On Kantian Metaphysics


Review of The Poverty of Conceptual Truth. Kant’s Analytic/Synthetic Distinction and the Limits of Metaphysics, by R. Lanier Anderson

Oxford University Press, 2015

Lanier Anderson’s book covers a great deal of material and could fairly be said to amount to two or three books in one: a book about the pre-Kantian, especially Wolffian, understanding of logical form, and the relation between that issue and metaphysics; a book about when, and in consideration of what issues, Kant broke with his metaphysical heritage and insisted that there had to be irreducibly synthetic judgments; a smallish book about the right way to understand Kant’s philosophy of mathematics and its reliance on intuition, very engaged with recent secondary literature; and finally, the heart of the matter: a reading of the critique of metaphysics in the Transcendental Dialectic meant to show the centrality of what he calls the “syntheticity” argument, the “master argument,” in that critique. Actually there is yet another (excellent) excursus, on the vexing issue of empirical concept formation (Chapter 13). There are also three appendices on more scholarly issues. Nevertheless, despite this variety, and the magnitude of the issues, Anderson finally pulls enough of the various threads together that the whole thing works as a book. And is a terrific book.

Part I takes on the task of showing that Kant’s attack on philosophers who denied any distinction between analytic and synthetic judgments was not aimed at straw men, and that those whom he attacked were not just blind to the obvious. There were philosophical reasons, serious ones, motivating the Wolffian position. (A side benefit of this discussion is the demonstration of interesting differences between Leibniz and Wolff on the main issue, as at 4.42.) Anderson also argues that analyticity was understood by Kant and his predecessors not in a methodological or epistemological way, at least not primarily (how we know that a predicate inheres in a subject) but in a “logical” sense (what constitutes analyticity is a special logical relation between predicate and subject, “containment,” one that relies on nothing psychological, one that invokes a “technical notion of containment.”) That “technical notion” requires a distinction between contained in (logical intension, the marks necessary and sufficient for the concept’s identity) and contained under (logical extension, the lower order concepts falling under it) (e.g. 4.7). This all reflects the basic metaphysical idea behind this understanding of logical form – the understanding of the world as a Porphyrian structure flowing from a highest genus by the addition of species differentia. Anderson also argues that these two senses of containment are strictly linked; there is what he calls a “reciprocity” between both. He means that whatever is included in the content of some concept must cover that concept within its extension, and conversely, whatever concepts fall under a given concept in its extension must include it in their contents. Moreover, concepts with the same extension also have the same content, and vice-versa.

This was all very helpfully set out. This exfoliation of lower order species concepts from higher ones is the basis for the logical structure requiring containment relations in these senses. This allows Anderson to say that the Wolffians were not engaged in mere hand-waving when they claimed “containment.” There were “clear rules” for understanding containment (these genus-species relations, laid out in syllogistic reasoning) and there were important philosophical issues at stake in their characterization of the logic of true judgments. Aside from L.W. Beck, there is no work in English known to me, which devotes this much philosophical attention to pre-Kantian metaphysics, and certainly none that so helpfully contextualizes Kant’s development. This in itself is an important scholarly achievement. The philosophical defense of the containment view of analyticity, Anderson’s account of that “technical notion” and of “reciprocity” are also original and important.

I am not sure I would go so far as to say that this shows that Wolff’s method could therefore be said to be a “method of discovery.” (3.15) At least I don’t know how that would work. It is clear enough what the discovery would be: the specification of a differentia that determines a species as such. But since Anderson has separated out the epistemological and logical senses of analyticity (perhaps they should not be so strictly separated as alternatives; perhaps they are more two sides of the same coin?), we are not in a position to know what we appeal to in order to make such a claim. So how do we make “discoveries”? One could say that in syllogistic reasoning, one discovers, via a use of the middle term, a connection that had not been noticed, but that just pushes the question back to “how we knew” the original and decisive containment relations involving the middle term. To some degree, would not this appeal to analysis ultimately have to rely, for genuine discovery, on some notion like “the light of reason,” noesis, a passive form of intellectual intuition, and would not that be the source of discovery? If so, this might mean that, in principle, a pre-Kantian metaphysician could admit that nothing can be derived from a concept merely “by thinking it” (I’m not sure any Leibnizian ever believed that), that we require the exercise of an intellectually intuitive power to “see” the connection. If that is so, then such a philosopher would have no great stake in some absolute notion of analyticity. Such a philosopher would not, of course, be Christian Wolff (more likely, Plato) and it is not much addressed by Kant, but it is a possibility within the field of possibilities around the issue. And Anderson often speaks as if his Kant thought he had discovered the Achilles heel of all metaphysics, not just Wolffian. That form is supposed to be paradigmatic, not unique.

I should note something else that will be important later. After the introduction of mathematical syntheticity, or Kant’s full blown doctrine, it becomes clear that the main issue in the attack on prior metaphysics’s doctrine of containment is the Kantian denial of its claim that conceptual relations alone, especially the heart of the matter, containment relations, are or can be “object implicating.” But the simple laying out of the Porphyrian structure of the world, while it might look like an existential commitment to genera and species as special “objects,” need not involve that. The species form of a dog in Aristotle (arguably) does not posit an existent. Primary form does not exist separately from its object; it spells out the energeia, the “being at work” of the dog in its distinctive way; it is not an “element” or part of the dog. This is not crucial to Anderson’s case, but not all metaphysical questions are questions about what exists and the Porphyrian “tree” is not so much about the “existence” of such a tree, but about the way the world is, such that it can be an intelligible world.

Part II (“A Difficult Birth”) is an impressive display of erudition and there are important results for scholarship. Anderson, for my money, compellingly, refutes Adickes’ claim that Kant came up with the mature analytic-synthetic distinction in the late 1760’s. This has always been a difficult claim because the distinction does not surface in the 1770 Dissertation and that fact would seem dispositive. But Anderson also shows that the “real/logical distinction,” despite appearances, also got Kant no closer to the mature doctrine, and he makes great use of L.W. Beck’s famous argument about how one might render a synthetic judgments analytic to show that the epistemological account of analyticity cannot be right. We could require experience to learn that one concept actually “contained” another, but that would tell us only about the order of discovery. The order of justification would still finally rest on a containment claim with a system of Wolffian science, or on an analytic claim. Anderson also shows that Kant’s invocation of analytic and synthetic methodologies in decomposing concepts or building them up is also consistent with leaving the containment claim unchallenged. Even in the Dissertation, when Kant was no longer considering sensibility a confused mode of intellection, and where there were several other pieces in place suggesting the mature distinction, Kant still seemed to think of philosophy as at work wholly “inside” the conceptual. (Anderson also points out helpfully some truly bizarre things Kant is willing to say about judgment. (7.5). Or what appear to be claims by Kant that mathematical knowledge is empirical. (7.11ff.)) I know of no other work that tracks Kant’s development with this degree of acuteness, with this much attention to the range of possibilities in play for Kant.

Light begins to dawn with the famous letter to Herz of 1772, and in several Reflexionen in the two years afterwards, and finally, in a note dated 1776, we see the whole mature picture. (7.31). Anderson argues here, as before, that the motivation for the mature doctrine and its actual formulation does not stem from “epistemological” considerations but “logical” ones. (He is worried for Kant about Beck’s recuperation strategy.) That is, it stemmed from the consideration that there must be judgments whose logical form does not involve predicate containment. But that seems inevitably, immediately even, to raise the question of what the relation is. “Not contained” is an “indeterminate” negation in Hegel’s sense. The point seems inherently and unavoidably also epistemological: “not contained” has to mean known to be ascribable to the subject otherwise than by appeal to whatever allows us to characterize the form as one of containment. But I am not clear how much of anything hangs on this. At any rate this part is a masterful display of scholarship, everywhere intelligently and fairly argued, utterly convincing in the fine grain of its details.

Part III is the most important element of the book’s whole argument, “Ineliminable Synthetic Truth in Mathematics.” As a matter of Kant interpretation, Anderson claims that the usual characterization of Kant’s views on the nature of mathematical knowledge – that because such claims rely on intuition, the judgments must be synthetic – has everything backwards; that Kant wanted to claim that because mathematical judgments must be synthetic, they must rely on intuition, and rely on them in a way that reflects that genuine, independently established, syntheticity. (The former, traditional claim would not suggest syntheticity to pre-Kantians because they could accept it and keep absolute analyticity; they did not recognize a distinction in logical kind between concepts and intuitions.) This all leads Anderson into the recent controversies over a “logical” interpretation of the role of intuitions in mathematical reasoning (intuitions are indispensable in mathematical inference) versus a “phenomenological” reading (intuitions provide a unique sort of evidence for mathematical judgments). Anderson first rejects Hintikka’s version of the logical reading (as “taking in too much,” appealing to singular terms in general, rather than to a Kantian understanding of intuition), sides with Friedman’s logical reading against Parsons, takes account of Carson’s later formulation and than adds his own contribution (8.17). He wants to argue that the large picture he has been painting of Kant’s evolving understanding of the analytic/synthetic difference can contribute significantly to our understanding the issue. For Anderson, we have to show first that mathematics exhibits “non-conceptual structure” (8.18). What he calls “the syntheticity argument” is what drives us to a doctrine of intuition to satisfy what it demands. It is because mathematical knowledge must be synthetic that there must be a non-conceptual form of representation. (Given this structure, this raised for me the question of whether Kant needs a four step, not a two step argument, each of which must be argued for. (i) Mathematical knowledge must be synthetic; (ii) it requires non-conceptual representation; (iii) that non-conceptual representation must be an intuition, understood as Kant does, marked by singularity and immediacy. And (iv) granted intuition does satisfy that demand; must we not also show that only intuition understood in the Kantian sense will satisfy the demand?)

A lot of the discussion here was a marshaling of various options in the secondary literature to make the point Anderson needs, but it was all very well done and put together in a convincing way. From Sutherland he gets the claim we need for mathematics a logical homogeneity that does not exclude specific differences. (A purely conceptual approach cannot really explain denumerability; or, there is no conceptual way to represent the equivalence of non-identicals.) Considerations like these are advanced and eventually get us to the claims that there are “ineliminably intuitive” elements to mathematical proof and evidence (as in: one angle is greater than another.) He then goes on to address similar issues in a synthetic theory of arithmetic. The result is a very sensible, a sort of “split the difference” position. Both the inferential and the phenomenological accounts of intuition contribute something to our understanding of the role of intuitions. But for the argument of the book, what is important is the demonstration of the “expressive poverty” of conceptualist approaches to mathematics (the “no equivalence of non-identicals would be possible” argument). That establishes the logical option’s importance. But we must then show what does make mathematical knowledge possible (intuitions as “evidence,” or, following Friedman, aspects of “diagrammatic reasoning”). I don’t think that any of these discusses will convince contemporary philosophers of mathematics that arithmetic is synthetic, but within the confines of the Kantian assumptions, this is all very fine work.

Part 4, or Chapters Ten, Eleven, and Twelve make Anderson’s central argument for the priority in importance of the syntheticity claim, the “master argument” for the critique of metaphysics (or at least the critique of Wolffian metaphysics). The claims are original and will be controversial. A standard view, typified by someone like Karl Ameriks or Henry Allison, is that the Dialectic proceeds by showing the “subreptions” or paralogistic reasoning or equivocations or antinomial results of metaphysical arguments themselves, internally, and then diagnosing those failures by appeal to transcendental idealism, especially its core claim, that we can know only appearances not things in themselves. The latter thesis would be question-begging against Kant’s opponents if it were the prime “weight bearing” element in the critique, but it is not. The failure to establish, by the arguments used, what the metaphysicians want to establish is the key element. The underscored phrase here is essential, because such negative results leave open the possibility that the various claims could still be true (there could well be immaterial souls, a necessary being and so forth) and so a practical metaphysics is still possible. We don’t hear much about transcendental idealism and the subjectivity of the forms of intuition in Anderson’s treatment. His case for his “master argument,” already an innovation in his approach, goes beyond this and sometimes seems to establish something very strong: that no successful way of even referring to such entities is possible and that claims which do so are “fantasies.” This seems a quasi-verificationsit claim and stems from the importance in Anderson of the “conditions for objective reference” element of his syntheticity argument, derived from his analysis of Kant on mathematical knowledge (e.g. conditions for any modes of reasoning about individuals). For most accounts, Kant’s establishing of conditions necessary for any reasoning about “the real” is essentially and necessarily limited (the forms of intuition are the forms of a finite human cognizer) and so the Dialectic trades only on “what could be objectively known to be real for beings who depend on sensible intuition for content,” not referential conditions in general as a semantic point.(Anderson’s stronger, apparently semantic claim is: “the synthetic claims of metaphysics depend on the satisfaction of the conditions for definite objective reference to individuals, whatever those turn out to be.” 10. 9) Again, the traditional reading has it that Kant’s criticisms are more in the way of showing an internal dialectic, that the metaphysical arguments under consideration are based on equivocations and paralogistic reasoning, or they allow contradictory conclusions. Metaphysics so understood cannot establish, by those arguments, the conclusions desired; not that metaphysics itself would be impossible in any sense, by appeal to any different sorts of arguments or considerations. It does not seem (to many commentators) that Kant wants to establish that no sorts of considerations could establish conditions for some sort of referential possibility. On many readings, Kant is out to show that metaphysical questions are undecidable, not impossible, meaningless or fantastical.

Anderson’s case for his approach is built on a Kantian distinction between, in the series of conditions for a conditioned, a “collective unity” versus a “distributive unity.” The latter can provide a principle of explanation for all instances, but not a ground for any one instance and need involve no claim about the completion or even the status of the whole series. The sufficient reason for a conditioned instance would require that the whole series be given as one (i.e. the “collective unity”) such that the sufficient reason for the one could be given. It is this emphasis on the givenness of this unusual singular  one” that looks to Anderson like a singular existence claim. (10.18-20)

The counter to Anderson will be that this formulation fits at best only the Antinomies, and, more importantly, that Kant’s own argument does not seem to hinge on, to invoke a term Anderson frequency uses, but that could stand more of a gloss, “forcing” a commitment to a singular object. (Metaphysics, primarily, for Anderson’s Kant, involves the claim that conceptual relations alone “force” a commitment to a singular object.)  But the surface form of Kant’s argument is that the three syllogistic forms of inferential reasoning (from conditioneds to their conditions) require indirectly a commitment to a condition (immaterial souls (not some individual soul) the beginning of the world, a simplest particle, a free being (some free beings), a necessary being) in order to fulfill the conditions of explanatory adequacy for anything conditioned. The controversy with Anderson will be whether his is forcing this form into the shape required by his reliance on conditions for objective reference. For example, in the Paralogisms, both sides agree that for there to be thinking, there must be thinkers, an “I” thinking. But the rational psychologist insists that the unity of such a thinker can only be accounted for if such a subject is immaterial. They disagree, in other words, about what a thinker is. (So that metaphysics in this sense would be answers to ultimate “what is it?” questions, not necessarily to “what is there?” questions.) Granted, all such questions could be put in the form of a claim about existence, and that always means that any claim for the existence of such things involves an existential commitment to at least one such thing, but the question is whether Kant’s arguments, as Anderson portrays them, stretching from the insights into mathematical proof to the Dialectic, are built around a consideration of the conditions for singular reference. The form of the argument rather seems to be that while thinking requires a subject of thought, no conclusion whatsoever can be drawn about what thinks. Doing so would confuse a formal condition with a substantive conclusion. This is all the proof Kant needs, and its form looks closer to the main consideration underlying the Dialectic, our noumenal ignorance. (Thus, see 11.12-3). Anderson is aware of the equivocation charge – he quotes B409 (“the logical exposition of thinking in general is falsely held to be a metaphysical determination of the object”),– but glosses this with his Master Argument claim. (The Dialectic basically rests “on a deep insight into the expressive limitations of mere, one-place general concepts.” 12.27) He certainly has a point, but this will be a contested issue. Especially since some of his own formulations seem like a sweeping one-step argument that brushes aside any metaphysical claim in one move and raises the begging-the-question issue he has raised against traditional interpretations. 11.9: “By restricting itself to mere one-place general concepts, whose logical power derives precisely from their abstraction from any such singular reference, metaphysics deprives itself of the resources needed to meet this challenge.” (The “challenge” referred to is to show how the claim fulfills the “objective reference” condition.) That looks like a game-set-and-match point before we even get started. (He seems to invoke this argument at various points as doing all the work, as if mostly just repeated by Kant (see 11.20)) Again, this is all a very interesting way of looking at the structure of the Dialectic. I want only to indicate the contestable points.

The ontological argument for God’s existence looks to be the very best candidate for Anderson’s claims about the underlying argumentative structure of the whole Dialectic. And this discussion is one of the best in the book, and one of the best, most thorough, discussions of the argument in the literature. Again the issue will be whether Kant can rest content with a negative conclusion, as, for a lot of commentators, he seems to – that the actual argument for God’s existence confuses logical issues relevant to concept determinacy ((the principle of determinability) with metaphysical claims about reality (the principle of thoroughgoing determination) – and so that there is nothing in the ontological argument itself that justifies any claim about such determination, certainly not about existence as a determination. Or, whether an appeal to “The Master Argument” is at work in the actual claims against the rational theologian (against the possibility of such a claim). One could put this point by asking whether Kant is out to show that a paradigmatic form of the ontological argument does fail, or whether it must fail, and if so why. A conventional view would be that he does both; the former is shown by an internal analysis of the argument, and the latter is claimed on the basis of transcendental idealism. That is not Anderson’s claim. See 12.7-8, where he seems to worry about the possible petitio in his own position mentioned above, but he moves ahead anyway.

There is also a point in this discussion where Anderson seems to realize his invocation of conditions for objective reference, especially if construed in a semantic spirit, may prove too much. So we read:

I suspect that this interest led Kant to underestimate the corrosive force of his own critique, for if the master argument really reaches the semantic conclusion that we are not even entitled to a representation of the singular ens realissimum as anything more than a vague fiction of the

imagination, then it is hard to see why we should admit the conception of the original being as an object into philosophy even for practical purposes. 12.13

This is admirably honest and straightforward, but it is not marked as a problem, and it will be for more orthodox Kantians, since Kant certainly does refer, he thinks quite successfully, to the ens realissimum for practical purposes (not to a “vague fiction”). Without more of a gloss, this formulation can sound like what Kant called “skeptical hopelessness” and so the “euthanasia of pure reason” at A407/B443-4. Moreover, Anderson’s tendency to conflate all metaphysics with indefensible existence claims has an obvious problem. There is no question that Kant believed that there could be, in some sense, valuable metaphysical results in the form of analytic judgments. The “Metaphysical Expositions” of Space and Time embody such an analytic metaphysics, a specification of what space is by analysis of the concept. (More precisely by Kant’s familiar disjunctive syllogism. A is either x or y or z. Not x (Newton). Not y (Leibniz). Therefore z (subjective forms.)

In Chapter Thirteen, Anderson has some very interesting, often compelling things to say about the recent debates concerning conceptual content, and the conceptualist/non-conceptualist discussion of Kant (the treatment of Ginsborg is especially insightful, and his suggestion about empirical concepts as “provisional bets” (13.41) is a very good one).

There is much to admire in this book, and much to learn from it. On interpretive,  philosophical, and meta-philosophical levels, it is a major accomplishment and richly deserves the attention it will no doubt receive for many years to come.

Posted on 4 November 2015

ROBERT PIPPIN is the Evelyn Stefansson Nef Distinguished Service Professor in the Committee on Social Thought, the Department of Philosophy, and the College at the University of Chicago.