A Last Shot at Kant and Incongruent Counterparts

Rusnock, Paul; George, Rolf

doi:10.1515/kant.1995.86.3.257

Cited by 15 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The notions of similarity and equality can be traced back to antiquity, but Leibniz seems to have been the first to formulate a general notion of “similarity.” Hence, the general thesis that all equal and similar things are congruent seems to be originally Leibniz's. For discussion, see Rusnock and George (1995), Sutherland (2005), and the present author's (2005). 7 Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality (in Kant, 1992), 2: 275–301, relevant passages in 2: 276 f. 8 For a further discussion, see Jong (1995), and the present author's (2005). 9 For discussion, see the essays mentioned in endnotes 4 and 5 above. 10 On Kant's early uses of Leibniz's relational view of space, and his attempts to reconcile it with Newtonian science, see Torretti (1967, part I), and Friedman (1992, introduction). 11 De Mundi Sensibilis atque Intelligibilis Forma et Principiis , 2: 385–419 (English translation in Kant, 1992). 12 (English translation taken from Kant, 2002.)…”

mentioning

confidence: 80%

“…They roughly mean indistinguishability when each object is considered in isolation, and sameness in magnitude, respectively. For two enlightening discussions of the history of those notions, which can be traced back to Antiquity, and further references, see Rusnock and George (1995), especially pp. 256–62, and Sutherland (2005).…”

mentioning

confidence: 99%

“…), the Prolegomena (1783, 4: 285 f.), the Metaphysische Anfangsgründe der Naturwissenschaft (1786, 4: 484), and in “Was heist: Sich im Denken orientieren” (1786, 8: 131 ff.). They are also discussed in Herder's lecture notes of Kant's 1763 metaphysics course ( Metaphysik Herder , 28.1: 15). 4 See, for example, Torretti (1967), part one; Buroker (1981); several of the essays in Van Cleve and Frederick (1991); Rusnock and George (1995); and Walford (2001). 5 But see Remnant (1963), Torretti (1967), Mühlhölzer (1992), Rusnock and George (1995), Walford (2001), and the present author's (2005).…”

mentioning

confidence: 99%

See 2 more Smart Citations

A PUZZLE ABOUT INCONGRUENT COUNTERPARTS AND THE CRITIQUE OF PURE REASON

Severo

2007

Pacific Philosophical Qtr

View full text Add to dashboard Cite

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 .

show abstract

mentioning

confidence: 80%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

A PUZZLE ABOUT INCONGRUENT COUNTERPARTS AND THE CRITIQUE OF PURE REASON

Severo

2007

Pacific Philosophical Qtr

View full text Add to dashboard Cite

show abstract

“…Put another way, Kant had too much respect for the mathematical acumen of others, and not enough for his own. (Rusnock and George 1995: 274)…”

Section: A Standard Objectionmentioning

confidence: 99%

Kant on Spatial Orientation

Bernecker

2012

European J of Philosophy

View full text Add to dashboard Cite

show abstract

“…7 7 On the origin of the distinction, inner/outer, in Leibniz's analysis situs , see Rusnock and George (1995, pp. 261–262). …”

mentioning

confidence: 99%

Kant vs. Legendre on Symmetry: Mirror Images in Philosophy and Mathematics

Hon

2005

Centaurus

View full text Add to dashboard Cite

Abstract. In 1768, Kant published a short essay in which he inquired into the possibility of determining the directionality of space. Kant's central argument invokes the strategy that if one were to demonstrate directionality, then the relational view of space that Leibniz propounded would be refuted. This paper has been considered a major turning point in Kant's philosophical development towards his critical philosophy of transcendental idealism. I demonstrate that in this study, Kant came very close to the modern concept of symmetry. His novel construction of incongruent counterpart (inkongruentes Gegenstück) contains elements essential to the modern notion of symmetry. However, Kant does not consider the incongruent counterparts, which he designates as ‘Right’ and ‘Left’, symmetric; rather, he holds the French encyclopaedist view that symmetry is a kind of balance. This study convinced Kant that the solution to the problem of the nature of space lies not in mathematics but in metaphysics. He was wrong in this conclusion, at least with respect to symmetry. The solution was found within the framework of mathematics, that is, solid geometry. In 1794, Legendre recast the traditional encyclopaedist concept of symmetry by calling a certain property of polyhedra symmetrical. The view of Kant is contrasted with that of Legendre by comparing their usages of mirror image as an aid for understanding. While in both cases mirror images are not considered illusions—perhaps for the first time in the history of mirror reflections—the differences are substantial, highlighting the limitation of Kant's position and the great potential of Legendre's new concept of symmetry.

show abstract

A Last Shot at Kant and Incongruent Counterparts

Cited by 15 publications

References 0 publications

A PUZZLE ABOUT INCONGRUENT COUNTERPARTS AND THE CRITIQUE OF PURE REASON

A PUZZLE ABOUT INCONGRUENT COUNTERPARTS AND THE CRITIQUE OF PURE REASON

Kant on Spatial Orientation

Kant vs. Legendre on Symmetry: Mirror Images in Philosophy and Mathematics

Contact Info

Product

Resources

About