual sensations are not inherently spatial, thus cannot, without some outside help, be presented as spatially arrayed. The outside help comes from the form.
Waxman rejects this depiction of Kant’s intentions in part because he believes that it misrepresents the meaning of Kant’s term appearances. Citing a text at A45/B62, Waxman points out that appearances for Kant are the non -perspectival objects (‘objective objects’ as Prauss has called them) of common sense, a rose for example.Footnote 5 But couldn’t it be that even these objective objects get their spatial relations from a form? Waxman maintains not, in part because of one text in which Kant says that all of our representations ‘are in the end subjected to the formal condition of inner sense, namely time, as that in which they must be all ordered, connected, and brought into relations’ (A98–9) and another in which he says that inner sense itself is a creation of the understanding (B153). If we now extend an analogous point to spatial appearances, it follows that only a bare multiplicity of items is given in sensibility: everything else comes from the understanding.
Synthesis
Waxman argues that the intuitive datum for Kant’s theory of synthesis is that there is more to our conscious experience of a complex of elements than the experience of the elements by themselves: an experience of the whole occurs as well. Thus we hear the sound of a horn and see the bugle making the sound all together in one consciousness. Kant connects to this intuitive datum in his discussion of the ‘synthesis of reproduction’ in section 2 of the A-deduction (A102). Kant there makes the point that our present memory experiences are continuous in a sense that would be impossible if memories just previously experienced ‘were lost’. This means that previous memory-moments must somehow be unified with a present memory-moment at the present moment. This is carried out by a process that Kant there calls ‘the synthesis of apprehension’. Waxman will call the output of this synthesis ‘the all encompassing original unity of consciousness of the manifold of intuition’ – ‘the all encompassing unity of consciousness’ as I will call it. What are the inputs?
In section 1 of the A-deduction, at A98–9, Kant says that there are two classes of inputs constituting the manifold of sensibility: those things that result from external affection (‘external sensations’) and those that result from internal affection (‘internal sensations’). However, Waxman maintains, for Kant sensations are not identical with appearances nor do they constitute the matter of appearances, rather appearances ‘exhibit’ sensations (p. 97). (I find Waxman’s account of this relationship uncharacteristically obscure.) The synthesis of apprehension generates appearances from sensations as inputs (p. 101).
Pure intuition
In section 1 of the A-deduction, ‘On the synthesis of apprehension in the intuition’, the synthesis of apprehension creates the unity of intuition, including, in a pure application, the unity of the pure intuitions of space and time (A99–100). So Waxman feels entitled to say that the unity of space and time and the all encompassing unity of consciousness are really one and the same thing. Since they are both products of the understanding acting synthetically, the pure intuitions of space and time fall not on the side of sensibility, as one might initially have thought, but on the side of the understanding: they are one and the same synthesis. This is one of Waxman’s central theses. Another is that this synthesis, though carried out by the understanding, is not category-guided: it is ‘pre-discursive’ (chapter 5).
Now (briefly) some problems and Waxman’s solutions.
First problem: Kant specifically says that the unity of space and time is given in sensibility. Solution: Waxman lays heavy stress on the note to B160 in which Kant seems to correct himself on this. He takes the ‘pre-conceptual’ synthesis described there by Kant to be the synthesis of apprehension.
Second problem: the unities of space and time have specific content, thus cannot be an ‘all encompassing unity’. Solution: Waxman argues that when we generalize from human experience to experience in general we abstract from the differences between the intuitions of space and time and encounter the notion of pure intuition in general (chapter 3). This is the synthesis that yields the all encompassing unity of consciousness in general.
Third problem: where do spatial and temporal relations get introduced, since they are not introduced with the manifold of sensibility? Solution: the synthesis of apprehension places both internal and external appearances – appearances, not sensations – in inner sense, thus in a temporal ordering. But the ordering is a subjective order in the sense of the Second Analogy. Similarly, the synthesis of apprehension also places (only) external appearances in a spatial ordering, but again, in a subjective order. Objective order is introduced by later syntheses.
Fourth problem: the inputs into the synthesis of apprehension are always appearances-cum-sensations, yet Kant says that there is a ‘pure’ synthesis of apprehension. What makes it pure? Solution: because the appearances as such are free from sensation-matter, they are ‘pure’ in Kant’s sense, hence the synthesis that operates on them is pure.
Fifth problem: it is clear that Kant does not locate pure intuition under the umbrella of the understanding applying concepts, so how can pure intuition be a synthesis of the understanding? Solution: Kant uses ‘understanding’ in a broad and a narrow sense; in the broad sense it is the faculty of spontaneity, in the narrow the faculty of applying concepts. It is in the broad sense only that the synthesis of apprehension is a product of the understanding.
Sixth problem: in his first systematic description of the operations of the understanding (A79/B105), Kant attributes synthesis to the imagination but the unity of synthesis to the categories, so how can the unity of consciousness produced by the synthesis of apprehension be other than category governed? Solution: Waxman argues that this claim is meant by Kant to be restricted to objective unities of consciousness (p. 150) and objectivity is introduced into our cognitions only by a late-stage synthesis, not by the early-stage synthesis of apprehension.
We are now through the first five chapters. Chapter 6 deals with Kant’s philosophy of mathematics wherein Waxman discounts any role for visualization in Kant’s account of mathematical construction and also argues that, for Kant, modern logic would fall under mathematics rather than general logic. Chapter 8 gives his account of Kant’s transcendental brand of idealism, briefly touched on above. Chapters 9–11 are central to Waxman’s reading of Kant’s doctrine of understanding, beginning with his discussion of the unity of apperception in chapter 9. I turn to these now.
Apperception
Waxman has been claiming from the outset that the unity of apperception is the same as the all encompassing unity of consciousness, a unity that is produced by the pre-discursive synthesis of apprehension, which is in turn identical with pure intuition in general. But the unity of apperception seems to lie at the heart of Kant’s theory of judgement and the theory of judgement is governed by the categories, or so it appears in the first part of the B-edition deduction and in many other texts. The unity of apperception then seems to be the central unity that the categories impose on things, the very opposite of the pre-discursive unity which, Waxman says, is the unity of apperception. Waxman works hard to deal with several problem-texts (pp. 132–7). But at the heart of his response is a three-fold distinction within types of the unity of apperception: the synthetic unity of apperception (SUA), the analytical unity of apperception (AUA) and the objective unity of apperception (OUA). Only the latter is category governed, the former is the all encompassing unity of consciousness and is not. Waxman’s central text is section 16 of the B-deduction, esp. B132–4 (Waxman’s discussion is at pp. 241–54).
In that section Kant uses the term ‘I think’ to stand for what he calls the unity of apperception, but in two senses of ‘I think’. In the first it ‘accompanies’ all my representations, in the second it is understood ‘as [a] representation’ itself, a particular ‘act of spontaneity’ which Waxman takes to be the all encompassing unity of consciousness, also called by Kant the transcendental unity of self-consciousness. In light of this latter characterization there is the need to account for the ‘self’ in self-consciousness, which is accomplished, Waxman maintains, by taking the ‘I think’ in its first meaning to be the ‘a priori representation of the identity of consciousness’ (p. 246), that is, a universal representation of what makes my representations mine, and mine alone. Further, if a group of representations belongs to a single subject of consciousness (in the formal sense only) then they are necessarily in an all encompassing unity of consciousness. So the ‘I think’ is also a universal representation of the all encompassing unity of consciousness. Later in section 16, when Kant distinguishes between AUA and SUA, Kant intends the first of these to designate the first sense of ‘I think’ and the second to designate the second. Thus the synthetic unity of apperception is the all encompassing unity of consciousness, thus is represented by the analytic unity of apperception. That is how the analytic unity of apperception depends on the synthetic unity (B134).
Waxman also notes the close connection between AUA and another Kantian unity, the analytical unity of consciousness. This is the kind of unity that a concept imposes on the things falling under it. There is, Waxman thinks, a close connection between the two analytical unities. When the analytical unity of apperception is conjoined with all my representations that are not initially concepts it transforms them into concepts (analytical unities of consciousness) simply by being so conjoined with them. Thus a concept or ‘universal’ as Waxman calls it, is simply [r+AUA] (my formulation), where ‘r’ is a particular representation and AUA is the analytical unity of apperception. Waxman takes this operation to be a way that concepts are formed additional to the method of reflection/comparison/abstraction.
This operation is a kind of magic elixir (my term) allowing Kant to do something that would otherwise be impossible: apply (in several instalments) the conceptual apparatus of the understanding to unconceptualized appearances unified by the pre-discursive synthesis of apprehension. The first such application is in Kant’s formation-rules for judgements.
Judgement and categories (chapters 10 and 11)
Waxman’s thesis is that the ‘function of judgement’ creates basic judgements out of concepts ([r1+AUA]+[r2+AUA] … ) and creates relations between basic judgements. The various results of these operations are given in the Table of Judgements, and the basic form of judgement is the categorical type. Waxman’s chief text for this thesis is A73/B98. Here Kant claims that the categorical judgement-form is the subject-predicate judgment-form and that in this ‘kind of judgment only two concepts are considered to be in relation to one another’. Whatever asymmetry we might think is implied by Kant calling these judgments ‘subject-predicate’ Waxman discounts, taking categorical judgments to be concepts combined by a synthesis whose product is ‘reversible’ (symmetrical): A+B=B+A. However, when we make subject-predicate judgements in normal discourse we are of course making an ‘irreversible’ (asymmetrical) judgement: predicating a property of an object. How is this irreversibility to be explained in light of the reversible structure of categorical propositions? According to Waxman, Kant’s answer is that an additional set of formation-rules comes in on top of those creating basic judgements whose job is to introduce asymmetry into the union of the two concepts. The initial asymmetry consists in the designation of one of these concepts as being only a subject and one only a predicate. The resulting logical form is subject-only [r1+AUA] R predicate-only [r2+AUA] where the relation R is indicated in natural language by the copula – ‘is’ in English. Objective judgements all take this form. The ‘additional set of rules’ in question here are Kant’s categories, particularly the categories of substance and cause and effect. Waxman refers to the texts in question (section 9) by Kant’s term, as the Metaphysical Deduction.
Surely there must be more to the categories of cause and effect than simply the grammatical function of changing a reversible judgement-form into an irreversible judgement-form? Waxman’s reply (p. 560) is that they could amount to more than this only if a source in sense experience could be found for them. But Hume’s central doctrine is that there is no such source, and Kant follows Hume on this – so Waxman contends.
The deductions (chapters 13 and 14)
Waxman’s account of the Transcendental Deduction in the A-edition (chapter 13) is extensive but its results can be quickly summarized: given that there are empirical associations, for example, in memory, there must be an affinity which grounds these associations, including a transcendental affinity. The latter is realized in an objective time line, a categorized version of the pure intuition of time. Waxman maintains that the Deduction in the B-edition is essentially the same in content as that in the A-edition but the former makes the reasoning more perspicuous by a division into two parts (sections 15–20 and 22–7) based on a distinction between synthesis intellectualis and synthesis speciosa (B150–2). Both are intellectual syntheses, thus operate only on concepts guided by the rules of the categories, the former of which is the operation introducing irreversibility into the forms of judgement, already discussed in the Metaphysical Deduction. This reasoning is recapitulated in the first section. Synthesis speciosa, on the other hand, operates on the pure manifold of intuitions, the internal and external appearances discussed previously, also by means of the category rules, to produce a special, objectivized and serialized version of pure intuition itself. The argument for this is carried out in the second part of the B-deduction, something that is much more than just a recapitulation of the Metaphysical Deduction.
Synthesis speciosa (chapter 15)
Pure intuition, so far just an all-encompassing-unity-of-consciousness-producing synthesis (the synthesis of apprehension) gets turned into a representation of an object of predication by application of the category of substance. But categories in general cannot apply to intuitions directly, they must always apply to concepts. This is achieved, says Waxman, by Kant again applying the magic elixir: the addition of the AUA to any set of representations. This is applied to create a conceptualized input-manifold for the synthesis speciosa: [[r1+r2+…]+AUA]. The output is a substance: the pure intuition of time as object.Footnote 6 The next step is the creation of differentiated elements within this structure. How is this accomplished? First there is the subjective spatial and temporal order of ‘the entire inexhaustibly infinite manifold of juxtaposed and successive intuitions apprehensible in pure space and time’ (the intuitions are appearances, as discussed above), then the magic elixir is applied to each element in the series producing ‘a manifold of equally many concepts of juxtaposition and succession’ (p. 411). But this manifold of concepts is not itself ordered yet – it is just an infinite number of elements. The temporal serializing of these elements is accomplished by applying the irreversibilizing function of the category of causality to the now differentiated and conceptualized infinite manifold, yielding a differentiated and temporally serialized pure intuition as a substance. Waxman calls this entity the ‘objective time line’. This brings the B-deduction to the same terminus as the A-deduction.
Schematism (chapter 16)
The synthesis that locates series of empirical events in objective time does so by coordinating the elements of the series with the elements of the objective time line. This action, according to Waxman, is carried out by yet another synthesis,Footnote 7 the schematism of the pure concepts of the understanding.
This concludes my exposition of the main lines of interpretation up to Waxman’s treatment of the pure principles of the understanding. These I touch upon in my treatment of the proof of the causal maxim in the Second Analogy.
3. Kant’s Proof of the Causal Maxim in the Second Analogy
The A-edition version of the Second Analogy employs the schematized version of the law of causality, not the law in its proper, categorial sense. The latter is asserted only in the B-edition version: ‘All alterations occur in accordance with the law of cause and effect’ (B232). Waxman’s discussion takes the principle in its A-edition sense but I take the B-edition version to better reflect Kant’s reasoning in both versions. I also take the notion of cause and effect to be primitive for Kant, understood in the usual full-blooded sense.
In the argument of the Second Analogy Kant assumes the existence of an objective order of time distinct from the subjective order in which our inner experiences occur. He also asserts a close connection between the objective ordering of events and a requirement that each preceding event causes the next event to occur. What is the connection? On some interpretations Kant is defining objective temporal order among empirical events in terms of causal order among empirical events, that is, Kant is asserting a causal theory of time. Waxman’s seems to be one of these interpretations (pp. 499–500). But there is another: that the notion of an objective order among empirical events is defined independently, and that a causal order among empirical events is an epistemic condition for assigning certain empirical events an objective temporal order; we know that a series of empirical events should be given an objective order just in case those events are in a causal order. The ‘independent way’ is placing the representation of the empirical series in correspondence with the objective time line.
Which of these accounts we attribute to Kant is relevant to the proof-structure we attribute to Kant for the causal maxim. If it is the causal theory of time, then the proof of the maxim is simple and direct: from the premise that a universal objective time-order is operating, we infer that a universal causal order is operating, since these are one and the same thing. On the other hand, if the causal ordering has merely epistemic significance, then an independent proof of the causal maxim is required. It is this interpretation that I will adopt. What, then, is the independent proof?
The principles under discussion in the Second Analogy are pure synthetic a priori principles of the understanding, distinguished from the categories – also principles of the understanding – in that the latter are used subjectively as part of the explanation of how and why we think as we do whereas the former are ‘an objective use of the categories’ (A161/B200). Now, Kant’s use of the differentiating term ‘objective’ may puzzle us: after all, the categories themselves are just what make our objective experience objective. Isn’t Kant’s phrase ‘an objective use of the categories’ just like saying that a black cat is black? In the preceding section, where Kant explains the general idea of synthetic a priori principles of the understanding, he draws a similar distinction, that between experience and objects of experience (A158/B197), a distinction that looks like the distinction between objectivity of mental content (‘experience’) and the objectivity of the empirical world (‘the object of experience’). Now, this formulation of the distinction is also puzzling in light of Kant’s phenomenalism – aren’t objects of experience and the objectivity of mental content just the same thing? Isn’t that the main point of the concept-of-an-object discussions in the A-deduction (A104–10)?
It is indeed one of the main points, but not the only one. A second is that our ability to construct phenomenalistic concepts of objects itself depends on a subjective use of certain principles, subjective in that they serve as premises in reasoning. But we also ‘find’ them objectively in nature (the term finden occurs at A125), that is, as nomological principles instantiated in nature. What reasoning we engage in in the course of constructing our representations of nature is found by the methods of transcendental cognitive science, what laws we find in nature itself are found by the methods of the physical sciences, and these are different methods. I contend that this is the practical import of the distinction Kant is recognizing between experience and objects of experience. But these methods yield principles that are the same in content! How can that be? Kant’s answer constitutes the Copernican revolution in metaphysics: they are the same because we require nature to instantiate the same principles that we use as categorial premises. This is Kant’s nomic prescriptivism. I also contend that Kant assigns to the Transcendental Deduction the task of establishing this doctrine.Footnote 8
Prior to the proof of nomic prescriptivism, we access what turns out to be a set of content-identical categorial premises/laws of nature in two different ways. But after the proof we have an additional route to the natural world since we now know that the categorial premises and the laws of nature have identical content. If we have already proven that there is a categorial premise with content C but have not been able to prove that there is a law of nature with the same content, we can now infer the law of nature with content C from the categorial premise C and the doctrine of nomic prescriptivism. This is a special kind of scientific inference dependent on Kant’s transcendental psychology, which I shall call ‘transcendental scientific inference’.
We now can prove the objective form of the causal maxim by means of this inference. Asserting that the causal maxim is the content of a categorial premise – the penultimate result of Kant’s A-edition deduction, as I argue elsewhereFootnote 9 – we now infer, in the presence of nomic prescriptivism, that there is the corresponding law of nature. And this is what Kant set out to prove in the Second Analogy.
A final point. We might ask: if there are methods in the physical sciences that reveal laws of nature empirically, why not for the law of causality? It is here that Kant’s debt to Hume looms large: it is because we cannot perceive causality, force or any of the other forms of necessity in nature that we cannot use empirical methods to ascertain their existence. The same can be said of the category of substance, or indeed of any of the other categories. ButFootnote 10 we can use observation and empirical methods to demonstrate the generalization, Any object we encounter in space can be spatially connected to any other, in such a wide variety of cases to justify nomic status for that generalization. Since that generalization also serves as a fundamental premise in our reasoning about an objective world – it is a conceptual objectivity-condition but, though not a categorial premise in Kant’s technical sense, it functions the same way – it is a generalization that can provide the categorial-like-premise/natural law pair with the same content, upon which the proof of nomic prescriptivism itself relies.
