KIYOSHI CHIBA | Kants Ontologie der raumzeitlichen Wirklichkeit | Walter de Gruyter 2012
By Chris Onof
9. Potential and Actual Infinity
Chiba returns to the antinomy of pure reason once he has discussed the details of his particular brand of anti-realism, with a very interesting discussion of the difference between the regress in indefinitum, and the regress in infinitum. Chiba takes it that the regresses of the first type (illustrated by the second antinomy) are characterised by (where the description in words of the characterisation is followed by its formalisation in first-order logic):
(Q): Every member [of the series] has successor members [∀x∃y (y is successor of x)] (p.305, my trans.)
where the successor refers to the next term in the ascending regress that constitutes the series of conditions for the given conditioned. The regresses of the other antinomies are such that one can only say that:
(R): There is no member [of the series] which has no successor members [∀x¬¬∃y (y is successor of x)] (ibid.).
If this is indeed the contrast between the two types of regresses, then this provides a powerful argument against the adoption of a bivalent logic to interpret Kant. Since Kant clearly distinguishes between the two types of regress, and since in bivalent logic, (Q) and (R) have the same truth-value because ¬¬p=p , this would invalidate the assumption that Kant’s logic is bivalent. Unlike realism in terms of the CI/¬CI distinction, anti-realism involves the discarding of bivalence: there are statements that can be verified, others whose negation can be verified, and others for which neither the statement nor its negation are verifiable. So if (Q) and (R) are indeed the valid interpretations of Kant’s views on these regresses, then realism about the existence of spatio-temporal objects has to be abandoned in favour of CI/¬CI anti-realism.
But one can certainly question Chiba’s interpretation here: while he is right to interpret the second antinomy regresses as involving the truth of proposition (Q), this would seem also to apply to the other antinomies. Indeed, when, in regard to the first antinomy’s regress, Kant says that “I never know anything more than that from any given member of the series of conditions I must always proceed empirically to a higher (more remote) member” (A519/B547), he is implying that it is indeed possible to proceed to such a member, which is just what (Q) claims. But (Q) is not sufficient to characterise the regresses. Indeed the last quote specifies that “I never know anything more”, which one can contrast with the claim, for the second antinomy’s regresses, that for the “regress from the conditioned to its condition […] the conditions are all given along with it [i.e. the conditioned]” (A523-4/B551-2).
The key difference is expressed by Kant at A519/B547 when he says that for the other antinomies, the regress cannot be said to go to infinity because “this would anticipate the members to which the regress has not yet attained”. On the contrary, in the case of the regress of the second antinomy, ‘the conditions are all given along with it [the conditioned]’ insofar as the latter contains them as a whole (A524/B552). Since Kant also insists that it is not possible to say of this whole that ‘it consists of infinitely many parts’ (ibid.), the relevant sense in which the conditions are given, is through the rule which here enables us to anticipate all the members of the series, but not in the case of the other antinomies. So the difference between the two regresses should rather be expressed as follows (where it is noteworthy that the formalisation now involves second-order logic):
(Q′): ‘Every member [of the series] has successor members, and there is a rule identifying the successor for any condition in the series’, i.e.
⟶ (Sy and y is successor of x)) and ∃R (R is a rule and ∀x∀y ([Sx and Sy and y is successor of x]
⟶ y = R(x)))]
where S is the predicate ‘is a spatio-temporal object or state of affairds’, describes the second antinomy, while:
(R′): ‘Every member [of the series] has successor members, and there is no rule identifying the successor for any condition in the series’, i.e.
⟶ (Sy and y is successor of x)) and ¬∃R (R is a rule and ∀x∀y ([Sx and Sy and y is successor of x]
⟶ y = R(x)))]
describes the other antinomies.
While this interpretation no longer suggests that Kant is abandoning bivalent logic here, and thereby does away with any support from this passage in the Antinomy for Chiba’s CI/¬CI antirealist stance as regards the existence of spatio-temporal objects, this also enables us to understand why the existence of objects cannot be said to be constituted by our cognition as Chiba’s CI/¬CI antirealist interpretation would have it. Since the analogies are dynamical principles of experience, they make claims about the existence of objects fulfilling certain conditions (substrate of change, cause of an event, etc.) but do not provide rules to identify these objects. It is not therefore possible to say, for such objects, that the possibility of cognising them is relevant to their existence. It is therefore the particular status of the dynamical principles that pertain to the existence of objects, which explains this claim: they are constitutive of our experience, but regulative for our intuition as Kant puts it later in CPR (A664/B692), which means that they do not provide rules for the determination of specific conditions (causes, substrates, etc.), but only rules guiding the search for these conditions. The error of the CI/¬CI anti-realist take upon existence is to overlook this regulative status vis-à-vis our intuition. We note that this is not an objection that would affect an anti-realist position defined in terms of the CT/¬CT distinction.
Since verification (presumably) involves intuition of the object or of some other objects that are lawfully related to it (e.g. in the case of unobservable particles), i.e. for which there is a rule explaining how they are related, this analysis of Chiba’s discussion of the notion of potential infinity has now shed further light upon what is wrong about the CI/¬CI anti-realist interpretation (but not its CT/¬CT variant): it views what is regulative for intuition as constitutive for it.
10. The Fourth Paralogism
But Chiba has another important piece of textual evidence to support an anti-realist interpretation of TI against realism, namely the Fourth Paralogism in the A edition (p.158). Although for Chiba the realist can provide a plausible interpretation of much of the text before A372, he points out a key passage in support of his interpretation to be Kant’s claim about “the objects we understand by the representations of matter and corporeal things”, not only that “they are mere modes of representation” (which is the claim mentioned in section 4 that appears in similar forms in other places in CPR), but more strikingly, that “their reality, just as much as that of my own thoughts, rests on immediate consciousness” (A372). Chiba is right to single out this passage as it certainly presents a challenge for the realist, and also for an anti-realism based upon the CT/¬CT dichotomy about spatio-temporal existence. For here, it would appear that there is a denial of any claim that the existence of objects is independent of actual acts of cognition (referred to here through the terms of ‘immediate consciousness’). So, much as the above discussion has veered towards the greater plausibility of understanding TI in terms of the CT/¬CT dichotomy for the existence of spatio-temporal objects, there would seem to be evidence for Chiba’s claim that an CI/¬CI anti-realism is the appropriate interpretation here.
I think that, while this certainly points to the difficulty of finding an interpretation that fits the whole of Kant’s text, we must also stress the point that Chiba underplays by taking Kant’s statement that his position has not altered between the two editions very literally (p.159). Namely, this Fourth Paralogism is in the A-version only, and the whole text of the Paralogism is revised in the B-edition.
One reason why this difference between the two editions should not be brushed aside too quickly, is that there are grounds for thinking that Kant will have been dissatisfied with the way he formulated some claims in the A-edition, in particular that which we have just been examining. For the claim that the “reality” of appearances, “just as much as that of my own thoughts, rests on immediate consciousness” (A372), could be read in a straightforward subjective idealist fashion, and indeed was read in this way by the likes of Garve and Eberhard. Now this claim appears in the Fourth Paralogism where Kant precisely distinguishes TI from dogmatic or sceptical idealism, which respectively deny and doubt the existence of matter, i.e. of objects in outer sense that are distinct from our representations. Therefore it cannot be the case that a subjective realist reading of the above quote is the right one. As noted earlier, this also applies to how one is to read the earlier part of the quote which refers to appearances as “mere modes of representation, which are always found only in us” (ibid.). But the worry W we flagged above (Part I; Section 4) resurfaces here. Since Chiba views such passages as providing support for his anti-realist stance, an account is needed of how such statements support it in a way which does not also support the kind of subjective idealism about spatio-temporal objects that Garve and Eberhard charged Kant with.
Chiba does note (p.171) that such statements are problematic, and suggests not taking Kant’s words literally, particularly in view of the fact that Kant also refers to the objects of my representations in the same passage (A370ff.), so that, for instance, there is room for an understanding of the object as an intentional one.
The consequence of this point is that the passage is no longer worrisome for a CT/¬CT anti-realist. Indeed if, as Chiba, rightly I think, claims, the point Kant is making about the existence of external objects is properly expressed when he says that they are “something only through these representations, but are nothing separated from them” (A370), this can be read as expressing either an ¬CI dependence or a ¬CT relation. So Chiba’s argument against the realist is basically successful, but not to the point that it allows for a distinction between these two forms of anti-realism.
11. Anti-Realism about Form and Existence
The issues examined above all pertain to the existence of objects. Before drawing any conclusions, it is important to say something about the determinations of these objects, as they are to be understood on Chiba’s account. Here, we must note that Chiba shows that his anti-realism is compatible with an existence claim about things in themselves, and that he provides an account of how they affect us (Chapter 8). This is a very important part of the book upon which I cannot comment here, but which I commend to the reader for its clarity and, I think, the correctness of many of the conclusions the author reaches. Noteworthy is the discussion of how the determination of objects is (in different senses) constrained both by a priori factors (our transcendental apparatus), and the nature of that which affects us (p.386). I think that these claims, as combined with an CI/¬CI anti-realist understanding of the nature of the determinations of the object (as distinct from the issue of the existence of the object), provide a plausible account of Kant’s basic epistemological claims, although, as indicated above (Part I; Section 7), the nature of the verification would need to be specified.
As we have just seen, this anti-realism means that the truth of statements about the properties of spatio-temporal objects is constituted by the possibility of some cognition/verification of these statements in the progress of our knowledge. This seems right as an interpretation of Kant’s understanding of all the determinations of spatio-temporal objects. For the possibility of such an event of cognition/verification of particular determinations of an object just is the possibility of knowledge as defined by the mathematical principles of the understanding which are constitutive for the determination of the intuitions that (I assume, although this has not been discussed – see Section 7) are at the core of such events of cognition/verification. That is, in terms of the determination of properties of objects, Chiba’s CI/¬CI antirealism does account for the transcendental conditions that define their objectivity.
But, as we saw earlier (Sections 6 and 8), when dealing with existence, defining what is possible in terms of what might be actual does not match up with defining it in terms of the constraints of transcendental logic. This is what was shown in the case of appearances (e.g. those defined by series in the antinomies) which are intuited by a very large number of representations (Section 6). That existence may thus have to be dealt with differently, is given further support when Kant explains in presenting the logical function in judgements, that “the modality of judgement […] contributes nothing to the content of judgement” (A74/B99-100). Existence is not a further determination of a spatio-temporal object in the sense that it would add to the object’s total determinations/predicates (“A hundred actual Thalers do not contain the least bit more than a hundred possible ones” (A599/B627, my trans.). To view judgements about the existence of an object as any other judgement about the determinations of an object would amount to overlooking the role of the categories of modality: to bring an object under the category of existence is to make the judgement that it exists, and does not amount to determining its existence in the way that one determines a particular property of an object (see Schulting 2011). So, while statements about the knowledge of the properties of spatial-temporal objects would seem to be correctly interpreted as anti-realist claims on Chiba’s understanding of anti-realism in terms of the CI/¬CI dichotomy, this is not the case for statements about the existence of these objects, as this paper has shown.
That there should thus be a distinction between how we deal with the determinations of spatial-temporal objects and with their existence proper is confirmed by Kant’s distinction between the way the determinations of an object are brought about, and the existence of the object comes about. Kant says (A92/B125) that “representation in itself […] does not produce its object as far as its existence is concerned”, where he is considering the two ways in which “synthetic representation and its objects can come together” (A92/B124).
Chiba (p.64) notes that this passage (and similar ones) constitutes a problem (he describes it as ‘objection F’) for his interpretation – and claims that the aim of the statement is the differentiation between the theoretical and the practical relation to an object. This is not very convincing given the context, and the existence of other similar statements Kant makes in a context which is clearly not related to practical philosophy (e.g. in the letter to Herz, AA10:131). Focussing upon this statement, we find that Kant describes the relations between object and representation as involving the one making the other possible, so it seems that ‘produce’ in the above quote should be understood as ‘making possible’, which is exactly ‘being constitutive of’, rather than any practical notion of production. But this would mean that in this statement Kant is making it clear that the kind of cognition-dependence definitive of Chiba’s CI/¬CI anti-realism does not apply to the existence of the objects (but only to its determinations).
12. What Kind of Existence?
Rather than supporting a form of CT/¬CT anti-realism for spatio-temporal existence, one could argue that the problems encountered by Chiba’s CI/¬CI anti-realism suggest that we should be realists about spatio-temporal objects (even though there are problems with both the realist dual-aspect and two-world interpretations). And indeed, as Chiba notes (p.64) Allais exploits the passage quoted in the last section as evidence that the existence of spatio-temporal objects is independent of us, i.e. that they are real. But is this realism the same as that which applies to things-in-themselves?
The metaphysical dual-aspect theory (Allais, Rosefeldt) has it that these objects just are the same things as when considered as things-in-themselves, so that the existence in question has the same ontological status whether these things are viewed as being in themselves or being spatio-temporal objects. We saw earlier (Section 2) that this encounters a powerful objection (p.52–4) insofar as this leads to noumenal individuation conflicting with the role of the transcendental unity of apperception. We can see now why the methodological dual-aspect option (Allison, Bird, Prauss) is attractive as it avoids the whole issue of ontological claims. But Chiba brought out its incoherence (Section 3) in not making any ontological commitment (p.78–9).
Here, it is worth recalling that argument A (Section 5) failed because of a covert equivocation over the distinct properties of cognition independence (CI) and cognition transcendence (CT). And we noted earlier (Section 5), a two-world interpretation of TI in which only things in themselves have CT existence would indeed be a possible interpretative option. Given the problems encountered by the dual-aspect readings, both metaphysical and methodological, it would seem that such an option is attractive. And it is not only by elimination that this option becomes attractive. Rather, its key feature is the non-CT nature of the existence of spatio-temporal objects: such a property seems to be what is called for by the definition of the category of actuality and its related form of judgement. Namely, existence is a feature of the relation of the object to the understanding (ours in this case). So it should, by definition, not be cognition transcendent.
We note however that the only motivation for the ‘two-worldness’ of this interpretation lies in the rejection of the ‘dual-aspectness’ of the other interpretations Chiba correctly rejects. However, as Chiba points out (p.85–6), there are other options, among which he mentions Robinson’s (1994) and the related one which I sketched in Onof (2011), which we might loosely describe as dual perspective theories, so that the rejection of ‘dual-aspect’ does not obviously entail the endorsement of ‘two-world’. Indeed, although there is no space to argue for this point here, argument A reformulated in a CT/¬CT context, together with an existence claim for things in themselves, suggest that the two-world interpretation is not tenable. Additionally, if the notions of the existence of things in themselves and the existence of spatio-temporal objects are not unrelated, talking of two distinct worlds is problematic because it is not clear ‘where’ (in which world?) the relation between these worlds would find its place. That is, even taking into account Kant’s ignorance thesis, there must still be a fact of the matter as to the nature of the relation between things in themselves and appearances, and such a relation cannot be viewed as belonging to either world. Postulating that it lies between these two worlds, in effect, leads to defining a third world of which one can then ask about its relations to the other two, thus leading to an infinite regress.
Leaving these considerations aside, and returning to the topic of TI as a form of anti-realism, I conclude that as far as the existence of spatio-temporal objects is concerned, it would be more appropriate to consider defining anti-realism in terms of the denial of CT for such an interpretation of TI to be plausible. This is because:
- of CI/¬CI anti-realism’s ignoring the double constitutive/regulative distinction defined in CPR (Section 9);
- as we noted above (Section 5) argument A would be successful if realism were to be defined in terms of CT;
- objection F (Section 11) disappears on this understanding of anti-realism;
- this resolves the problems encountered in the interpretation of the antinomies (Sections 6 and 8).
There are also non-Kantian grounds for viewing this to constitute the proper interpretation of Dummett’s anti-realism, as Chiba himself notes when he discusses Crispin Wright’s understanding of Dummett’s anti-realism (p.21). It is interesting to read in this footnote that, exegetical questions relating to Dummett aside, Chiba seems to decide to opt for a notion of realism defined in terms of CI chiefly because it avoids having Allais and Rosefeldt’s dual-aspect interpretations of TI classified as forms of anti-realism. That may be a good motivation, but if we are to follow the implication of Kant’s point discussed above (A92/B125), namely that the question of the existence of spatio-temporal objects and the question of the determinations of objects should be dealt with separately, then in terms of the question of existence, Allais and Rosefeldt’s interpretations would remain firmly in the realist camp. So the obstacle for endorsing Crispin Wright’s understanding of Dummettian anti-realism would disappear. And I would say that the overall claim of Chiba’s book, namely that Kant’s TI should be understood as defining an anti-realist notion of the existence of spatio-temporal objects, could be said to have been provided with strong exegetical evidence on this somewhat different understanding of anti-realism.
We note that this form of antirealism is much weaker than Chiba’s insofar as it clearly distinguishes itself from any phenomenalism. On the dual-perspective version of this view the construction of objectivity starts with something which is assumed to exist independently of our cognition, although, insofar as we have any intuition of it, it is not cognition transcendent. There are no grounds for abandoning bivalence about the existence of spatio-temporal objects on such a view, since this existence is a matter that is independent of our cognition (and ¬CT). I would argue that Kant’s notion of truth is, moreover, distinct from one based upon verifiability, in that it involves, rather than the possibility of some verification, that there be a connection with some actual perception according to the laws of empirical connection of appearances. There are therefore no grounds for abandoning bivalence about the determinations of spatio-temporal objects on such a view because for any empirical judgement, it will be the case that either it is or is not thus connected with some perception.
A final thought about these two forms of anti-realism: some of the resistance to an anti-realist interpretation of TI might be connected with its focus upon the Transcendental Analytic and the negative claims of the Transcendental Dialectic. Much as Chiba’s CI/¬CI picture of the spatio-temporal world is accompanied by claims about the existence of, and affection by, things in themselves, this affection triggers the determination of objects very much as in a virtual world insofar as the whole of spatio-temporal objectivity, in its very existence, is constructed by my cognition on that account. In particular, it is thus not clear where the notion of a convergence of empirical knowledge towards ever greater unity under the guidance of regulative principles would find its place on this account. On the other hand, with a CT/¬CT anti-realism about the existence of spatio-temporal objects where these objects exist in a single world, the spatio-temporal domain of objectivity is properly anchored in reality. It thereby makes sense to ask what guides the further determination of the objects that the subject constitutes in this world. This is where the regulative ideas of reason have a role to play by representing how reason frames for itself an order that stands over and against the unknowability of things in themselves.
13. Brief Concluding Note
The emphasis I have put upon my disagreement with Chiba about the sense in which one could be anti-realist about the existence of spatio-temporal objects has left out the many issues upon which I agree with him, and I therefore want to conclude with a reminder of what I take to be some important contributions that Chiba makes to the discussion about the meaning of TI. Chiba has, first and foremost, made the claim that TI is in some sense anti-realist about spatio-temporal objects, a very plausible one, and hopefully thereby contributed to overturn a widespread concern that anti-realist interpretations are to be avoided at all costs if one is to make Kant’s TI palatable to a wider contemporary audience. Second, and relatedly, he has shown through distinct arguments that both methodological and metaphysical dual-aspect theories of the relation between appearances and things in themselves, as well as the realist two-world interpretation, suffer from severe problems. This result is all the more important as these theories are probably the dominant options in current Kant scholarship. Third, he has provided a detailed defence of the claim that things in themselves exist for Kant, and that one can make sense of the relation of affection of the latter to appearances, both issues that are at the heart of the cogency of TI. I therefore think that his is a very important book for contemporary Kant scholarship, and I hope that a future translation into English will make it available to a wider audience.
Allais, L. (2004) ‘Kant’s One World. Interpreting Transcendental Idealism’, British Journal for the History of Philosophy 12: 655-84.
Allison, H. (1983) Kant’s Transcendental Idealism: An interpretation and Defense, New Haven: Yale University Press.
Bird, G. (2006) The Revolutionary Kant: A Commentary on the Critique of Pure Reason, La Salle, Illinois: Open Court.
Guyer, P. (1987) Kant and the Claims of Knowledge, Cambridge: Cambridge University Press.
Onof, C. (2011) ‘Thinking The In-Itself and Its Relation to Appearances’, in D. Schulting & J. Verburgt (eds) Kant’s Idealism. New Interpretations of a Controversial Doctrine, Dordrecht: Springer, pp. 211–36.
Prauss, G. (1974) Kant und das Problem der Dinge an sich, Bonn: Bouvier Verlag.
Robinson, H. (1996) ‘Kantian Appearances and Intentional Objects’, Kant-Studien 87: 448–54.
Rosefeldt, T. (2007) ‘Dinge an sich und sekundäre Qualitäten’, in J. Stolzenberg (ed.) Kant in der Gegenwart, Berlin: de Gruyter, pp.167–209.
Schulting, D. (2011) ‘Limitation and Idealism: Kant’s “Long” Argument from the Categories’, in D. Schulting & J. Verburgt (eds) Kant’s Idealism. New Interpretations of a Controversial Doctrine, Dordrecht: Springer, pp. 159–94.
 Note that we are only discussing the existence of spatio-temporal objects here. As far as their determinations are concerned, a case could be made to view transcendental logic as non bivalent. The issue of bivalence is briefly discussed further below.
 Chiba recognises that Kant does not abandon bivalence but sees a contradiction therein. To avoid this, the proposed two-perspective view has the advantage that it provides an anchoring in a cognition independent reality that defines constraints upon the truth ensuring that such bivalence holds.
Acknowledgements: I am very grateful to thoughtful comments by Kiyoshi Chiba and Dennis Schulting, which have helped to make the text clearer.
© 2013, Christian J. Onof
Christian Onof is Reader in Systems at the Faculty of Engineering, Imperial College, London, and Honorary Fellow in Philosophy at Birkbeck College, University of London. He holds Ph.D.s both in Engineering Mathematics (Imperial) and in Philosophy (UCL). He has published many articles on Kant’s moral and theoretical philosophy, Sartre, existentialism in general and philosophy of mind in journals such as Kant-Studien, The Kant Year Book, Philosophy and Phenomenological Research and Journal of Mind and Behavior. Currently, he collaborates with Dennis Schulting on the research project ‘Kant, Space and Nonconceptualism’, the first fruits of which will shortly be published in Kantian Review. He is also the co-founder of the journal Episteme.