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. (shrink)

Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations, there are few examples that have become widely accepted as exhibiting the distinction between mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds. This essay offers some examples of proofs that mathematicians have considered explanatory, and it argues that these examples suggest a (...) particular account of explanation in mathematics. The essay compares its account to Steiner's and Kitcher's. Among the topics that arise are proofs that exploit symmetries, mathematical coincidences, brute-force proofs, simplicity in mathematics, merely clever proofs, and proofs that unify what other proofs treat as separate cases. (shrink)

No agreed-upon account of mirror reversal is currently available although it has been discussed for more than two thousand years since Plato. Mirror reversal usually refers to recognized left-right reversal of a mirror image. Depending on the nature and layout of a reflected object, however, top-bottom reversal may be recognized instead of left-right reversal; no reversal at all may be recognized; and the presence or absence of reversal may not be decidable. Takano (1998) proposed a psycho-optic theory to explain all (...) these cases of mirror image recognition in a consistent manner. The proposed theory assumes different causes of mirror reversal depending on whether an object's left-right axis is parallel or perpendicular to a mirror's surface. This theory was later criticized in that it provided no explanation when the left-right axis is neither parallel nor perpendicular but at an intermediate angle between zero and 90 degrees with a mirror. This article completes the theory by presenting psycho-optic anal.. (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)

This paper revisits Kant’s 1768 incongruent counterpart argument that space is absolute. Most commentators today dismiss Kant’s argument as begging the question against the relationalist. I argue that this dismissal is too quick, and that we have something to learn by considering what might have led him to argue as he does. My focus is on the role of geometrical intuitions and the extent to which they can provide defeasible warrant for claims about space. By “geometrical intuitions” I mean both (...) the geometrical intuitions of spatial figures in imagination as well as the claims that seem to directly follow from them. My focus includes uncovering the metaphysical assumptions that are implicated in those geometrical intuitions. Whether or not Kant’s argument ultimately succeeds, the role of geometrical intuitions is worth exploring. Moreover, Kant appeals to geometrical intuitions, and any adequate interpretation of Kant will have to take them into account. (shrink)

This paper develops a novel interpretation of Kant's argument from incongruent counterparts to the effect that the representations of space and time are intuitions rather than concepts. When properly understood, the argument anticipates the contemporary position whereby the meaning of indexicals cannot be captured by descriptive contents.

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is (...) detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (shrink)

Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealis-mo 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. (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)