Has the Aristotelian “resemblance theory”
of representation been abandoned, when we embark on a computational analysis of
cognitive processes? This question came to my mind when reading Geir Kirkebøen’s
excellent article on “Descartes’ psychology of vision and cognitive science”
(1998). I stumbled upon it after Fodor’s modularity book had sent me to reading
texts on computational neuroscience and I came across David Marr’s influential
book on vision (1982). It appeared posthumously after his death of leukaemia
only at the age of 35. A reprint of the book has been issued quite recently.
There are several good reviews of Marr’s conceptualisations. Kirkebøen traces the historical antecedents of Marr’s view and demonstrates
its similarity with Descartes’ theory of vision. This article, once again,
demonstrates the immeasurable value of a historical approach to the theoretical
issues of psychology. If you can get hold of this article, do read it.
Kirkebøen argues that Marr’s computational understanding is a
restatement of Descartes’ solution to the problem, how res
extensa can become res cogitas. Descartes
showed that extension (a “picture” on the retina) is transformed into
mechanical movements in the optical nerve by a computational process that
models two-dimensional objects like his analytical geometry modelled Euclidean
forms. This seems indeed to be the end
of the “resemblance theory” of representations, as Fodor pointed out.
However, the idea that our visual
perception uses algorithmic procedures to generate three-dimensional
perceptibles from two-dimensional sense data does not abolish the problem of
the relationship between the source and its retinal imprint. Oron Shagrir’s recent (2010) commentary on Marr’s
theory is helpful here. The following quotations are terminologically difficult
for us who are not trained in the language of computational neuroscience, but I
believe you can recognise the point:
“In the case of edge detection, Marr (1982, 68ff.)
refers to the constraint of spatial localization, which means (in this context)
that the things in the world that give rise to intensity changes are spatially
localized… Another pertinent physical fact is that intensity changes in the [retinal] image result from “surface
discontinuities or from reflectance or illumination boundaries.” (Shagrir,
2010, p. 488)
“Marr’s explanation appeals to similarity between the
internal mapping relations and external relations between the features that are
being represented. The similarity is not at
the level of physical properties. After all, the physiological
properties of the brain are quite different from the physical and optical
properties that make up our visual field. The similarity is at a more abstract
level of mathematical properties.” (p. 489)
“Thus, Marr not only demonstrates that the internal
mathematical function correlates with the contingent world that we live in. He
also underscores the basis of this correlation, which is a similarity of
mathematical structures. This mathematically based similarity, I maintain, is
the key in addressing the appropriateness problem…” (p. 489)
Shagrir does not refer
to Kirkebøen’s paper
and is perhaps not familiar with it. The second quotation, however, reproduces
almost literally the Cartesian solution to the difference between the optic
imprint and the physiological properties
of the brain. The similarity is established by mathematical modelling.
To me this is a restatement of the resemblance theory. It is still about “form
without matter” even if the form is not any more understood in pictorial terms. Shagrir also restates Aristotle's idea that vision is about distinguishing light from darkness.
