Every philosopher who has not been living under a rock since 1787 knows that, according to Kant, ‘The real problem of pure reason is now contained in the question: How are synthetic judgements a priori possible?’ (B19). If R. Lanier Anderson is right, then every philosopher interested in Kant’s place in the history of metaphysics should know that Kant secured that place partly by answering the question: how are non-analytic judgements possible? Once answered, Anderson’s thesis is that ‘Kant’s distinction between analytic and synthetic judgments underwrites a powerful argument against the entire metaphysical program of his Leibnizian-Wolffian predecessors’ (p. vii). As he explains, for these predecessors, metaphysics was a science of conceptual truths. And conceptual truths just are those expressed by Kant’s analytic judgements. Kant’s place in the history of metaphysics is revolutionary, on Anderson’s retelling, because Kant shows that metaphysical truths are in fact synthetic, thereby demonstrating ‘the poverty of conceptual truth’.

Anderson’s scholarship is impressive, and I learned much. He establishes his thesis historically, by investigating Kant’s predecessors’ views as well as Kant’s own development of the analytic/synthetic distinction, and philosophically, by engaging the resulting views directly. Moreover, by focusing on syntheticity generally rather than synthetic apriority specifically, Anderson illuminates for us post-Kantians (and indeed post-Quineans) why Kant’s analytic/synthetic distinction was itself so innovative.

In what follows I summarize Anderson’s main moves. Then I offer overall impressions (all positive) and close with complaints (all minor). Anderson’s introduction explains why for the pre-Kantian German rationalists all truths were ultimately conceptual. He then reminds us that Kant himself introduces three criteria for analyticity, based on conceptual containment, contradiction and explication (A6–7/B10–11). Breaking with influential interpretations, Anderson argues that, for Kant, the first is basic. He contrasts this conceptual-containment notion, which he calls ‘logical’, with Kant’s pre-Critical methodological and epistemological notions. The methodological concerns how concepts are formed, while the epistemological concerns how they can be known. Both, Anderson maintains, allow analytic and synthetic judgements to be interconvertible: judgements can be formed or learned, respectively, in each other’s way. Only the logical treats them as non-interconvertible.

Part I defends Kant’s notion of conceptual containment and considers Leibniz’s and Wolff’s handling of it. Anderson maintains that Kant’s notion was not metaphorical. Rather, conceptual containment concerns the (complete or partial) identity of constituent concepts. Anderson then explains that, for Wolff, knowledge involves correctly describing a hierarchy of concepts, arranged inferentially and so analytically. Leibniz differs by maintaining that some analyses would in principle be infinite and so unknowable by human beings; God directly intuits rather than analyses them. Leibniz therefore offers the principle of sufficient reason as an extra-logical principle to acquire metaphysical knowledge, while for Wolff the principle is derivable from the principle of non-contradiction. Hence choosing between Wolff and Leibniz involves a trade-off. Wolff’s system permits explicitness and transparency but has less expressive power. Moreover, because Leibniz takes the principle of sufficient reason to be extra-logical while Wolff does not, Wolff is committed to necessitarianism while Leibniz is not.

Part II traces Kant’s development of the analytic/synthetic distinction. Engaging the secondary literature as well as the pre-Critical Kant, Anderson elaborates on how Kant’s logical notion of conceptual containment is his mature notion, and how only it treats analytic and synthetic as non-interconvertible. He then focuses on Kant’s 1772 letter to Herz, in which Kant asks: ‘What is the ground of the relation of that which we call representation to the object?’ (10: 124). This, Anderson claims, breaks decisively with Wolffian rationalism particularly. For Wolff, the goal of inquiry is for our analytically determined hierarchy of concepts to mirror those of the divine mind, thereby, as I would put it, only coincidentally relating to their objects. Here Kant is asking how representations (including concepts) relate to their objects non-coincidentally. And, on Anderson’s retelling, only when Kant attempts to establish principled limits on metaphysics does he realize that synthetic judgements implicate objects while analytic judgements – the only sort that the Wolffian admits – do not.

Part III focuses on Kant’s claim that mathematics is synthetic. Anderson offers the best explanation that I have seen for why Kant claims this. He embeds this within his historical narrative. If arithmetic, which was taken to be paradigmatically secure knowledge, is synthetic, then it was not so difficult to believe that metaphysics itself is. Anderson offers as evidence of the correctness of this narrative the ‘breathtaking rapidity’ (p. 264, his emphasis) with which the Critical philosophy displaced the Wolffian paradigm generally.

Anderson’s discussion of Kant on mathematics is most original in its focus not on synthetic apriority but on syntheticity simpliciter. As I explain below, he treats synthetic largely as non-analytic. Mathematical truths do not express conceptual claims. Anderson therefore does not focus on intuition. In fact, he rightly observes, Leibniz and Wolff could argue that intuitions are confused concepts. So Kant needs to establish the analytic/synthetic distinction before appealing to intuition per se. Nonetheless Anderson does discuss different interpretations in the secondary literature of the role of intuition. But the heart of his discussion concerns the nature of concepts. According to Kant, concepts are general representations, not objects, nor do they by themselves relate to objects; moreover, each particular concept is strictly identical with only itself. While adding <rational> and <animal> might yield <human>, adding <1> and <1> yields <1>, not <2>. Anderson explains: ‘conceptual means alone, in the sense of the Leibnizian-Wolffian philosophy, cannot distinguish any other equivalence relation from strict identity’ (p. 231, his emphasis).

Part IV presents what Anderson calls the ‘master argument’ of Kant’s Transcendental Dialectic. Reminding us that concepts are not objects nor by themselves object-related, Anderson notes that rational psychology, cosmology and theology each maintain that there is an object – soul, cosmos and God, respectively – to which concepts can by themselves relate. Because only synthetic judgements can relate to objects, however, those rational disciplines are illusory. Anderson then considers Kant’s specific arguments in the Paralogisms, Antinomy and Ideal of Pure Reason. Often it is clear how each specific argument relates to the master argument. Sometimes Anderson must clarify this himself; one might wonder whether his interpretation, that the analytic/synthetic distinction underwrites a ‘master’ argument, overreaches. Nonetheless, as Anderson observes, in the Transcendental Dialectic Kant makes many sometimes independent moves against rationalist metaphysics. Moreover, the Transcendental Aesthetic and Analytic already establish the limits of knowledge. So on any interpretation Kant is doing more in the Dialectic than merely maintaining that there can be no (theoretical) knowledge of the soul, cosmos and God.

In his Epilogue Anderson considers empirical concept formation, and in three appendices discusses Kant’s pre-Critical criticisms of the ontological argument, Reflexionen concerning Kant’s emerging analytic/synthetic distinction and Michael Friedman’s interpretation of intuition.

The Poverty of Conceptual Truth is a significant work. It contributes greatly to our understanding of Kant, Leibnizian and Wolffian philosophy, and the history of metaphysics and philosophy generally. I would recommend it unreservedly. It is as simple as that.

I do however have five quibbles. None subtracts from the importance of Anderson’s book. First, as already mentioned, Anderson often treats Kant’s analytic/synthetic distinction simply as an analytic/non-analytic distinction. Admittedly, if he is right, all that Kant needs to establish the poverty of conceptual truth is that metaphysics is non-analytic. So Anderson himself can prescind from Kant’s arguments in the Transcendental Analytic and Aesthetic concerning the positive nature of syntheticity. Nonetheless Anderson does occasionally offer positive thoughts on syntheticity himself, and when he does so he might have said more. For starters, he routinely says that synthetic judgements ‘relate to their objects’ or are ‘object-directed’. Are the objects noumenal or phenomenal; and, when he says this in the context of the pre-Critical Kant, what do these locutions mean? Moreover, when discussing mathematics he says that synthetic judgements concern ‘intuition’, without explaining how intuition connects to these other notions. Now Anderson did warn us that he would not focus on intuition. But he does consider different interpretations of intuition’s role. More importantly, mathematical truths concern the forms of intuition, space and time, about which Anderson says nothing. Since he does talk about intuition, drawing some connection between it and object-directedness, not to mention intuitive forms, would not have been unwarranted.

Second, and relatedly, synthetic truths are not merely object-directed, based on intuition or spatial and temporal. Their spatial and temporal intuitive forms are essentially human. As Allison emphasizes (Reference Allison2004: 27–35), for Kant, one important difference between analytic and synthetic truths is that the latter are essentially ‘anthropocentric’. The Leibnizian-Wolffian paradigm treats all truths as ‘theocentric’. All human judgements count as knowledge insofar as they mirror those of the divine intellect. Kant not only treats synthetic judgements as anthropocentric, however. He also demotes analytic judgements to trivialities, descendants of Locke’s ‘trifling propositions’, because – à la Anderson – they do not implicate objects. So Kant’s analytic/synthetic distinction is congruent with a trifling/anthropocentric distinction. Now ‘impoverished’ and ‘trifling’ may not markedly differ. Regardless of Anderson’s focus on the poverty of conceptual truth, however, by omitting that Kant contrasts ‘impoverished’ with ‘anthropocentric’, he omits one of Kant’s most important insights.

Third, and also relatedly, it is interesting that a book explaining the development from the Leibnizian-Wolffian paradigm through the pre-Critical to the Critical Kant says nothing about transcendental idealism. Again, though this is not Anderson’s focus, he might nevertheless have mentioned transcendental idealism if only to bracket it. For the analytic/synthetic distinction is implicated in transcendental idealism.

Fourth, in chapter 4.2 and elsewhere, Anderson observes that, even if certain metaphysical claims did turn out to be conceptual-containment truths, Leibniz’s, Wolff’s and Kant’s logical apparatus were restricted to monadic propositions. Any conceptual truths generated via polyadic logic could not be handled by Leibniz or Wolff, on the one hand, and would be synthetic for Kant, on the other. (As an aside, it would help had Anderson offered an example of such putative truths.) While each time he reminds us of this, Anderson does so to attack Leibniz and Wolff for thinking that all truths are conceptual, and to defend Kant for recognizing that some are not, the force of the attack and defence strike me as muted. If for Leibniz and Wolff all truths are conceptual, and as we know there can be claims generated via polyadic logic, then it is unclear that Leibniz and Wolff would count such claims as unintelligible rather than conceptual with all the rest. Moreover, to us post-Fregeans, if anywhere, the dividing line is not between truths generated via monadic logic, on the one hand, and those generated via polyadic logic plus empirical truths, on the other. It is between all truths generated via logic, on the one hand, and empirical truths, on the other. Admittedly that would be a contemporary rather than Kant’s own version of the analytic/synthetic distinction. In any case, the placement of Kant’s dividing line seems more a quirk of the history of logic (neither Kant nor his predecessors were aware of polyadic logic) than a principled philosophical distinction.

And fifth, as Anderson himself notes (p. ix), his book is long. It contains 384 orthographically dense pages. Though Anderson dedicates most of that space to careful and generally engaging exposition, there are occasional unnecessary redundancies. Examples include retelling differences between Leibnizian and Wolffian philosophy, multiple signposting of Kant’s argument that mathematics is synthetic and repeating Kant’s ‘master argument’ in the Dialectic. (There is also the occasional ‘sensu Kant’, which made me want either English for the first word or Latin for the second.)

But really this is an important work. And really I do recommend it unreservedly.