The Development of Descartes’ Idea of Representation by Correspondence
Hanoch Ben-Yami, Central European University
In my book, Descartes’ Philosophical Revolution: A Reassessment (Ben-Yami 2015), I have shown in some detail that Descartes was the first thinker to hold a theory of representational perception with all the following characteristics:
• When we see colours, we are immediately aware of ideas of colour in our mind.
- The colour in the things we see causes our idea of colour.
- The idea of colour represents the colour in seen things.
- The colour in seen things does not resemble the idea of colour.
- The representation, when adequate, is so because it corresponds with what it represents.
(I focus here on vision, although the theory is supposed to apply to other sensory modalities as well). These characterisations of Descartes’ view are all found in the scholarly literature and most are common in it, yet like so much else in this literature, some have been challenged. I provided in my book evidence for this interpretation of Descartes’ theory and argued against some alternative ones (Ben-Yami 2015, chapter 2), and I shall assume it in what follows. Theories of representational perception were common from antiquity onwards (Ben-Yami 2015, section 2.3, 33–43), yet Descartes’ theory is original in several respects. For instance, Descartes is the first to hold that the representation of which we are directly aware is in the mind and not in the sense organs.
This aspect of his theory, however, is one on which I shall not dwell in this paper. The innovative claim I shall discuss below is that the representation is adequate not through resembling what it represents but through having some sort of correspondence with it. This representation through correspondence, without resemblance, is true not only for the representation of colours by the ideas of colour in the mind, but also for their representation in the nervous system by various patterns of flow of animal spirits. I have provided in my book a historical survey to support my claim that the correspondence-without-resemblance view of representation was an innovation of Descartes’ (section 2.3). Descartes was aware of this innovative aspect of his theory of representation and of the consequent need to explain and justify it, something he therefore does at a few places in his writings. One place in which we find such a detailed explanation is the fourth discourse of his Optics. Descartes first explains why representation by means of resemblance is impossible in the case of vision:
We must take care not to assume — as our philosophers commonly do — that in order to perceive, the soul must contemplate certain images transmitted by objects to the brain; or at any rate we must conceive the nature of these images in an entirely different manner from that of the philosophers. For since their conception of the images is confined to the requirement that they should resemble the objects they represent [avoir de la ressemblance avec les objets qu’elles représentent], the philosophers cannot possibly show us how the images can be formed by the objects, or how they can be received by the external sense organs and transmitted by the nerves to the brain (Optics, Discourse IV, AT 6, 112; CSM 1, 165; emphasis added).
Having noted this, he continues to show, with an example taken from perspectival engravings, how an adequate representation sometimes should not resemble what it represents:
Moreover, in accordance with the rule of perspective, [engravings] often represent circles by ovals better than by other circles, squares by rhombuses better than by other squares, and similarly for other shapes. Thus it often happens that in order to be more perfect as an image and to represent an object better, an engraving ought not to resemble it (Optics, Discourse IV, AT 6, 113; CSM 1, 165–66).
He concludes that this is the case with vision, where what is crucial is correspondence between representation and what is represented, and not resemblance:
Now we must think of the images formed in our brain in just the same way, and note that the problem is to know simply how they can enable the soul to perceive all the various qualities of the objects to which they correspond [les diverses qualités des objets auxquels elles se rapportent] — not to know how they can resemble these objects (Optics, Discourse IV, AT 6, 113; CSM 1, 166; emphasis added).
His theory of representation in perception indeed involves correspondence without resemblance. This was a breakthrough in the understanding of representation generally and in the implementation of the idea in theories of perception, in philosophy as well as in physiology. From Descartes on, physiologists have developed models that explain how the nervous system preserves the information about the perceived objects, and did not try to explain how the colours of the things we see are reproduced in the brain. A question that arises at this place is, why was Descartes the first to think of this kind of representation? One might of course claim that Descartes was a genius of sorts, and that a genius was needed to come up with this idea. History, however, has not been short of geniuses, and yet it was Descartes who first understood this possibility, so this response is insufficient. We need to understand what was special in Descartes’ circumstances that made the idea of representation by correspondence accessible to him. The answer I suggested in my book (section 3.3) was that Descartes transferred the idea of such a representation from analytic geometry to the theory of perception. In analytic geometry, algebraic entities represent geometric ones, and vice versa. This representation is of course devoid of any resemblance, while the different domains have corresponding structures that enable the representation. Accordingly, the idea of representation by correspondence was available to Descartes from his work in analytic geometry. In mathematics, work done during the last decades of the sixteenth century prepared the ground for the development of analytic geometry, which was indeed developed independently by Descartes and Fermat in the sixteen-twenties (Ben-Yami 2015, 241, note 20). However, the treatment of the subject in my book left much work to be done. I did not trace there the development of Descartes’ mathematical thought in a way which shows that the idea was available to him by the time he developed his theory of perception, and neither did I show in detail how the transfer of the idea from one domain to the other was accomplished. This is what I intend to do in this paper. Descartes’ mathematical thought developed gradually. We find him working on mathematical problems and methods quite early, in November 1618, following his meeting with Beeckman, but this does not mean that the developed techniques of his 1637 Geometry, their articulation and their application to complex problems occurred immediately. For instance, Descartes tried to solve Pappus’s problem, which plays a central role in his Geometry and in demonstrating the power of his method, only in late 1631, after the Dutch mathematician Jacobus Golius had urged him to do so (Shea 1991, 60; Sasaki 2003, 3 and 206–7). Moreover, the stages of the development of Descartes’ mathematical thought are controversial (see e.g., Rabouin 2010). His mature theory of perception, on the other hand, is already present in The World, which he started writing in 1629. To defend the thesis of this paper it needs to be shown that his understanding of representation by correspondence had been developed before that time. The use of a technique and its clear conceptualisation do not necessarily arise together. In fact, one often acquires the former, albeit possibly to a limited degree, before the latter, and can describe it only through reflection on its existing use, a description that can then contribute to the technique’s improvement. We should therefore expect that these stages might be found in Descartes’ writings as well. Yet, as we shall see, both the technique and its articulation had been fully developed before Descartes started to work on The World. Recourse to analytic geometry in order to explain the origin of the idea of representation by correspondence without resemblance might seem to introduce redundant complexities: hasn’t language been available to Descartes, demonstrating this sort of representation? Moreover, doesn’t Descartes use language to demonstrate this very idea of representation, already on the first pages of The World (AT 11, 4)? — I think that Descartes did not think of language as a representational medium, and that in the mentioned passage in The World he is arguing for a different point, namely, the possible lack of resemblance between cause and effect, as is also clearly seen in its later reworking in the Principles of Philosophy IV:197. Since I argued for this in detail in (Ben-Yami 2021), I shall not discuss it again in this paper.