It is a well-known fact that Peirce treated visual perceptions as results of unconscious inferences (Hull 2017, p. 150). On his view, any percept is essentially a product of a long history of gradually habitualized, piecemeal adjustments and readjustments to the ever-changing environment. Every visual experience, considered as such readjustment, Peirce says, is “constructed at the suggestion of previous sensations,” all of which are “quite inadequate to forming an image or representation absolutely determinate” (W2: 235). Peirce’s overall conclusion here is that “when we see, we are put in a condition in which we are able to get a very large and perhaps indefinitely great amount of knowledge of the visible qualities of objects” (W2: 236; emphasis added). All this knowledge is constitutive for our vision, and yet what it represents cannot become an object of perception in its entirety as a set of fully determinate particulars. This means that, in order to see and make perceptual judgments, we need to be able to lay stress on some features and drop some others. This inferential selectiveness of vision results from a process that is beyond our conscious control. During the construction of mathematical diagrams, the same selective process takes place, but in this case, we carefully and attentively skeletonize whatever is available within our visual field. Diagrammatization, which, according to Peirce, plays a prominent role in mathematics, is, therefore, inevitably (albeit in a somewhat different vein) performed in every act of vision. The selectiveness of perception also implies that, as Peirce has it, we cannot but admit that “either we perceive some indeterminate properties or we perceive nothing at all” (Wilson 2017, p. 16). Whatever is dropped out from our direct awareness still remains within our perceptual field and plays a constitutive, if not entirely realized, part in our visual integration.
