Paolucci’s objection is that, given that Peirce denies all power to intuition and asserts that all cognition arises from a previous cognition, not even a unrelated sensation, be it thermal, tactile, or visual, can be recognized (and therefore known) except by bringing into play an inferential process that, however instantaneous and unconscious it may be, guarantees its reliability.
Nevertheless, the problem that ought to interest a reconstructionist (more “-ologist” than “-ist”) is the following: Is it possible that a sensible person like Peirce should deny that in some fashion the inferential process that leads me to say “I burned myself by touching the coffeepot” arises from a sensation of scorching that compels me (like any other animal) to withdraw the limb from the point of stimulus, even before recognizing it as something other than myself that opposes resistance? Furthermore, Peirce could not deny it because his realism, whether Scotist or otherwise, was based on the fact that all knowledge refers to a Dynamical Object that lies outside of myself and my cognitive acts, and precedes every possible inference—even if by chance this Dynamical Object were to remain forever unattainable, multiplying itself into an infinite series of Immediate Objects. Peirce could not deny that the perceptual process seems to begin in a vague and marshy zone between Firstness, Secondness, and Thirdness, and the knot of inferences that leads it to perfect itself in perceptual judgment appears to situate itself after the apparition of something, not before—which is tantamount to saying that in order to interpret there must be something there to interpret, otherwise we would not be Peirceans but Deconstructionists or Nietzscheans (see K & P, sect. 1.9).
How can we, then, from an anti-intuitionist standpoint, according to which all experience is always of an inferential nature, how can we speak of a point where inference begins? Is this primum a primum in absolute terms or it is a primum for me, at that moment, and (to use a Peircean expression) is it such only in some respect or capacity?
The problem, quintessentially Peircean, of the respect or capacity that makes something a sign, licenses me to introduce a distinction between molecular pertinentization and molar pertinentization.
15.3. Peirce vs. The Phantom Blot
In January 2006 I engaged in a debate in Rome with Achille Varzi, inspired by his 2005 essay “Teoria e pratica dei confini,” (“The Theory and Practice of Boundaries”).3 Taking the notion of “boundary” as his starting point, Varzi proceeded to discuss the evident difference between purely de dicto demarcations (like the boundaries between two states) and demarcations we might be tempted to consider de re (like the boundary that separates the inside of an apple from its outside, a human body from what surrounds it, or even life from nonlife or life from death, as is the case in discussions about abortion, stem cells, or euthanasia). Varzi recognized that:
it is not clear what the relationship is between a boundary and the entity of which it is the boundary.… We never encounter points, lines and surfaces in complete isolation. We cannot eat all the three-dimensional parts of an apple and keep only its surface, if by surface we mean, not the peel (which is a solid part), but the perfectly two-dimensional entity that circumscribes the peel on the outside, just as we cannot display in a museum the boundary of our town or the point of intersection between the equator and the Greenwich meridian. Still, this relationship of dependency is reciprocal: neither can we think of an apple without a surface, or a town without boundaries.… Certain entities commence their existence only when a boundary is drawn.4
And, after referring to the uncertain boundary between the water of the sea and the air of the sky remarked on by Leonardo, Varzi got to Peirce (The Logic of Quantity) and to the edge of a black spot on a white surface—a problem that seemed similar to him to the Aristotelian question whether at the precise moment when a body begins to move we should say that the body is at rest or in motion (Physics VI, 234a et seq.).
Varzi remarked, citing Jackendoff (1987), that we might be dealing with asymmetrical configurations in which one of the two entities is a figure in relation to the other which is the background: thus the spot is imposed on the sheet of paper that acts as the background, and so the line of demarcation that Peirce was looking for belongs to the spot not to the paper. The water wins out over the air that acts as the background, and hence the line of demarcation Leonardo was concerned with belongs to the sea. We never have two solid bodies in contact with each other, but always a body inserted into a certain background context, and it is therefore to the body itself that the boundary is to be assigned. Nevertheless, Varzi did not find the idea very convincing:
But what happens when two figures collide? We throw a stone into the sea. The stone is “closed,” and so is the water. How does the stone manage to enter, if two closed bodies cannot even touch each other? And granted that it manages to enter, which of them does the boundary line between stone and water belong to? Are we to say that upon entering the stone opened? That the sea is closed on the outside (toward the air) but open on the inside (toward the stone)? Or let us think of the white cliffs of Dover: it is hard to think of them as a topologically open background against which the waters of the English Channel stand out. This is also because the cliffs stand out in their turn against the sky. Are we to say then that that the cliffs are open along the zone that separates them from the water, but closed for that part of their surface that separates them from the air? And what are we to say of the line along which water, air and rock meet?
If we grant that the water continues to win out, how do the air and the rock manage to touch if they are both open? Obviously something is wrong. The topology of the continuous excludes the possibility of two closed bodies touching, but it also that of two open bodies touching.… The gradual process of dematerialization of matter that has marked the development of modern and contemporary physical theories presents us with a world in which even objects that to us appear perfectly rigid and compact are, if we look closely, swarms of microscopic particles frenetically in motion in the wide open spaces that surround them (the volume of an apple, if by this we mean the material part of the fruit, is less than a thousandth of what we are accustomed to calculate), and the surfaces of these systems of particles are no more smooth and continuous than a fakir’s bed of nails.
If this is how things are, it makes no sense to speak of contiguous objects separated by a common boundary line. It makes no sense to ask ourselves to which of them the boundary between two objects belongs. There are only dancing particles, and if we really insist on insisting, we will say that each of them must have its own boundary that separates it from the void: there is nothing else that can claim its possession. Put in another way, if we look closely, the spatial boundaries of common physical objects are imaginary entities whose form and localization involve the same degree of arbitrariness as the lines of a graph based on a limited amount of data, the same degree of idealization as a drawing obtained by “following the dots” on the page of a puzzle book, the same degree of abstraction as the outlines of the figures in an Impressionist painting. To ask ourselves who or what these lines belong to makes no sense, or it makes sense only if we conceive of them as abstract boundaries drawn by our unifying action, de dicto boundaries which, as such, may well be undetermined, as we have seen.
Varzi seemed to me to be tending toward an overconventional vision of the notion of boundary, going so far indeed as to extend the de dictu modalities to cover all those that were presumably de re.5 Still, in the course of the discussion that ensued, I accepted the idea that “even what are for us the most salient events and actions, that seem to be defined by de re boundaries, emerge upon further consideration from an intricate system of underlying processes that we select and unify according to laws that reflect our cognitive biases.” The problem of cognitive biases seems to bring us back to the difference between molecular and molar.
It is certainly difficult to define the boundaries of a black spot on a white sheet of paper, just as it is difficult to define the boundaries of a hole. Granted, it is usually the body that is topographically closed while the background remains open. But who decides which is the body and which the background? As a collector of rare books, I know that, when I come across a wormhole in the page of an incunabulum, I am concerned, not with the boundaries
