Things in Themselves and the Inner/Outer Dichotomy in Kant’s Amphiboly of the Concepts of Reflection

Abstract Langton’s (1998) and Allais’ (2015) metaphysical interpretations of Kant’s idealism have given special relevance to Kant’s analysis of the inner/outer dichotomy in the Amphiboly of the Concepts of Reflection, for they agree that this dichotomy is key to correctly grasping Kant’s distinction between appearances and things in themselves. In this article I argue that Langton’s and Allais’ accounts of Kant’s analysis of the inner/outer dichotomy have major limitations, and therefore that the text should not be read in the way they propose. In order to show these limitations, I examine the overall structure of Kant’s argument in the Amphiboly. Furthermore, I aim to establish the contribution brought by the Amphiboly to the issue of noumenal knowledge and the nature of things in themselves. Langton’s and Allais’ accounts of the relation between appearances and things in themselves as the inner nature of things not only prove to be unwarranted, but indeed to some extent opposite to what I claim to be Kant’s actual stance on things in themselves in the Amphiboly.


Langton's and Allais' interpretations: things in themselves as intrinsic natures
In her well-known book Kantian Humility (1998), Rae Langton claims that the main thesis of Kant's theoretical philosophy, as far as concerns the relationship between appearances and things in themselves, is what she calls 'Humility'. Langton explains the relationship between appearances and things in themselves through the distinction between intrinsic and relational properties of things (more specifically: of substances). This interpretation can be listed among those known in contemporary Kant scholarship as 'metaphysical dual-aspect' readings. The humility at issue here thus means the constitutive impossibility for the subject to cognize the intrinsic nature of substances. Instead, as spatiotemporal appearances, things have nothing but relational properties that, on the other hand, we are able to cognize. The main passages quoted by Langton as textual evidence come from the section of the Critique of Pure Reason titled 'On the amphiboly of the concepts of reflection'. According to Langton, in this section we can find compelling evidence that for Kant things in themselves are substances that have intrinsic properties, and that we can cognize only the relational properties of such substances, i.e. their appearance.
Langton's book has been the target of serious criticism (e.g. Bird 2000Bird , 2006Quarfood 2004;Onof 2011). One of the reasons for such criticism is that Langton explicitly understates the role of the ideality of space and time in Kant's arguments. In doing so, she also assigns a pivotal role in Kant's system to a section that is usually taken to be rather secondary in the Critiqueespecially if we consider that in the Amphiboly Kant's main concern is to refute a few (alleged) theses of Leibniz's philosophy. 1 More importantly, though, Langton has been accused of having decontextualizedand thereby greatly misunderstoodthe passages she used as evidence for her thesis.
Lucy Allais' approach is more cautious and more attentive to the context of claims that can be found in the Amphiboly. In her book Manifest Reality (2015), she presents her own well-argued metaphysical dual-aspect readingwhich also represents a kind of 'one-world' view. 2 According to her account, the object is one, despite having two metaphysically different sets of properties: 'I argue that [Kant] thinks that things have intrinsic, non-relational, categorical natures which ground their relational appearances' (Allais 2015: 231). The expression 'things in themselves' therefore seems to coincide with 'the intrinsic nature of things' (or 'things in regard to their intrinsic nature'), which would in turn be the 'inner' that Kant discusses in the Amphiboly. In short, Allais claims that Kant and Leibniz agree insofar as they are 'committed to something that grounds relational properties' and to the fact that we have knowledge 'only of spatial (and therefore relational) properties' (Allais 2015: 235), while, on the other hand, the two philosophers obviously disagree on the existence of monads. It is extremely relevant here that, in Allais' view, the fact that relational properties imply an intrinsic nature grounding them is an analytical truth whose negation results in a contradiction: we are thus compelled to acknowledge the existence of an intrinsic nature of things as they are in themselves. However, Allais readily acknowledges that we can never find intrinsic properties 3 in phenomenal reality (the only substance in experience being substantia phaenomenon), which seems to contradict the aforementioned analytical truth. Allais relies on her metaphysical dual-aspect reading to resolve this tension. She argues that Kant's solution lies in his transcendental idealism: as appearances things have nothing but relational properties, while in themselves things have an intrinsic nature that grounds such properties. Despite the impossibility of our cognizing such an intrinsic nature, according to Allais we can and indeed must establish its reality. That leads her to claim that Kant's distinction in the Amphiboly between what is thought by pure understanding and what is an object of sensible intuition and cognition somehow maps onto the distinction between things in themselves and appearances.
Langton's and Allais' works have of course already been criticized to some extent. 4 Nevertheless, as far as concerns the conclusions the two scholars draw from their analysis of the inner and the outer in the Amphiboly, I think that a more textually grounded critique is needed, one that is based upon a careful examination of the Amphiboly's text. In the following, I want to argue that in the Amphiboly Kant holds that we cannot even state with certainty that the objects of possible experience have an intrinsic nature. In fact, such a statement would have no positive ontological meaning: it cannot inform us about a putative reality in itself nor about the nature of appearances. 5 2. Kant's overall argumentative strategy in the Amphiboly and its application to the inner/outer dichotomy I will now illustrate the overall argument of the Amphiboly and discuss whether Allais' reading of the inner/outer dichotomy is consistent with the text. According to Kant, transcendental reflection is the capacity to compare different representations while taking into account the cognitive faculty in which each representation is situated. He lists four pairs of concepts of reflection, which express the relation 'in which the concepts in a state of mind can belong to each other'. In this respect, the relation between two representations can be of 'identity and difference, of agreement and opposition, of the inner and the outer, and finally of the determinable and the determination (matter and form)' (A261/B317). Overall, Kant aims at refuting Leibniz by showing how such relations lack a univocal meaning applicable to 'objects in general'. Rather, it is essential to distinguish whether the representations involved are mere concepts of the understanding or appearances. In short, Kant accuses Leibniz of having considered these four pairs of relations, i.e. the concepts of reflection, only with respect to the representations of pure understanding taken as positive noumena. Accordingly, argues Kant, Leibniz drew principles which he mistakenly took as valid for all possible objects in general. Kant then criticizes him by pointing to the spatiality of outer appearances, a feature that forces us to rethink the meaning of the concepts of reflection and nullifies Leibniz's allegedly analytical principles. Therefore, the conclusion is that, in order to compare representations, it is essential to take into account the cognitive faculty to which they belong. This is what Kant does in the Amphiboly. On the other hand, when discussing each pair of concepts of reflection, I will also highlight what I believe Kant does not do. I would like to make explicit in advance the kind of strategy that I think should not be attributed to Kant. In the Amphiboly, Kant is not concerned with establishing analytical principles that would be allegedly valid for 'things in general', as Leibniz maintains to have done. Much less does he attempt to validate similar principles by means of the application of one of each pair of concepts of reflection to objects taken as appearances, and the other concept of each pair to the same objects, only this time taken as things in themselves. Yet this is precisely the strategy that Allais claims Kant uses with regard to the concepts of inner and outer. My aim is to show that Langton's and Allais' reading is not tenable, under the assumption that it is reasonable to expect an overall coherence in the strategy executed by Kant in the Amphiboly.
I will start by discussing the concepts of identity and difference. In line with his preliminary statements, Kant argues that the criteria for establishing diversity and identity between two representations change depending on whether the latter are appearances or objects of pure understanding. According to Leibniz, every truth about an object is analytically included in its own concept, and thus can be reached through a complete conceptual analysis. 6 We might not be able to know every predicate of an object by analysing its concept, yet God can. Consequently, if two objects have exactly the same conceptualizable properties, then they actually are the same object, i.e. they are identical. More precisely, as Cord Friebe (forthcoming) makes clear, every concept for Leibniz, when completely determined through conceptual analysis, analytically refers to an individual. Therefore two individuals must necessarily be the referents of two such distinguished concepts. Conceptual analysis is Leibniz's criterion for indiscernibility, for there cannot be two referents for the same (thoroughly determined) concept. Kant argues instead that two objects (which for him are phenomena) can have the same properties, as far as concerns their concepts, and still be in two different locations in space, which means that they indeed are two different objects. More specifically, concepts are for Kant always general, 7 and they are able to refer to an object only through synthesis. However, the referent is not an individual, but rather a singular entity. For example, the concept of 'table', like any other concept, is general and therefore it serves as the genus for the species under it. It makes no sense for Kant to speak of different tables in thoughtunless of course one means different species of it. In the essay 'What Real Progress has Metaphysics Made in Germany since the Time of Leibniz and Wolff?', Kant indeed writes that it 'is a contradiction to think, by mere concepts of the understanding, of two things as external to one another : : : ; it is always merely one and the same thing thought twice over (numerically one)' (20: 280). Space, however, enables us to count numerically distinct tables. Every empirical table, as a referent of the concept 'table', is not individual, but rather merely singular. For I can unproblematically say that I see two or more tables in the room. That said, what matters for our purposes here is that Kant's claim entails his broader criticism of Leibniz, namely, that the latter did not realize the specificity of sensibility, its irreducibility to mere logical concepts and the indispensable role it plays in the formation of cognitions. This criticism of Leibniz's epistemology extends to his metaphysics as well. Leibniz was unable to understand the ontological extension of his own principles: objects of pure thought are not all objects in general, therefore the principle of the identity of indiscernibles does not hold true for all possible objects. Nevertheless, there is no reason to believe that for Kant this principle would be valid if applied to things in themselves. 8 Rather, Kant accuses Leibniz of taking objects of pure thought as positively determinable noumena, claiming thereby to determine all objects in general through mere thought. In the last section of this article, I will discuss the notion of noumenon that emerges from the Amphiboly. What is important now is that Kant clearly does not ascribe one element in the identity/ difference pair to appearances and the other to things in themselves: it is unclear what this ascription would even amount to.
The same argumentative structure returns when Kant examines the 'agreement/ opposition' dichotomy. Kant apparently equates objects of the pure understanding and things in themselves: 'If reality is represented only through the pure understanding (realitas noumenon), then no opposition between realities can be thought' (A264/B320). The reader might think that Kant is stating that objects of pure understanding are actually things in themselves, and that we are able to affirm that there can be no real opposition between them. Nevertheless, despite the ambiguity of Kant's wording, this reading is incorrect. A few pages later, in fact, Kant reminds the reader that pure understanding alone cannot relate to objects, and that indeed there is no object of pure intellect at all: 'so would it in fact have to be if the pure understanding could be related to objects immediately' (A267/B323; emphasis mine); and again several pages later, in the Remark to the Amphiboly: 'we cannot thereby positively expand the field of the objects of our thinking beyond the conditions of our sensibility, and assume beyond appearances objects of pure thinking, i.e., noumena, since those do not have any positive significance that can be given' (A287/B343). Therefore, when Kant uses the expression 'realitas noumenon' he is doing nothing but adopting Leibniz's view as a hypothesis. As is often the case, Kant delves so much into the theses he is criticizing that it is sometimes unclear which thesis he is endorsing and which he opposes. As to the concepts of agreement and opposition, Kant argues that, while an opposition between Leibnizian objects of pure understanding is impossible, a real opposition is possible between actual objects belonging to phenomenal spatiotemporal reality. The effects of two forces acting in space, when opposing each other, might suppress each other. Also in this case, as with the previous pair of concepts, the agreement/opposition dichotomy as a whole acquires a new meaning when employed to compare appearances.
Moving now to the fourth pair of concepts, namely matter and form, the argumentative strategy adopted by Kant is by now predictable. In short, when comparing Leibniz's putative objects of pure understanding, matter, i.e. 'the determinable in general' (A266/B322), precedes form, i.e. determination of the determinable. However, in the case of Kant's phenomenal realm, the forms of intuition (space and time) 'precede all appearances and all data of appearances, and instead first make the latter possible' (A267/B323), that is, form precedes matter. 9 Once again, it should be noted here that the use of the concepts of reflection changes when the objects compared are indeed appearances. Now that we have seen how the overall argumentative structure of the Amphiboly works (and how it does not), I shall try to test my interpretation more closely on the third pair of concepts, namely, inner and outer. As I previously suggested with regard to the other paired concepts of refection, these two concepts as well have different meaning depending on whether they relate to appearances or putative objects of pure understanding. Some passages might seem ambiguous at firstfor example: 'In an object of the pure understanding only that is internal that has no relation : : : to anything that is different from it' (A265/B321). We have already seen, though, that with similar statements Kant does not mean to positively determine the object of pure understanding taken as a noumenon, since in the passage from A287/B343 previously quoted Kant writes that it is not even possible to allow for 'objects of pure thinking'. It is thus clear that the statement in question, however true it may be for Leibniz's concepts, has no actual objective validity for Kant. The text continues: 'The inner determinations of a substantia phaenomenon in space, on the contrary, are nothing but relations, and it is itself entirely a sum total of mere relations.' In the realm of spatiotemporal appearances the inner is reducible to the outer: the determinations of spatial objects are ultimately nothing but relations. 10 While Leibniz might conceive of representations of pure understanding as having an outer and inner nature, we learn from experience though that the inner of phenomenal objects is merely relative and not absolute, as their inner is ultimately nothing but their outer, i.e. a sum of relations. Once again in the Amphiboly, Kant shows how the meaning of a pair of concepts of comparisonthis time the concepts of inner and outerdepends on the kind of objects they relate to: objects of pure thinking or actual objects in space and time.
From what has been said thus far, the reader has no reason to expectas Langton and Allais dothat Kant would claim that the 'inner' of objects is their being-in-itself as a putative real object of pure understanding, and that their 'outer' is instead their relational aspect equivalent to the phenomenal manifestation of those same objects. Of course, a few lines below, Kant writes that, as an 'object of the pure understanding : : : every substance must have inner determinations and forces that pertain to its inner reality' (A265/B321). Nevertheless, these lines should again be read in light of A287/B343, where Kant warns us that such objects have no positive significance, for they are immediately followed by a description of Leibniz's viewmore specifically, by an account of how Leibniz derives the concept of monad. Kant's concern here is that Leibniz mistakenly believes that relations among concepts of pure understanding are objective relations and determinations which should be valid for all objects in general, taken as positive noumena. There is therefore no reason to read this paragraph as if Kant were claiming that relational properties of appearances necessarily entail an existing inner nature actually grounding them.

Relational properties without intrinsic natures: a logical impossibility?
I would now like to examine the issue from a slightly different perspective. According to Langton's and Allais' interpretations, the Amphiboly section shows that we are able to make some claims regarding things in themselves by means of pure thinking. Specifically, their thesis is that we know for sure that objects have an 'inner', an intrinsic nature, which is equivalent to the 'in itself' of appearances. Allais claims that Kant holds the following statement to be logically valid: 'there are no relational properties without an intrinsic nature underlying them'. Since in the phenomenal realm there can be nothing absolutely 'inner', we must then acknowledge that the inner of things is their being-in-itself. At this point, Allais anticipates a possible objection to the view she ascribes to Kant. As Allais herself acknowledges, one might accuse her of violating Kant's distinction between logical and real possibility: intrinsic natures are logically possible, but we cannot know whether they really are possible. However, Allais' response to this criticism goes as follows: Crucially, something's being logically possible is not enough (Kant thinks) to show that it is really possible, but something's being logically impossible is enough to show that it is really impossible. : : : In the Amphiboly, Kant clearly thinks that it is a logical truth that relations presuppose something non-relational. The idea of there being relations without there being something non-relational simply does not (Kant thinks) make sense; it is not any kind of possibility. (Allais 2015: 240) Therefore, through this analytical truth Kant would be able after all to claim something about things in themselves and their relation to the realm of appearances, namely, that they have intrinsic properties. More than that, Allais maintains that Kant is led to make this claim about the nature of things in themselves by the need to overcome the incompatibility between the logical necessity of intrinsic natures and the fact that no such nature can be found in phenomenal reality. However, in the Amphiboly Kant repeatedly deems as invalid any attempt to make claims concerning representations in general that is not based on a preliminarily reflection on the source of the latter. I believe that Allais' interpretation is not correct, for her reading eludes precisely this preliminary reflectionas I will now proceed to argue.
The alleged logical impossibility to which Allais refers can be formulated in the following way (which, for a reason to be made clear, I call 'i3'): (i3) It is impossible for there to be relational properties without intrinsic natures grounding them.
From this proposition, following Allais, it could be said that Kant obtains a truth about things in themselves, namely, that they constitute the actual intrinsic nature that grounds phenomenal relational properties. I suggest now that we could analogously put forward three propositions concerning the remaining pair of concepts of reflection. These too result from the comparison between representations of pure understanding in abstraction from sensibility. If we call the previous alleged logical impossibility 'i3', then we have: (i1) It is impossible for two things having the same internal determinations not to be identical with each other.
(i2) It is impossible for there to be any real opposition between two things.
(i4) It is impossible for form to precede matter.
Had Kant adopted the strategy attributed to him by Allais regarding the inner/outer dichotomy to obtain a truth about things in themselves, he could have consistently derived these other three propositions, from which we would obtain as many truths about things considered in themselves. However, as I illustrated above, what Kant actually does in the Amphiboly is rather to refute those very claims through transcendental reflection on the sources of representations. Sensibility is what makes the difference here: since sensibility cannot be reduced to conceptual features (such as Leibniz's confused perceptions), the objective validity of any universal claim would require taking into account the specific role of sensibility in cognition. In fact Leibniz claims to obtain truths that are valid for all objects (and therefore for what Kant calls things in themselves) by deriving them from the aforementioned impossibilities, which in turn arose from the mere comparison between concepts without taking into account the specific contribution of sensibility in the constitution of objectivity.
Here are two passages, from the Remark to the Amphiboly, that make Kant's argument explicit: [C]ategories alone are not sufficient for the cognition of things in themselves, and without the data of sensibility they would be merely subjective forms of the unity of the understanding, but without any object. : : : And one cannot call the noumenon such an object : : : The concept of the noumenon is therefore not the concept of an object, but rather the problem, unavoidably connected with the limitation of our sensibility, of whether there may not be objects entirely exempt from the intuition of our sensibility : : : (A287/ B343-4) [S]ince something is contained in the intuition that does not lie at all in the mere concept of a thing in general, and this yields the substratum that cannot be cognized through mere concepts, namely a space that, along with every thing that it contains, consists of purely formal or also real relations, I cannot say that since without something absolutely inner no thing can be represented through mere concepts, there is also nothing outer that does not have something absolutely internal as its ground in the things themselves that are contained under these concepts (italics mine) and in their intuition. (A284/B340) The four propositions i1, i2, i3, i4 are not genuinely valid, and indeed, while interchangeable with four other propositions which would have to be, given Allais' approach, analytically necessary, they are in particular not analytically necessary. For example, in the case that concerns us the most here: it is not truly necessary at all for relational properties to always be grounded in some intrinsic nature; therefore it is also not true that it is impossible for there to be relational properties without intrinsic natures grounding them. The phenomenal realm is not a kind of exception to the rule that Kant needs to explain by means of his idealism, as Allais believes, but it is rather the proof that those purported necessities are not logical truths in the first place. 11 This point has been missed by Allais because she has evaded the requirement of preliminary transcendental reflection mentioned by Kant at the beginning of the Amphiboly, which means that the source of the representations that are being compared needs to be taken into account. The comparison between representations of pure understanding in complete abstraction from sensibility in no way informs us about objects 'in general', 12 either about appearances orgiven that noumena, as Kant insists, are not even objects in the strict sense (cf. A287/B343-4)about noumena. Accordingly, Kant in fact writes in a note about the relation of real opposition: If one wanted to make use of the usual escape here, that at least realitates noumena cannot act in opposition to each other, one would still have to introduce an example of such pure and non-sensible reality in order to understand whether such a reality represents something or nothing at all. But no example can be derived from anywhere except experience, which never offers more than phaenomena. (A282-3n./B338-9n.) In the same way, objects in space are nothing but mere relations, and there is nothing wrong with that. As Kant emphasizes, they are indeed mere appearances. If anything objective, a positive noumenon, corresponded to what we represent 'through mere concepts', then we could perhaps say that such an object would have an intrinsic nature. However, such an object is not given to us, i.e. we are not able, as Kant demands in the note, to 'introduce an example of such pure and non-sensible reality'. Appearances are all we have access to; hence, the previous hypothetical statement is empty, which means that the notion of intrinsic nature has no objective application. After all, as Kant writes, 'the concept of a noumenon is problematic, i.e., the representation of a thing of which we can say neither that it is possible nor that it is impossible' (A286-7/B343).

Kant's agnosticism about things in themselves in the Amphiboly
I shall now add a few concluding observations on the conception of a thing in itself that emerges from the Amphiboly (and the Remark attached to it). The Amphiboly section has been used by Langton as the main source of her strong metaphysical reading of Kant, and Allais draws similar conclusions from it. It is not my concern here to examine as a whole their interpretations of the relationship between appearances and things in themselves. I would just like to point out that not only does the Amphiboly not easily fit their metaphysical dual-aspect reading, as they maintain, but on the contrary it is rather an obstacle to such a reading. In this section of the Critique Kant is committed to a strong form of agnosticism about the nature of things in themselves. First of all, as we have seen, this is the main point of his criticism of Leibniz, which leads Kant to argue for the impossibility of formulating principles that have any objective validity on the basis of a comparison between 'mere concepts'. Secondly, such agnosticism is explicit in several statementsmost of which have already been quotedin the concluding pages of the Remark to the Amphiboly. Here is another example: If by merely intelligible objects we understand those things that are thought through pure categories, without any schema of sensibility, then things of this sort are impossible. For the condition of the objective use of all our concepts of understanding is merely the manner of our sensible intuition, through which objects are given to us. (A286/B342) All that is left are noumena in the negative (or problematic) sense: [T]hey would then not say anything but that our manner of intuition does not pertain to all things, but only to objects of our senses, consequently that their objective validity is bounded, and room thus remains for some other sort of intuition and therefore also for things as its objects. (A286/B342-3) 13 Negative noumenon is the thought of a limitation of our cognitive faculty, rather than the thought of an object. Indeed, as for categories alone, 'without the data of sensibility they would be merely subjective forms of the unity of the understanding, but without any object' (A287/B343-4); that is, they express the way the cognitive subject necessarily thinks of objects instead of the objective determination of a putative nonphenomenal object. Statements such as those just quoted seem to better fit, for example, Bird's (2006) 'merely empirical realist' interpretation, or also a variety of 'methodological dual-aspect' views of the sort proposed by Quarfood, both of whom contrast their own interpretations with Langton's. 14 Indeed, Quarfood writes: 'these structural properties of things in themselves represent the way we have to think when we abstract from the conditions of sensibility. : : : When we try to attain knowledge of things by mere concepts, what we obtain is, one might say, the mirror image of the structure of our discursivity' (Quarfood 2004: 58). Although it is not my purpose here to endorse Bird's nor Quarfood's view, I believe that their interpretations of Kant's idealism at least have the advantage, over Langton's and Allais', of being more attentive to the constraints on noumenal knowledge imposed by Kant in the Amphiboly.
Besides Langton's and Allais', another interpretation that misunderstands Kant's point about things in themselves in the Amphiboly is Wood's. On his account, Kant considers the identity of indiscernibles as a valid positive principle that we are able to apply to things in themselves. More precisely, according to Wood's socalled 'identity interpretation', objects of pure understanding mentioned by Kant are obtained through the process of thinking appearances in abstraction from sensible intuition: Although things in themselves cannot be sensed, appearances can be thought through the pure understanding, simply by thinking of them in abstraction from the ways they can appear to us. Thus while the sensible criterion for identity cannot apply across the gulf separating phenomena from noumena, the intelligible criterion can apply. This seems in fact to be precisely the way in which Kant himself often arrives at the concept of a noumenon or thing in itself. We begin with particular sensible things (appearances) and then represent them as they are apart from our sensing them, solely through concepts of understanding. (Wood 2005: 69) Moreover, since for Wood they are the same object (though considered in two different ways), we are perfectly able to compare appearances and things in themselves in reflection. Therefore, we can affirm their identity. In short, Wood's reading faces at least the following three problems. First, as I showed earlier, nothing in Kant's argument suggests that he accepts Leibniz's principle of identity as valid for things in themselves. That is not the point of Kant's argument in the Amphiboly, which instead criticizes Leibniz much more radically. This makes it questionable to speak of a useful 'intelligible criterion' for identity. Secondly, we are able to compare appearances and things in themselves and state their identity, as Wood claims, only if we have first already assumed that they are the same thingwhich is what has yet to be proved. Finally, indeed, Wood's claim that we are able to grasp the being-in-itself of an appearance through pure understanding by a process of abstraction is at odds with Kant's rejection of the Leibnizian idea of an object in general thought by means of pure understanding alone, since 'objects of pure thinking : : : do not have any positive significance that can be given' (A287/B343).
It is worth spending a few more words on Wood's interpretation of things in themselves. Wood claims: [T]he criterion of identity or distinctness involving things in themselves (if we need one at all) is Leibnizian (sameness or distinctness of concept). Once we have abstracted from the sensiblee.g. the spatio-temporalproperties of the object as appearance, hence from our empirical cognition of it, it must be the same as itself thought solely through pure concepts of the understanding and distinct from any thing which is represented as other than it (for instance, from a different appearance regarded as it is in itself). (Wood 2005: 69).
We have seen in section 2 that there is no point for Kant in counting different referents of the same concept if these referents are taken to be mere thought entities, for reference requires synthesis. It is then clear that it makes no sense to discuss the identity or difference of putative thought objects, since no numerically distinct singular objects can be given in pure thought (i.e. in abstraction from any spatiotemporal properties). Entities of pure thought are just concepts and thereby general. It seems, however, that Wood's notion of a thing in itself is that of a singular thought-entity with no spatiotemporal features. But given Kant's account of concept reference, we are not really able to positively think such purported entities as singular, that is, we are not able to connect a referent to the concept of a particular non-spatiotemporal entity. The only way to do it without involving sensibility would be through intellectual intuition. An intuitive understanding would in principle immediately grasp the referent of a concept, or rather the concept as a completely determined individual. However, 'If by a noumenon we understand : : : an object of a non-sensible intuition, then we assume a special kind of intuition, namely intellectual intuition, which, however, is not our own, and the possibility of which we cannot understand, and this would be the noumenon in a positive sense' (B307). My point is that by holding Leibniz's principle of the identity of indiscernibles as an 'intelligible criterion' valid for things in themselves, and indeed already by making claims concerning the identity or difference (both of which presuppose distinctness) of things in themselves taken as entities of pure thought, Wood is making illicit claims about positive noumena. In conclusion, on the basis of the Amphiboly, there is good reason to reject Wood's own brand of 'one-object' 15 interpretation of Kant's idealism.
To recap, Kant claims several times in the Amphiboly section that we are not entitled to make positive statements about things in themselves. We are not even able to decide whether positive noumena 16 exist or not -'whether such a reality represents something or nothing at all' (A282-3n./B338-9n.). At the same time, Kant explicitly writes that the concept of negative noumenon is a problematic one, for it is a problem for us to reflect upon concerning the limitation of our sensibility (A287/B343-4). As Kant emphasizes (see again A282-3n./B338-9n.), we cannotat least from a theoretical standpointescape from the necessity of taking into account experience and its forms, and we cannot claim objective validity for concepts that find no sensible correlate just by applying them to things in themselves. In the third chapter of her book, Allais insists on the distinction between negative and positive noumena, and has no problem admitting that we have no insight into the latter, that we cannot even be certain about their mere existence. On the other hand, she also notes that 'Kant makes it clear that his notion of things as they are in themselves should be understood in terms of a negative conception of noumena' (Allais 2015: 61). However, we have just seen that the negative noumenon, being the concept of a problem, is strictly speaking not an actual object at all and cannot be positively determined. Therefore, as we in fact learn from Kant himself in the Amphiboly, we have no right to claim that things in themselves have an intrinsic naturecontrary to what Allais and Langton believe.
Once again, what we are left with in the Amphiboly is spatiotemporal reality and the problem of its bounds and grounds.

Conclusion
I have attempted to establish what Kant's analysis of the concepts of 'inner' and 'outer' in the Amphiboly of Pure Reason suggests about his stance on the possibility of making claims about things in themselves. I started with a brief account of Langton's and Allais' view, as both have found in this text an important source for their reading of Kant's transcendental idealism. The core of the issue has then been addressed by outlining Kant's overall argument in the Amphiboly, and it has been proposed that the argument should not be interpreted as Langton and Allais do if some coherence is to be found in its structure. Afterwards, the discussion switched to Allais's interpretative stance according to which Kant believes that it is impossible for there to be relational properties without intrinsic natures grounding them. This impossibility would have led Kant to the metaphysical claim that the intrinsic nature of appearances is their being-in-itself. The outcome of my analysis is that Allais' position on the matter ultimately contradicts the thrust of Kant's criticism of Leibniz in the Amphiboly. Finally, I have argued that the Amphiboly and the Remark attached to it, far from being key evidence for any 'metaphysical dual-aspect' view, pose instead a complex challenge to it, as they represent a notable case of Kant's agnosticism about things in themselves.

Notes
1 Several interpreters have discussed in detail Kant's criticism of Leibniz's monadology in the Amphiboly (see e.g. Zinkin 2008; Brandt Bolton 2021), or more generally the relationship between the two philosophers. However, that is not the aim of this article. I am not concerned with Kant's view of Leibniz, nor with the effectiveness and fairness of the Amphiboly's argument as a criticism of him. Also, Longuenesse's outstanding analysis of the concepts of reflection (Longuenesse 1998: ch. 6)which predates both works I am discussing herehas broader and more ambitious aims that will not be discussed here. 2 In her book, Allais does not use the label 'dual-aspect view' to describe her position, but I agree with Quarfood's use of the expression to describe Allais' stance on the problem of Kant's transcendental idealism (Quarfood 2004). As for the label 'one-world', mine is of course a simplification. For Allais does not argue for a kind of one-to-one correspondence between appearances and things in themselves: a single thing in itself could in fact appear as different spatiotemporal objects. Nevertheless, what matters here is that appearances and things in themselves are not just completely separate and independent objects that have only some kind of unspecified relation to each other. features of his own interpretation of Kant's transcendental idealism. Heidemann's article about things in themselves shows, only very briefly, a set of seriously problematic aspects of Allais' metaphysical dualaspect view, and he does not mean to provide a strong textual analysis of the Amphiboly nor of other parts of the Critique. The scope of both papers is thus different from mine. As for Anderson's review, see n. 12. 5 One might argue that this statement about the nature of things in themselves can be construed as a need for our thoughtbut in the present contest I will not explore such possibility, however interesting it might be. 6 This thesis is clearly stated, for example, in his Discourse on Metaphysics. For instance: 'that the notion of an individual substance includes once and for all everything that can ever happen to it, and that by considering this notion, one can see in it everything that can be truly stated about it, as we can see in the nature of the circle all the properties that can be deduced from it' (Leibniz 2020 : 17). 7 Of course Kant speaks of one individual concept, namely, the transcendental ideal. It is however not a concept among others, but rather the mere prototypon of an individual, which cannot be given (which means that it has no actual referent) and serves as an ideal which our discursive understanding can never attain.
8 Contrary to what Allen Wood, for example, believes. I will discuss this issue more in detail in the last section. 9 Longuenesse (1998: ch. 5) brilliantly shows how the priority of form actually extends to all aspects of Kant's philosophy, and how important is this fact. 10 Langton (1998: 53) correctly observes that the notion of substantia phaenomenon echoes Baumgarten's definition of phaenomena substantiata (Metaphysica, §193), something that appears to be a substance and yet it is not. This something is actually an accident, whose relative subsistence leads us to take it for a substance. Now, that for Baumgarten it is a kind of false substance which actually presupposes a proper substance (i.e. the monad) is indeed correct: every proper substance is a monad, otherwise it is nothing but a phaenomenon substantiatum (Metaphysica, §234). Nevertheless, unlike what Langton seems to believe, this fact does not prove that for Kant as well a substantia phaenomenon necessarily presupposes a substantia noumenon. It might be true that, for Kant, phenomenal substances are not absolutely persistent, and thus that we cannot cognize absolute substances. However, this concept of substance (the schematized category of substance) is for us the only one that has an objective content, for we are not theoretically entitled to assert the existence of an absolute (and thus noumenal) substance, a substantia noumenon. 11 This point is stressed by Kant in a passage from the essay 'What Real Progress has Metaphysics Made in Germany since the Time of Leibniz and Wolff?': 'Leibniz's law of indiscernibility : : : is violently in conflict with reason, since there is no understanding why a drop of water at one place should prevent an identical drop from being encountered at another. But this collision proves at once that, in order to be known, things in space must be represented, not merely through concepts of the understanding, as things-in-themselves, but also in accordance with their sensory intuition as appearances' (20: 280; emphasis mine). 12 This point is also stressed by Anderson's (2016Anderson's ( : 1666 criticism of Allais and I agree with most of his insightful observations. Nevertheless, I believe that my argument goes beyond Anderson's remarks, for it shows in detail how Allais' line of thought unnecessarily turns the Amphiboly into an incoherent argument (by generating the false claims i1, i2 and i4). And this was possible through a more extended analysis of Kant's text, that is, only after taking into account all the dichotomies in section 2 and showing concretely Kant's strategy. Allais (2016) attempts to address Anderson's remarks by claiming once more that Kant's point is merely to stress the transcendental ideality of space and the need for another level of reality, that is, the realm of intrinsic natures. However, it should be clear that this kind of reply cannot affect the argument that I propose here. 13 Here is another interesting passage: 'the transcendental object, however, which might be the ground of this appearance that we call matter, is a mere something, about which we would not understand what it is even if someone could tell us. For we cannot understand any thing except that which has something corresponding to our words in intuition' (A277/B333). The relationship between the notions of 'noumenon', 'thing in itself' and 'transcendental object' is notoriously unclear. For the present purpose though, I think it is acceptable to stick with the meaning given to it by Kant in the quoted sentence, i.e. the nonphenomenal ground of appearances/matter, a meaning that echoes the notion of a thing in itself. 14 Quarfood is explicitly inspired by Allison's well-known interpretation of Kant's transcendental idealism. It is worth noting that, in the revised edition of his book, Allison mentions and criticizes Langton's view (see Allison 2004: ch. 1).
15 Wood seems committed to a very strict identity, or sameness, between an object as appearance and as a thing in itself: 'If I arrive at the concept of the chair in the corner first by cognizing it empirically and then by abstracting from those conditions of cognition, so that I think of it existing in itself outside those conditions, then it is obvious that I am thinking of the same object, not of two different objects' (Wood 2005: 69-70). On this account we would be able to talk about a chair as it appears and the very same chair as it is in itself, in abstraction from sensibility. However, it is fair to raise an objection, at least on philosophical grounds. As Lance Hickey rhetorically asks, imagine that we 'abstract away all the empirical properties of the object, i.e., all the properties that give the cup [or Wood's chair] the character of an appearance in space and time. What are we left with? Certainly not the cup' (Hickey 2001: 129), nor the chair, as Wood seems to believe. 16 The distinction between a positive and a negative concept of noumenon is suggested by Kant in the chapter titled 'On the ground of the distinction of all objects in general into phenomena and noumena'.