In Intuition in Kant, Daniel Smyth develops an ‘apperceptive, top-down approach to Kantian intuition’ according to which the role of intuition depends crucially on its cognitive function within self-consciousness. This approach is a variant of intellectualism because intuition cannot do anything from the bottom, e.g. it cannot give any object alone but only as providing intellect’s ‘cognitive access to grounds of truth’ (61). So, intuition is not a self-standing capacity that gives objects to the mind, creates immediate contact with objects, and so on, but only insofar as intellectual power is active. However, and this is specific to this variant of intellectualism – the intellectual power is essentially insufficient or incomplete: for synthetic reasoning needs a non-intellectual capacity for the epistemic access to the grounds of truth, and thus intuition plays a significantly distinct but still cognitive role.
From this top-down perspective, the defining characteristics of intuition – givenness, immediacy, and singularity – must accordingly be explained. In particular, Smyth explains from this perspective why the pure intuition of space (and time) must be infinitary – continuous and boundless. Whereas the pre-Kantian tradition considers sensibility as finite, Kant takes it to be infinite. And rather than being such an infinitist that allows only for potential infinities, as the Kant literature usually assumes, Kant holds that (pure) intuition is actually infinite (see 156). This is so, Smyth argues, because the ‘finite complexity of discursive contents’ (169) needs infinitary structure of intuition as its complement.
The book has two parts. In the first (chapters 1 to 5), Smyth interprets the opening chapters of the (first) Critique up to the Metaphysical Exposition of space (and time) along the apperceptive approach. In the second (chapters 6 to 8), he presents his own schema of genera and species of intuition, called Stufenleiter, in which the different characteristics of intuition turn out to be on different levels of abstraction. Both parts ‘can be read independently and in either order’ (11), the author suggests, but I have difficulty to grasp the consistency between the two parts.
On the highest level of abstraction, i.e. valid for all kinds of intuition, namely ‘intuition überhaupt’ (195), givenness of the object is the fundamental criterion, and this allegedly implies the existence of the object for truth-evaluability: ‘The object’s availability to cognition involves its existence’ (201). As it seems, the capability of truth value, ‘objective validity’ in Kant’s terms, requires the existence of the object, and only intuition, the reasoning goes, can secure the existence of the object. By contrast, in the first part Smyth merely claims: ‘Kant consistently treats discursive thought as ontically sterile and, thus, as dependent on intuition for its modal force’ (80).
This modal force explicitly includes the non-existence of geometrical figures (see 68, fn. 35), their mere metaphysical possibility. The contrast between merely possible, mathematical objects and (possibly) actual objects in nature, as Kant clarifies in the introduction of the Metaphysical Foundations of Natural Science (see MF, 4: 467.02–04). It is a merit of Smyth’s work that he takes seriously the contrast case of mathematical constructions (see 56ff.), but then intuitive givenness, precisely ‘in terms of cognitive access to grounds of truth for synthetic judgements’ (57), does not imply existence.
Even regarding empirical cognition, in which givenness of the object is affection-dependent, intuition does not secure the existence of its (empirical) object. It is a further merit of Smyth’s work that he also takes seriously the contrast case of a divine mind with a faculty of spontaneous intuition (see, e.g., 72), in order to get a comprehensive view of Kant’s conception of intuition in all its species. But, again, then it is apparently natural to assume that only spontaneously intuitive givenness secures the existence of its object, whereas receptively intuitive givenness, in the empirical case, (only) opens the modal contrast between existence and non-existence. It establishes actuality as contingency, epistemically in the sense that a human mind is fallible, and ontologically in the sense that a true existence claim could have been false. Thus, in empirical cognition, the ‘cognitive access to grounds of truth’ has been provided by intuition even in such a case of non-veridical cognition in which its object does not exist.
Considering the first part independently of the second, chapter 5 is the core of the book. Chapters 1 to 4 establish the top-down approach in analogy to Kant’s treatment of pure general logic as Selbsterkenntnis of reason and with the essential contrast between analyticity and synthetic reasoning. The grounds of truth for analytic judgements are internal, intellectual, while the grounds of truth for synthetic judgements must be external, intuitive. Chapter 5, then, is devoted to the central claim, the sub-title of the book: ‘ The Boundlessness of Sense ’. The infinitary structure of intuition – boundless both in division and in extent – is to be explained, along the guiding line, by the incompleteness of discursive thought.
Although I would happily agree with the view that Kantian intuition is actually infinite, the argumentation presented in favour of this claim is largely unconvincing. Firstly, it is not sufficient to defend this kind of infinitism by interpreting only the Metaphysical Expositions, because the opposing view has its relevant support from the (alleged) solution of the cosmological antinomies. As the standard view holds, Kant rejects both finitism – e.g. that the world has a beginning in time – as well as actual infinitism – e.g. that the world is spatially boundless – in favour of potential infinitism, i.e. the view that the successive synthesis of scientific cognition has no limit. Now, the thesis that pure intuition is actually infinite should not imply that the (empirical) world includes an all-encompassing space. For this is probably in conflict with current empirical cosmology, and Kant repeatedly rejects the idea that appearances could be surrounded by empty space. So, the (not addressed) question arises of how the thesis that sensation-content is transcendentally conditioned by all-encompassing pure intuition fits with the (not to be questioned) claim that appearances are not empirically conditioned by empty space.
Secondly, it is inadequate to agree (literally) with Kant that ‘discursive representations are intrinsically finite in complexity’ because ‘[o]ur concepts can only be as fine-grained as the distinctions we can make’ (167). For it is unjustified to claim that there cannot be infinitely many distinguishing conceptual marks, and that the distinctions one can make cannot be infinitely fine-grained. In mathematics, one has the conceptual capacity to write down a formula that describes an infinitely complex geometrical figure, and in physics, the electromagnetic field can be described conceptually by an infinitely complex wave function. To literally agree with Kant is further in contradiction with an essential aspect of Kant’s transcendental idealism, namely, with his rejection of Leibniz’s Principle of the Identity of Indiscernibles.
Leibniz holds that an empirical object is qualitatively exclusive, i.e. objects are unique individuals in the modal sense that there could not have been a second such thing. Correspondingly, an individual concept uniquely refers to such an object, i.e. objects are given not by intuition but by the distinguishing concepts. Kant rejects all of this: an appearance is not qualitatively exclusive, i.e. empirical objects are not unique but merely single individuals, they are not einzig(artig) but einzeln. There could have been a second such drop of water, for instance. Accordingly, concepts are general, i.e. by distinguishing alone one cannot refer to such an object, instead, objects must be given by intuition, or general concepts must be applied to intuition, otherwise they would be ‘ontically sterile’ (80).
The ‘modal force’ (80) intuition provides is hence essentially the force that characterises appearances as anti-Leibniz individuals, and this has nothing to do with a quantitative difference. By contrast, Smyth’s suggestion seems to be that it has to do with the difference between finite and infinite complexity. However, a general concept can be maximally comprehensive, even infinitely comprehensive, but never complete in Leibniz’s sense. Its incompleteness is purely modal, not quantitative. An electromagnetic field can be described by a conceptually infinitely complex wave function, but, according to Kant, it is a merely single individual (Einzelgegenstand): there could have been a second such wave or, perhaps, an incongruent counterpart wave.
Smyth agrees, but should disagree, with Hintikka’s claim that ‘Kant’s notion of intuition is not very far from what we would call a singular term’ (quoted on 239), because what they call a singular term is probably a (descriptive or directly referential) proper name. Such proper names, however, are not far from Leibniz’s individual concepts, because with them objects are given intellectually. The singular term that expresses a Kantian intuition must, rather, contain irreducible demonstratives such as ‘this, here and now’ that cannot be substituted without loss of meaning by labels, coordinates, or dates. Only then, reference requires a non-intellectual capacity.
Finally, Smyth overlooks the crucial difference between uniqueness and mere singleness by claiming that ‘each part of space is a singular individual just as much as the whole of space is’ (171). This is wrong: parts of space constitute singular individuals in the sense that there could have been more than one such part, and indiscernibles located at parts, whereas the whole of space is a singular individual in the uniqueness sense: there could not have been another one. (Therefore, it could only be pure intuition and not an empty space surrounding appearances.) The interpretation of A25/B39: ‘one can represent only one unitary [einigen] space’ (quoted on 133) as a mere unity of space is misleading, because this ‘one and the same solitary space’ is necessarily one and the same and not contingently solitary. In the parallel Metaphysical Exposition of time (not quoted), Kant says, unambiguously in the original German, that time is ‘ein […] einzige[r] Gegenstand’ (A32/B47), i.e. ‘einzig’ instead of ‘einig’, so unique – and not merely single, as by contrast the parts of time are.
These criticisms notwithstanding, Smyth offers an acute, profound, and comprehensive study of Kant’s fundamental notion of intuition that is worth being discussed in the Kant literature.
