Kant's argument from incongruent counterparts for substantival space is examined; it is concluded that the argument has no force against a relationist. The argument does suggest that a relationist cannot give an account of enantiomorphism, incongruent counterparts and orientability. The prospects for a relationist account of these notions are assessed, and it is found that they are good provided the relationist is some kind of modal relationist. An illustration and interpretation of these modal commitments is given.

The purpose of this paper is twofold. First, I want to examine some rather curious arguments of Kant’s which purport to show that some alleged properties of space can be derived from some alleged facts about incongruous counterparts. Secondly, I want to give some preliminary answers to some important questions about the distinction between right and left and the nature of space and space-time which are raised by Kant’s argument. As a byproduct, I hope that the discussion will provide (...) an example of how science can illuminate philosophical issues and of how philosophy can at least lead one into interesting scientific issues. (shrink)

Left and right hands are incongruent counterparts. Yet each replicates the intrinsic properties of the other. This suggests that differing relations to space make the difference. Kant's and Weyl's discussions of the problem are critically discussed. It emerges that spatial relationism fails to explain how its relations may be interpreted. An excursion into visual geometry explains the basis of handedness in the orientable structure of space.

In a recent paper, Robert Hanna argues that Kant's incongruent counterparts example can be mobilized to show that some mental representations, which represent complex states of affairs as complex, do so entirely non-conceptually. I will argue that Hanna is right to see that Kant uses incongruent counterparts to show that there must be a non-conceptual component to cognition, but goes too far in concluding that there must be entirely non-conceptual representations that represent objects as existing in (...) space and time. Kant is deeply committed to the thesis that no representation of a complex state of affairs as complex can be entirely non-conceptual. For Kant, all representations of complex states of affairs as complex (including those of incongruent counterparts) are conceptually structured. I present an interpretation of the Transcendental Aesthetic according to which Kant not only aims at Leibnizian and Newtonian accounts of space and time, but also Hume's. Hume's account fails to make representations of complex states of affairs sufficiently determinate. Kant offers an account later in the Critique that is meant to correct this failing by requiring that all representations of complex states of affairs as complex be conceptually (inferentially) structured. (shrink)

This article argues that Kant’s argument from incongruent counterparts in his essay, Directions in Space yields not the conclusion that space is an objective reality, but rather that it is an absolute and dynamical framework that grounds spatial properties, a view which is neutral with respect to the objective/subjective nature of space. It is suggested that, so construed, Kant’s argument in this essay can be made consistent with his later employment in support of transcendental idealism with regard to (...) space. (shrink)

RESUMEN Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealismo trascendental, constituye un marco adecuado para solucionar la paradoja de las contrapartidas incongruentes. Se incluyen dos hipótesis: a) la solución kantiana implica una referencia a la conciencia de la propia corporalidad, para comprender cómo poseemos la capacidad para orientarnos en el espacio; b) no existe contradicción en el uso kantiano de las contrapartidas incongruentes en diferentes estadios de su pensamiento. La solución kantiana de (...) 1768 constituye una versión germinal del desarrollo que culminará en la teoría idealista trascendental acerca del espacio como una forma de nuestra sensibilidad. ABSTRACT The article argues that the Kantian theory of space, in the context of transcendental idealism, constitutes an adequate framework to resolve the paradox of incongruent counterparts. Two hypotheses are considered: a) the Kantian solution implies a reference to the awareness of one's corporeity in order to understand how we have the capacity to orient ourselves in space; b) there is no contradiction in the Kantian use of incongruent counterparts throughout the different stages of his thought. The Kantian solution of 1768 is a germinal version of the development leading up to the transcendental idealist theory of space as a form of our sensibility. (shrink)

Despite its first page this paper is not yet another piece on Kant! Rather, the paper is a contribution to the literature on incongruent counterparts. Specifically, it concerns the question of whether we can construct a temporal version of the puzzle of incongruent counterparts—a question which (as far as 1 can tell) has been thoroughly neglected. I maintain that we can construct such a version of the puzzle, and that this temporal variant on the phenomenon has (...) something to teach us about popular arguments for the possibility (or even actuality) of four‐dimensional space. (shrink)

Two puzzles with regard to the Kritik der reinen Vernunft are incongruent counterparts and causality. In De mundi sensibilis atque intelligibilis forma et principiis, Kant indicates that the experience of things like left and right hands, so-called incongruent counterparts, involve certain pure intuitions, and hence constitute one line of evidence for the claim that the concept of space itself is a pure intuition. In KrV, Kant again argues that the concept of space itself is a pure (...) intuition, but does not cite the experience of incongruent counterparts as evidence for this claim. Since there is ostensibly nothing in KrV which tells against the existence of the experiences of incongruent counterparts, the natural question is: “Why, in KrV, does Kant not cite the experience of incongruent counterparts as evidence for the claim that the concept of space is a pure intuition?” The problem with causality is as follows. One of the most primary and basic claims of KrV is that empirical experience is structured by non-empirical concepts, such as substantiality and causality. In a portion of KrV entitled the Transcendental Deduction, Kant gives section 20 the heading “All sensible intuitions stand under the categories, as conditions under which alone their the manifold can come together in one consciousness”. Since categories are those concepts which structure empirical experience, section 20 has demonstrated that all sensible intuitions are subject to substantiality and causality. However, there is a later portion of KrV entitled the Second Analogy with the heading “Principle of temporal sequence according to the law of causality: All alterations occur in accordance with the law of the connection of cause and effect”. Thus, the natural question is: “What does the Second Analogy demonstrate about causality which the Transcendental Deduction did not already demonstrate about causality?”. (shrink)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which (...) explains that textual absence as a result of the synthetic method of presentation intended for the Critique. (shrink)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which (...) explains that textual absence as a result of the synthetic method of presentation intended for the Critique. (shrink)

Consider your right hand and a mirror image duplicate of it. Kant calls such pairs incongruent counterparts. According to him they have the following puzzling features. The relation and situation of the parts of your hand with respect to one another are not sufficient to distinguish it from its mirror duplicate. Nevertheless, there is a spatial difference between the two. Turn and twist them how you will, you cannot make one of them occupy the exact boundaries now occupied (...) by the other. In his 1768 paper, ‘Concerning the Ultimate Foundations of the Differentiation of Regions in Space’, Kant uses these claims to argue against relational accounts of space and goes on to argue that the difference between incongruent counterparts depends on a relation to absolute space as a whole. In his 1770 Inaugural Dissertation he argued that this difference could not be captured by concepts alone but required appeal to intuition. In the Prolegomena (1783) and again in the Metaphysical Foundations of Natural Science (1786) Kant appealed to these puzzling features of incongruent counterparts to support his transcendental idealism about space. (shrink)

Abstract:Russell (in Principles of Mathematics) and Wittgenstein (in Tractatus Logico-Philosophicus) largely agree on the twin questions of why pairs of congruent objects cannot always be made to coincide and why surfaces can never be uniformly two colours at once. Both philosophers take space and colour to be mathematically representable, construe the relevant impossibilities as mathematical and hold that mathematical impossibility is at root logical. It is not by chance that Russell says nothing about the phenomena in his Introduction to the (...) Tractatus or surprising that Wittgenstein was unmoved by the objection that his account of colour incompatibility puts paid to his early philosophy. (shrink)

Peter Alexander; I*—The Presidential Address: Incongruent Counterparts and Absolute Space, Proceedings of the Aristotelian Society, Volume 85, Issue 1, 1 June 1.

Peter Alexander; I*—The Presidential Address: Incongruent Counterparts and Absolute Space, Proceedings of the Aristotelian Society, Volume 85, Issue 1, 1 June 1.

Paper begins: I have two gloves, a left glove and a right glove. I can fit the left glove onto my left hand, but not the right glove. Why? Because the right glove is the wrong shape to go on my left hand. So the two gloves are different shapes….

I argue that, by the time of his essay "Concerning the Ultimate Ground of the Differentiation of Directions in Space" (1768), Kant had come to question the status of the Principle of Sufficient Reason as a result, at least in part, of his recognition of the existence of incongruent counterparts. Though Kant's argument against absolute space based on the existence of incongruent counterparts has been much discussed in recent years, its importance as a useful benchmark by (...) which to judge the direction of Kant’s thinking during this period has gone unnoticed. This paper is a modest attempt to remedy this deficiency. (shrink)

Kant’s treatments of incongruent counterparts have been criticized in the recent literature. His 1768 essay has been charged with an ambiguous use of the notion of ‘inner ground’, and his 1770 claim that those differences cannot be apprehended conceptually is thought to be false. The author argues that those two charges rest on an uncharitable reading. ‘Inner ground’ is equivocal only if misread as mapping onto Leibniz notion of quality. Concepts suffice to distinguish counterparts, but are insufficient (...) to specify their spatial forms. Kant’s claims are reasonable and plausible, and have been reaffirmed repeatedly in contemporary discussions of demonstrative identification. (shrink)

The aim of this paper is to explore Deleuze's use of Kant's argument from incongruent counterparts, which Kant uses to show the existence of what he calls an “internal difference” within things. I want to explore how Deleuze draws out an important distinction between the concept and the Idea, and provides an incisive account of his relationship to both the Kantian and Leibnizian projects. First, I look at Kant's use of the argument to provide a refutation of the (...) Leibnizian account of space, before showing how this criticism in fact rests on the question of the conceptual determination of object. Second, I show how Deleuze develops a taxonomy of difference on the basis of his reading of Kant's argument. Finally, I look at what Deleuze sees as the limitations in Kant's understanding of this concept and Deleuze's attempt to overcome these limitations through the introduction of the notion of the Idea, which will provide a genetic and nonconceptual account of the object. In doing so, I show why Deleuze takes the formulation of an adequate account of difference to be one of the central aims of his own metaphysics. (shrink)

In his 1768 essay ‘Concerning the Ultimate Foundation of the Differentiation of the Regions in Space’, Kant used incongruent counterparts in an attempt to refute a Leibnizian-relationist account of space. It is hard to imagine that scholars could be more divided on how to understand Kant’s argument and on how to assess its effectiveness. Two years later in 1770 incongruent counterparts resurface in Kant’s Inaugural Dissertation, this time as part of a proof that our knowledge of (...) space is intuitive. They appear yet again in the Prolegomena and the Metaphysical Foundations of Natural Science as part of the argument for transcendental idealism. Not surprisingly, scholars are also at odds on how to explain the shifts in the roles Kant wanted incongruent counterparts to play and how to assess the importance of these matters for the development of his critical philosophy. (shrink)

INTRODUCTION TO THE ARGUMENT OF 1768 Some ordinary facts about the world we live in can be readily explained by other ordinary facts. One can, for example, explain the fact that when we are facing north the sun rises on the right and ...

When a body is turned through 180°, reversal occurs in two dimensions. If it is turned about the vertical axis, then left and right sides change places, and also front and back. If it is turned about the horizontal axis which runs from side to side, then top and bottom change places, and also front and back. If, finally, it is turned about the horizontal axis which runs from front to back, then left and right change places as well as (...) top and bottom. All this appears to follow from the properties of three-dimensional space and of rigid bodies. If XOX' is the axis of rotation of a three-dimensional structure, then there are two axes YOY' and ZOZ' at right angles to XOX', and if one of these moves round 180°, then so must the other. It follows that a body is always reversed in two dimensions whenever it is turned about an axis in the third. It follows also that there are always two ways of turning a body in space so as to reverse it in a given dimension: namely by turning it about either of two axes perpendicular to the given dimension. (shrink)

This article responds to henry allison's criticisms of the author's claim that kant's incongruent counterparts argument supports his critical conclusions that things in themselves must be both non-Spatial and unknowable. The first part of the article treats four objections allison raises. The second part discusses differences between allison's and the author's readings of kant's claims about things in themselves.

In this paper we are dealing with Kant's view on the phenomenon of incongruous counterparts, in particular with the argument from his article 'On the First Ground of the Distinction of Regions in Space', where the phenomenon of incongruous counterparts is used as an argument for the existence of the absolute and objective space, and with the argument from Kant's Inaugural Dissertation in which he uses the phenomenon of incongruous counterparts again, but this time for a different (...) purpose - as an argument in favor of the idea of space as a pure intuition. Our aim is to show that Kant's argument from 'On the First Ground of the Distinction of Regions in Space', although it shows the inadequacy of Leibniz's definition of congruence, does not in fact represent the reductio ad absurdum of the relationist view, for his argument in favor of the existence of the absolute space represents merely the inference to the best explanation. We also propound an alternative account of the phenomenon of incongruous counterparts, which is in line with the relationist theory. Furthermore, we call in question Kant's argument from the Inaugural Dissertation, according to which incongruence could not be explained discursively, and we put forward a conceptual determination of incongruence in terms of the notions of similarity, equality and congruence, taken as the possibility of objects to be included within the same spatial boundaries. U ovom radu bavimo se Kantovim shvatanjem fenomena inkongruentnih pandana pre svega njegovim argumentom iz spisa 'O osnovnim principima razlikovanja smerova u prostoru', gde Kant fenomen inkongruentnih pandana koristi kao argument u prilog tvrdnje o postojanju apsolutnog i objektivnog prostora, kao i argumentom iz Kantove Inauguralne disertacije, u kojoj se on ponovo poziva na fenomen inkongruentnih pandana, ali ovoga puta sa drugacijim ciljem - kao argument u prilog shvatanja prostora kao cistog opazaja. Cilj nam je da pokazemo kako Kantov argument iz spisa 'O osnovnim principima razlikovanja smerova u prostoru', iako pokazuje neadekvatnost Lajbnicove definicije kongruencije, ipak ne predstavlja reductio ad absurdum relacionisticke pozicije, buduci da njegov argument u prilog postojanja apsolutnog prostora predstavlja samo zakljucak na najbolje moguce objasnjenje, kao i da ponudimo alternativno objasnjenje fenomena inkongruentnih pandana, koje je u skladu sa relacionistickom teorijom. Takodje, dovodimo u pitanje Kantov argument iz Inauguralne disertacije, prema kojem se inkongruencija ne moze izraziti diskurzivno, nudeci pri tome pojmovno odredjenje inkongruencije preko pojmova slicnosti, jednakosti i kongruencije, shvacene kao sposobnost objekata da zauzmu istovetne prostorne granice. (shrink)

At various times in his "Pre-critical" and "Critical" periods, Kant presented an argument about the nature of space that has come to be called the "Incongruous Counterparts" argument. First presented in his 1768 essay, Concerning the Ultimate Foundation for the Differentiation of Regions in Space, the argument holds that two objects, such as two human hands, might be exact counterparts, that is, identical in "size and proportion and... the situation of the parts relative to each other," and yet (...) might be still "incongruent," that there is no continuous rigid motion which brings them into coincidence in space; or, that they are, though counterparts, incongruently left and right hands. This argument appears in 1768, in the Dissertation of 1770, the Prolegomena of 1783 and the Metaphysical Foundations of Natural Science in 1786. Unfortunately, while the details of the argument are virtually the same, the conclusions are not. Kant seems to have claimed that the argument shows: that a Leibnizean, relational theory of space was wrong; that a theory of absolute space was correct; that space was a pure form of sensibility and that space was transcendentally ideal, i.e., that space was not and could not be a feature of things in themselves. In the secondary literature, commentators who have dealt with this issue have simply noted the odd history of the argument and lamented it. Buroker's ambitious and interesting thesis in this book is not only that Kant's use of the argument is consistent and interconnected, but that the argument can be seen as the "origin" of Kant's idealism. She argues both of these points by arguing, in the great majority of cases, more for a logical than an actual or historical connection among the conclusions Kant drew from the argument; i.e., that she can illuminate the reasoning that led Kant from a rejection of Leibniz's relational view to his radical separation between sensibility and understanding, and then to his view that things in themselves are both unknowable and non-spatial. (shrink)