The ‘eye of the mind’ and the ‘eye of the body’: Descartes and Leibniz on truth, mathematics, and visuality

Abstract

In the conflict between rationalism and empiricism, the rationalist is regarded as a philosopher whose source of knowledge is reason rather than sense perception. And yet the terminology of “sight” plays a striking role in rationalist philosophy. This paradox of the simultaneous “devaluation” and “valuation” of seeing is normally explained in terms of the difference between the “eye of the mind” and the “eye of the body”. The rationalist, according to this view, transforms sight into the activity of reasoning, whereby the “intellectual eye” sees all the more clearly the more the body’s eyes remain blind. This essay is aimed at correcting this understanding by means of looking at the epistemologies of Descartes and Leibniz. An investigation into the epistemological meaning of the mathematical innovations of both philosophers will help rehabilitate the role of bodily sight in rationalist forms of knowing. It is proposed (i) that the calculization in mathematics, to which Descartes’ Analytical Geometry and Leibniz’s Infinitesimal Calculus contributed significantly, promotes a specific type of visuality which is called “tactile seeing” or “seeing with the hand”. And it is demonstrated (ii) that traces of calculization, in form of the core rationalist move of reducing truth to correctness, can be found in epistemology. The rationalists devalue “ocular seeing”, since it is closely tied with the illusionary, but they value “tactile seeing”, which is not a “seeing with the mind”, but a “seeing with the hand.”