Handedness, Idealism, and Freedom

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments.

Incongruent counterparts and the absolute nature of space in Kant’s 1768 essay, "Directions in Space"

This article argues that Kant’s argument from incongruent counterparts in his essay, Directions in Space (1768) 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.

Embodied Cognition in Berkeley and Kant: The Body’s Own Space

Berkeley and Kant are known for having developed philosophical critiques of materialism, critiques which lead them to propose instead an epistemology based on the coherence of our mental representations. For all that the two had in common, however, Kant was adamant in distinguishing his own ‘transcendental idealism’ from the immaterialist consequences entailed by Berkeley’s account. In this essay I return to their respective theories of spatial intuition, since it is by paying attention to Berkeley’s account of space that we discover a surprising account of embodied cognition, of spatial distance and size that can only be known by way of the body’s motion and touch. More striking than this, is the manner in which Kant’s approach to the problem of incongruent counterparts also relies on a proprioceptive cognition. Thus while cognition theorists today have recognized that certain challenges faced by perception and cognition can only be resolved by way of an appeal to the facts of embodiment, my aim in this essay is to show that such recourse is not new.

The Legacy of Newton for the Pre-Critical Kant

This chapter assesses Newton’s legacy for Kant by concentrating on the evolution of Kant’s view of space in the pre-Critical period (1748–1768), with two main goals in mind. The first goal is to draw attention to the role that Newton’s matter theory and chemistry played for the young Kant. The second is to argue against the received view that has portrayed the young Kant as embracing Newton’s absolute space in 1768 via the argument from incongruent counterparts (short-lived as this conversion to Newton’s absolute space proved to be). By contrast to the received view, this chapter shows that in the period 1748–1768, Kant was working with a thoroughgoing relationalism, consonant with Kant’s matter theory, which was, in turn, inspired by speculative Newtonian experimentalism itself. Hence, the case is made for a slightly different interpretive stance on Newton’s legacy for the young Kant.

The Asymmetry of Space: Kant’s Theory of Absolute Space in 1768

I propose that we interpret Kant’s argument from incongruent counterparts in the 1768 article ‘Concerning the Ultimate Ground of the Differentiation of Directions in Space’ in light of a theory of dynamic absolute space that he accepted throughout the 1750s and 1760s. This force-based or material conception of space was not an unusual interpretation of the Newtonian notion of absolute space. Nevertheless, commentators have continually argued that Kant’s argument is an utter failure that shifts from the metaphysics of space to its epistemology, because he has no way to connect ‘directionality’ and ‘handedness’ to absolute space. This supposed failure is based on an understanding of absolute space in purely mathematical terms and as an absolute void that lacks any qualitative or dynamic features. If we recognize that Kant held that space had an intrinsic directional asymmetry then his argument successfully connects incongruent counterparts to absolute space. The presence of this notion in Kant’s pre-Critical thought is rarely noted, and its necessity in understanding his incongruence argument is novel.

The semantic basis of taste-shape associations

Previous research shows that people systematically match tastes with shapes. Here, we assess the extent to which matched taste and shape stimuli share a common semantic space and whether semantically congruent versus incongruent taste/shape associations can influence the speed with which people respond to both shapes and taste words. In Experiment 1, semantic differentiation was used to assess the semantic space of both taste words and shapes. The results suggest a common semantic space containing two principal components (seemingly, intensity and hedonics) and two principal clusters, one including round shapes and the taste word “sweet,” and the other including angular shapes and the taste words “salty,” “sour,” and “bitter.” The former cluster appears more positively-valenced whilst less potent than the latter. In Experiment 2, two speeded classification tasks assessed whether congruent versus incongruent mappings of stimuli and responses (e.g., sweet with round versus sweet with angular) would influence the speed of participants’ responding, to both shapes and taste words. The results revealed an overall effect of congruence with congruent trials yielding faster responses than their incongruent counterparts. These results are consistent with previous evidence suggesting a close relation (or crossmodal correspondence) between tastes and shape curvature that may derive from common semantic coding, perhaps along the intensity and hedonic dimensions.

Russell and Wittgenstein on Incongruent Counterparts and Incompatible Colours

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