From the Tree to the Labyrinth

15

The Threshold and the Infinite

Peirce and Primary Iconism

This essay was written in response to a number of objections raised by the section in my Kant and the Platypus (hereinafter K & P) in which I proposed the notion of “primary iconism” to explain the perceptual processes. I hypothesized a starting point or primum, which was at the origin of all subsequent inferential processes. The fact that I insisted on this point reflected a concern first evidenced in 1990 with my Limits of Interpretation and which became clearer in philosophical terms in the opening chapter of K & P, where I postulated a “hard core of Being.” The nucleus of my thesis was that, if and precisely because we are arguing for a theory of interpretation, we cannot avoid admitting that we have been given something to interpret.

Let me make it clear from the outset, if it were not already obvious, that the primum that forms the starting point for any interpretation may also be a previous interpretation (as when, let’s say, a judge interprets the statements of a witness who gives his own interpretation of what took place). In such cases too, however, the previous interpretation (to be interpreted) is taken as a given, and that, and nothing else, is what is to be interpreted. If anything, the interesting problem is why the judge decides to start from that particular piece of evidence and not another. But this is precisely the theme of what follows.

15.1. Peirce Reinterpreted

Having made that clear, let me recap briefly what I said in K & P. First of all, I put this whole discussion into a section (2.8) entitled “Peirce reinterpreted.” This title was ambiguous since it could be understood in two different ways: as just one more interpretation of Peirce’s theory (but such, naturally, as to present itself as the only faithful and trustworthy reading) or as a free reformulation of some of Peirce’s suggestions.

The fact that what I was proposing was meant in fact to be a reformulation ought to have been clear from the section’s beginning, where I reminded the reader that Peirce, in endeavoring to steer a course between Ground, perceptual judgment, and Immediate Object, was attempting to solve, from the standpoint of an inferential view of knowledge, the problem of Kantian schematism. Since, however, Peirce himself had given not one but several different answers, I felt authorized to come up with one of my own, without claiming it was his. In fact, I wrote: “And so I don’t think it is enough to trust in philology, at least I have no intention of doing so here. What I shall do is try to say how I think Peirce should be read (or reconstructed, if you will); in other words, I shall try to make him say what I wish he had said, because only that way will I be able to understand what he meant to say” (K & P, p. 99).

Suffice it to say therefore that my proposals regarding primary iconism were all my own work and that, not being Peirce, I have the right to think differently from him, so I can’t be accused of saying something that cannot be justified from the standpoint of Peircean semiotics.

As the Italian proverb says, it’s not fair to throw a stone and then hide your hand in your pocket (tirare il sasso e nascondere la mano). Not only were my proposals constantly based on Peirce’s texts, but the problem at issue touched closely on one of the fundamental principles of his semiotics, his anti-intuitionism, a principle with which I am still inclined to agree. Finally, the object of my discourse was precisely that stage of the semiosic process that Peirce called Firstness, and it is undeniable that Peirce identified Firstnesss with the Icon (as he identified Secondness with the Index and Thirdness with the Symbol), and this explains my use of a term like “primary iconism,” despite the fact that for some time now I have been attempting to demonstrate that “iconism” is an umbrella term that covers a range of phenomena differing considerably among themselves.

Reflecting today on what I wrote ten years ago, I believe we must make a clear distinction between “-ists” and “-ologists.” Thinkers who have not created a militant posterity are the objects of straight historiography and philology (of the kind “what did Plato really say?” or “what was Aristotle getting at?”) and the people who write about them are the “-ologists,” if we are at liberty to coin terms such as “Plato-oloists” or “Platologists,” in other words, specialists on Plato. There also exist, however, thinkers of whom many people still declare themselves to be militant followers: hence, there have been and continue to be Neo-Aristotelians, Neo-Thomists, Neo-Hegelians, and Neo-Kantians, and these are the ones I call, for convenience, “-ists.”

What distinguishes an “-ist” from an “-ologist”? The “-ologist,” often engaging in honest-to-goodness textual criticism, is supposed to tell us if such and such a thinker really did say such and such a thing. For example, a Thomologist has to admit that Thomas Aquinas really did say that original sin is transmitted by the semen like a natural infection (Summa Theologica, I–II, 81, 1), whereas the soul is individually created, because it cannot be dependent on corporal matter. (Thomas was a creationist not a traducianist). For Thomas vegetables have a vegetative soul, which in animals is absorbed by the sensitive soul, while in human beings these two functions are absorbed by the rational soul. But God introduces the rational soul only when the fetus has gradually acquired, first the vegetative, then the sensitive soul. Only at that point, when the body has already been formed, is the rational soul created (Summa Theologica I, 90 and Summa contra gentiles II, 89). Embryos have only a sensitive soul (Summa Theologica I, 76, 2 and I, 118, 2) and therefore cannot participate in the resurrection of the flesh (Supplementum 80, 4).

This is what makes a Thomologist. A Thomist on the other hand is someone intent on thinking ad mentem divi Thomae, as if Thomas were speaking today. Thus, a present-day Thomist might develop Saint Thomas’s premises to define lines of ethical conduct with regard to the current debates on abortion, the use of stem cells, and so on.

I still maintain that there exists a third position, between “-ists” and “-ologists,” and the best term I can come up with is that of “reconstructionists.” I take this position because, in my first work of philosophical history, devoted to the aesthetics of Thomas Aquinas, I found myself faced with the following problem: Thomas never devoted a specific text to aesthetics but simply scattered his works with statements regarding the nature of art and the beautiful. If he had had to write a specific text (the hypothesis is not too far-fetched, since for some time a De pulchro et bono, which turned out to be the work of his teacher Albertus Magnus, was attributed to him) or if he had been quizzed about it (then, in his own times), what would he have said, in the light (and only in the light) of the system that was in fact his (as even the “-ologists” describe it)? When one conducts experiments like this, one runs the risk of discovering that any system, subjected to an inspection of this kind, may reveal a few cracks. This is precisely what happened to me in the case of Thomas, in which, while recognizing that he had an implicit theory of beauty which could readily be reconstructed, I finally pointed out an aporia to be found in his system (precisely when that system was faithfully interpreted, as an “-ologist” ought to interpret it).

I am still pleased with the vaguely Gödelian flavor of that conclusion, but the purpose of this whole preamble is to say that in K & P I had made the “-ist” choice, while the objections subsequently brought against me (see section 15.2) were aimed at reconstructing the problem from an “-ologist” point of view.

My starting point was in fact a suggestion made by Armando Fumagalli (1995: ch. 3), who saw in the post-1885 Peirce an almost Kantian return to the immediacy of intuition, antecedent to any inferential activity (the Ground is no longer a predicate but a sensation, and indexicality becomes the kind of experience which takes the form of a shock; it is an impact with an individual, which “strikes” the subject without yet being a representation). In this connection, I attempted to say why precisely Peirce’s Firstness was exactly that, a “firstness” (primità), a sort of auroral moment that gives rise to the perceptual process. Speaking of the Ground, Peirce informs us that it is a Firstness, and if on occasion it has been interpreted as “background” or “basis,” or “foundation,” it is certainly not so in an ontological sense but in a gnoseological one. It is not something that presents itself as a candidate to be a subjectum, it is a possible predicate itself, more like the immediate recognition expressible as “red!” (comparable to the response “ouch!” to a blow that causes pain) than like the judgment expressible as “this is red.” In that phase there is not even something that resists us (this would be the moment of Secondness), and at a certain point Peirce tells us that it is “pure species,” in the sense of appearance, aspect (cf. Fabbrichesi 1981: 471), and he calls it icon, semblance, likeness.¹

Peirce says that the idea of the First is “so tender that you cannot touch it without spoiling it” (CP 1.358). The Firstness is a presence “such as it is,” a positive characteristic (CP 5.44), a “quality of feeling,” like a purple color noticed without any sense of the beginning or the end of the experience, it is not an object nor is it initially inherent to any recognizable object, it has no generality (CP 7.530). Only when both Secondness and Thirdness come into play can the interpretive process begin. But Firstness is still “mere maybe” (CP 1.304), “potentiality without existence” (CP 1.328), “mere possibility” (CP 8.329), and in any case the possibility of a perceptual process (CP 5.119), something that cannot be thought in an articulate way or asserted (CP 1.357). Elsewhere, by feeling Peirce means “that kind of consciousness which involves no analysis, comparison or any process whatsoever, nor consists in whole or in part of any act by which one stretch of consciousness is distinguished from another, which has its own positive quality which consists of nothing else, and which is of itself all that it is” (CP 1.306).

I thought I had recognized that, though this Firstness had the character of a nonmediated apprehension, it still could not be assimilated to Kantian intuition: it is not at all an intuition of the manifold offered by experience, but instead something absolutely simple, that I tried to assimilate to the phenomenon of qualia (cf. Dennett 1991).

Apropos of a quale Peirce is still not talking about perceptual judgment but about a mere “tone” of consciousness, which he defines as being resistant to all possible criticism. Peirce is telling us not that the sensation of red is “infallible,” but simply that once it has been, even if it was an illusion of the senses, it is indisputable that it has been. In this connection I gave the example (and it wasn’t meant to be flippant) of the housewife in the commercial, who declares: “I thought my sheet was white, but now that I’ve seen yours …” Seeing the detergent commercial, Peirce would have told us that the housewife initially perceived the whiteness of the first sheet (pure “tone” of awareness); then, once she had moved on to the recognition of the object (Secondness) and set in motion a comparison packed with inferences (Thirdness), she was able to declare that the second sheet was whiter than the first. But she could not cancel out the preceding impression, which as a pure quality has been, and therefore she says: “I was sure [before] I had seen something white, but now I recognize that there are different degrees of whiteness.” Only at this point, reacting to the album (white) of at least two different sheets, has the housewife moved on to the predicate of the albedo (whiteness), that is, to a general which can be named and for which there is an Immediate Object. It is one thing to perceive an object as white, without having become aware as yet that we are dealing with something external to our awareness, and it is another to perform the prescission whereby one predicates of that object the quality of being white.

But how are we to justify the fact that the starting point of all knowledge is not inferential in nature, because it is immediately manifest, without being open to discussion or denial, when Peirce’s entire anti-Cartesian polemic is based on the assumption that all knowledge is always inferential in nature?

15.2. Peirce and the Coffeepot

In his doctoral thesis Claudio Paolucci (2005) maintains with a wealth of arguments that there is no “realistic” turning-point in Peirce that leads him to consider the possibility of intuitions of a Kantian type, and in so doing he is very polemical in his criticism of both Fumagalli (1995) and Murphey (1961), to whom Fumagalli is referring. Let me say at once that I have no intention of contesting this contestation of Paolucci’s. I simply want to point out that in K & P I wrote: “Fumagalli observes that we have a Kantian return here to the immediacy of intuition, prior to all inferential activity. Nevertheless, since this intuition, as we shall see, remains the pure sentiment that I am confronted with something, the intuition would still be devoid of all intellectual content, and therefore (it seems to me) it could withstand the young Peirce’s anti-Cartesian polemic” (p. 99).

Paolucci still finds this “I am confronted with something” embarrassing, and he writes: “There is no question that Peirce, to describe the formal moment that gives body to the second phenomenological category, describes on several occasions a type of nonmediated relationship between a subject and an individual external object (a haecceitas or thisness). Should this type of relationship turn out to be a cognition (but, as we shall see, it isn’t), it would certainly be correct to speak of a return on the part of Peirce to the immediacy of intuition, since we would be dealing with a cognition not determined by previous cognitions.” Quod est impossibile, if we assume that Peirce always remained anti-Cartesian.

But, in K & P, was I really talking about cognitions?

The position Paolucci has always defended, including in his thesis, is that Peirce’s notion of synechism has to do, not with an amorphous continuum to be segmented (à la Hjelmslev), but with the series of cognitive inferences that, proceeding en abyme, always lead us to make a supposed primum that offers itself to our experience, the point of departure for a subsequent inference (and it is no accident that Paolucci has always appealed in this regard to the principles of infinitesimal analysis). Therefore, every cognitive phenomenon, even the most aurorally primal, must call upon all three categories. Assuredly, there are moments in which Firstness or Secondness seem preeminent, but they are never the exclusive components of the process because any kind of experience always needs to be made up of all three phenomenological categories. How then can we speak of a primary experience?

This is not all, but for Peirce the three categories are not cognitions but formal structures that found the possibility of all cognition (in this sense Peirce was a Kantian), or they are not kinds of experience but pure forms that make up experience. Therefore, if a sensation of redness is an example of Firstness or, in one of the examples I provided at the time, the burning I feel when I touch a hot coffeepot, this Firstness in itself is still nothing from the point of view of my cognitions (a “mere maybe”), and I recognize it as a burn from the coffeepot only if it is immediately placed in relation to Secondness and Thirdness.²

Naturally I agree that, indeed let me remind you that in K & P I made it clear that, even in the face of the immediacy of a quale (a sensation of redness, a burning feeling, the whiteness of a sheet), I can always become aware later, precisely when that Firstness becomes defined as such in the interplay of all three categories, that my first reaction was the result of an error (that I had experienced as red or scorching something that wasn’t), and that I might have received the stimulus in conditions (external or internal) that were such as to “deceive” my nerve terminals. Except that, as Peirce himself made clear, even after recognizing that my senses have been deceived, I cannot say that I have not experienced (let alone “that I have not known”!) a sensation of redness or excessive heat. Going back to the housewife with her sheet, she might say: “A short time ago, after having made my first over-hasty perceptual inference, I entertained the belief [(a cognitive fact)] that I had experienced a sensation of whiteness, upon further reflection however …”

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 of the hole, but with the boundaries of the page, because it is on the page that a letter may be eaten away or even cancelled by the hole. And when I write in my catalogue “with the partial loss of a letter on leaf A6 recto,” it is with the margins of the page and not of the hole that I am concerned.

This might mean that the definition of the limits (and of the relationship of figure to background) is merely a question of negotiation: it is a question of negotiation if I think like a collector and not like an informal artist who wishes to pantograph the hole (or the spot) and would be interested in that case in defining its edges with microscopic exactness. For a theorist of fractals, the edges of the hole could be analyzed en abyme so as to identify their curves and folds beyond any limit conceivable in terms of our normal perceptual habits. But, from my standpoint as collector and bibliophile, I respect the limits of my perceptual abilities, and I consider as undivided something that is, cosmologically speaking, susceptible in posse to further division.

This is also true of the boundary that separates an apple from its outside. Clearly, in terms of subatomic physics, what we have along that borderline, and before it and after it, is a host of dancing particles and not a line. But I was once guilty of an error in this connection. In La struttura assente, arguing against ingenuous conceptions of iconism, I said that a line drawing of a horse in profile, which ought to imitate the properties of a horse, exhibits the one property that a horse does not have, namely, a solid black line that separates the inside of the horse from the outside. I was forced to recant, following the lead of Gombrich (1982), who, correcting a conventionalist position he had taken earlier, observed that if it had once been affirmed that there are no lines in nature and that outlines are a human artifice, psychologists today tend to see them as a perceptual “surrogate” and as “indicators of discontinuity.” In fact “the outlines may serve as an anticipation of the motion parallax effect, because objects within our reach always stand out from their background, but will retain an intrinsic coherence however slightly we move our heads” (Gombrich 1985: 233).

This does not mean that the outline belongs to the horse, because, depending on whether I look up at the horse from a lying position or down from a balcony, I will see different aspects of the horse, and therefore the outline will shift with my point of view; and yet, even though it does depend on my point of view, at the moment when I look, the outline is an objective datum that I cannot ignore. The horse may display an infinite number of outlines, but in that particular respect or capacity it has only one.

Once I have decided to consider the leaf of the book from the collector’s point of view, if I write that there is a hole with the loss of one or two letters or half a letter, it is objectively true that one or two letters or half a letter is missing, and the difference between one or two letters is not a question of negotiation or of infinitely subdivisible borders. Either the letter is missing or it isn’t.

Once the level of pertinence has been decided—or the level of interest with which I focus on things (and in my case I have chosen a molar rather than a molecular level)—not only do nonnegotiable objective impossibilities become evident, but also starting points from which my inferential activity begins.

Let us talk, not about the borderline case of the holes, but about the normal case of the absence of holes. There can be no doubt that if I take a fresh sheet of standard 8.5 x 11 typing paper there are no holes in it. Similarly, if I were to attempt to walk from one room to another without using the door but by going through the wall (or going through the looking glass like Alice), I would come up against the fact that there are no holes (or ways through of any kind) in the paper or the wall or the looking glass. And yet—as one would have to admit from a molecular, if not a molar, point of view—using an extremely powerful microscope I would see in both the paper and the wall an infinite number of holes or empty spaces, just as I am aware that the crystal atoms of the mirror are miniature solar systems with empty interstellar spaces.

The point is that from my own point of view, or in some respect or capacity, those empty spaces are of no interest, and therefore as far as I am concerned do not exist.

15.4. Peirce and the Brain

Whether we call it primary iconism or use some other name, there is something we cannot get around as soon as we introduce an interpreting subject into the process of semiosis. In other words, if primary iconism does not exist cosmologically, it exists for the subject.

Let us take another look at the Peircean concepts. In CP 5.213 it is specified that “the term intuition will be taken as signifying a cognition not determined by a previous cognition of the same object, and therefore so determined by something out of the consciousness.”⁶ If denying all intuition, however, meant denying that everything that happens in our minds is not determined by something outside of our consciousness, we might be tempted to believe that Peirce was opting for a magical idealism à la Novalis. But Peirce does not say “everything that happens outside of our minds”; instead he speaks of cognitions. If someone kicks me and I cry out (and feel pain) can we speak of cognition? I would speak simply of stimulus-response, which is nonetheless something that involves our neuronal processes. Now, Peirce never said that stimulus-response processes are cognitions, or that the stimulus that I feel when kicked does not come from something outside of our minds (or our brain). Can we reasonably speak, without being accused of not thinking ad mentem divi Caroli, of the sensation of pain I would feel if (for example and per absurdum) Paolucci were to kick me in the shins?

Faced with this stimulus, my brain would probably perform processes of whose complexity I have no inkling, as it does when it inverts (as if there were nothing to it!) the retinal image. We can say therefore that processes occur in my neuronal circuit that we may define as inferential or in any case interpretive. But about these processes I know nothing and, just as it seems natural to see Paolucci walking with his feet on the ground and his head in the air, it seems natural to react with a cry of pain to his kick in the shins, even if to invite me to emit it my brain has performed who knows what labor. And that the brain labors to interpret, often making mistakes in interpretation, is proven by the fact that the brains of amputees cause them to suffer painful sensations that appear to come from the limb they have lost. This does not exclude the possibility that the sensation of pain itself (once involved in the triadic process that transforms it into cognition) may take on a semiosic character: it becomes a sign, to be specific a sign of the fact that someone (who through subsequent inferences I will discover was Paolucci) has given me a kick. But as soon as I become aware of pain and cry out, I assume that pain as a point of departure in an upward direction, to find out what it is and what caused it, and not in a downward direction, to understand how my brain processed the external stimulus. I consider that quale beneath a molar respect and capacity.

It is true (see Proni 1990: sect. 1.5.2.3.1, n. 6) that Peirce remains very ambiguous on the definition of sensation, and at times what I am calling the sensation of a quale is for him an impression (in the sense of a nonorganized aggregate of sensorial data), but there is no call (with a thinker who changed his terminology so often) to split hairs over lexical issues. In CP 1.374 it is said that the three categories, though they are imposed by logic and have a metaphysical valency, nevertheless have their origin in the nature of the mind and are “constant ingredients of our knowledge.” Of course, this could be simply meant to confirm that they are transcendental forms in the Kantian sense, and in fact Peirce makes it clear that they are not sensations. But in CP 1.381 he says that “feelings, in the sense in which alone they can be admitted as a great branch of mental phenomena, form the warp and woof of cognition” (emphasis mine), while in CP 1.386 he speaks of feeling as “immediate consciousness,” and something that “arises in a active state of nerve-cells” (emphasis mine). Nor can we forget that from CP 1.374 to 1.394 he speaks of the triads in psychology and physiology.

In short, if Peirce does not speak of sensations, and if he is vague when he speaks of impressions, he nonetheless alludes to states of immediate consciousness (see also CP 1.306). In CP 1.317 he says that “the whole content of consciousness is made up of qualities of feeling, as truly as the whole of space is made up of points or the whole of time of instants,” and in CP 1.318 he writes that these qualities of feeling are “a pure priman.”

I believe (when I read CP 5.291 carefully) that a sensation, insofar as it is recognized as such in an interpretive process, is already a semiosic phenomenon and functions as a hypothesis; but, as pure feeling, “a mere feeling of a particular sort, it is determined only by an inexplicable, occult power; and so far, it is not a representation, but only the material quality of a representation” (emphasis mine). “A feeling, therefore, as a feeling, is merely the material quality of a mental sign” (emphasis in original). What does the material quality of a mental sign mean? It means, I believe, that if I do not consider the word dog as a sign (and therefore, we would argue today, as a composite of expression and content, or signifier and signified), but consider only the phonation dog as it can be physically recorded and played back by someone who does not know English, I find myself faced with the material quality of the sign (the substance of the expression, so to speak), but not yet with the semiotic phenomenon developed and concluded in a representation and an act of cognition. The feeling, then, is not yet a hypothesis but the material occasion offered me or offered to my brain as a stimulus provided to allow it to proceed to the inference. “The hypothetic inference of the sensation is two-thirds written (the premises) by the nature of our sensorial system: it is a hypothesis, but our conscious intervention is limited simply to drawing the conclusion, which is obtained in an automatic manner.… The laws of logic construct the form of the sensation, but its content, that which arrives from without, is not part of it: the feeling is the material quality of the perceptual sign” (Proni 1990: 106).

I believe it is possible to reconcile this idea of the sensation as priman with a nonintuitionist theory of all knowledge as inference. Provided that what I assume to be the initial sensation or stimulus is recognized as such, at the molar level, in the respect and capacity of something that interests me at that moment, independently of all cosmological considerations.

15.5. Peirce and the Tortoise

When reading Peirce, we must not confuse cosmology and gnoseology. As I already remarked in K & P, two different but mutually interdependent perspectives are interwoven in Peirce’s thought: the metaphysical-cosmological and the cognitive. Unless we read them in a semiotic key, Peirce’s metaphysics and cosmology remain incomprehensible. But we would have to say the same thing of his semiotics with respect to his cosmology. Categories such as Firstness, Secondness, Thirdness, and the concept of interpretation itself not only define modi significandi, that is, the ways in which the world can be known: they are also modi essendi, ways in which the world behaves, procedures through which the world, in the course of evolution, interprets itself. In K & P, I cited Mameli (1997: 4): “Given that Peirce thinks and demonstrates that intelligibility is not an accidental characteristic of the universe, that it is not, that is, a mere epiphenomenon of how things are, but a characteristic that ‘shapes’ the universe, it follows that a theory of intelligibility is also a metaphysical theory of the structure of the universe” (K & P, p. 399, n. 28). The theory of intelligibility and metaphysical theory, however, must sometimes be kept separate.

Kant said that the fact that we believe we know things on the basis of the mere evidence of our senses depends on a vitium subreptionis or subreption: we are so accustomed from childhood to grasp things as if they appeared to us already given in intuition that we have never thematized the role played by the intellect in this process. Therefore even what were for him empirical intuitions were already the result of a work of inference.

We can construct a semiotics without a subject or (what amounts to the same thing) in which the subject is everywhere. In this semiotics there will never be a priman because interpretation will proceed by mise en abyme. But, if from the cosmological point of view the inferential process is infinite, because there are no intuitions, we cannot ignore the cognitive instance, that is, that edge of the semiosis that is formed when a subject (any instance capable of saying I that somehow enters into the semiosis from the material and corporal outside—what I am speaking about is a brain) installs itself and touches off a chain of inferences under the stimulus of something that, from its own point of view and only in this precise spatiotemporal segment, attracts its attention.⁷ The I in this case stands on that edge where on the one hand there stands, let’s say, the dog—the thing that interests him at that moment—and on the other hand, everything else—which does not interest him.

In this phase Firstness, as we saw, is a presence “such as it is,” nothing but a positive characteristic, like a purple color perceived without any sense of the beginning or the end of the experience, without any self-awareness separate from the sensation of the color; it is a potentiality without existence, the simple possibility of a perceptual process. In order to contest these qualia that precede any inference, we must take as our point of departure the principle that they constitute an intuitive moment, without our being able to conceive of further inferential processes behind it, in a sort of infinite fractalization. But I would like to remind the reader that the infinite fractalization of a sea coast does not prevent a human subject, who has a molar view compared with the molecular view of an ant, from covering in a single step what would be for the ant an extremely long and tortuous trajectory.

We are back, if you will, to the paradox of Achilles and the tortoise, in which we must take into account the distinction between potential infinity and infinity in act, already present in Aristotle.

In the paradox Achilles must first cover half the distance, but before that he must cover a quarter, and before that an eighth, and so on ad infinitum, so that he will never succeed in catching up with the tortoise. It has been observed, however, that, although this process of fractalization can continue infinitely, its result will never be greater than one—as occurs in any case with irrational numbers, so that 3.14, however successful we may be in analyzing it, will never be 4.

If we apply this argument to the fractal length of a coast, where the potential process of division could be infinite, at least insofar as we can always postulate smaller and smaller microbes, this does not prevent Achilles in practice covering this space with a single stride. Achilles will cover a unit of distance appropriate to him in a unit of time appropriate to him.

Already Aristotle (Physics III, 8, 206) objected to Zeno that, among magnitudes, there exists infinity by addition (I can always find an even number greater than the preceding one) but not by division, insofar as the infinity of the subintervals into which a unit of length is divisible is always contained in a limited totality (never greater than one) which may constitute the object of an empirical intuition.

In other words, if, cosmologically speaking, there is never perhaps a Firstness that is not the result of a previous Thirdness, cognitively speaking there is a limit to our perceptive abilities, which experience as undivided something that, cosmologically speaking, is in posse capable of being further divided. What is in posse belongs to cosmology. What is in actu belongs to the agent subject.

What happens when we put ourselves in the place of a perceiving subject? Zellini (2003: 26–27) reminds us that:

Adolf Grünbaum [(1969)] recently demonstrated that the measured structure of physical time justifies applying the arithmetical theory of limits to the solution of the paradox. Human awareness of time has a base limit of perceptibility, that is, a minimal threshold beyond which temporal intervals vanish into inconceivable smallness. If we consciously tried to contemplate ‘all’ the intervals of the series (a), it would be realized concretely as a countable infinity of mental acts, and the duration of each of these would be larger than the minimal threshold that time allows. But this insuperable ‘minimum’ is an Archimedean quantity: when added to itself infinite times, it yields an infinite result. Consequently, the mental contemplation of the entire series would result in an impossibly unlimited period of time. This would happen, for example, if one ‘counted’ the intervals of (a) one by one, assigning to each of them an ordinal number. This would take more time than the necessary minimum just to conceive or pronounce them. (But it is absurd, Aristotle objected [Physics 8, 8, 263a–263b], to maintain that whatever moves, moves while counting.) In reality, by raising doubts about the possibility of traversing the interval (0–1), Zeno exploits the unacceptable delay that is implied by reducing the series (a) to the corresponding mental acts of the counting process, but he fails to make clear that this process does not reproduce exactly the measurement of the physical time involved in the actual traversal.

Thus, Grünbaum finds Zeno’s argument illegitimate because it uses what is basically an inevitable confusion between two incompatible forms of thought. He explains that we do not experience the intervals into which we subdivide the traversal in any measure that corresponds to their actual nature. Rather, we derive our impression of their duration from the time needed for our acts of mental contemplation, which for each fraction of the distance must perforce exceed our minimal threshold or limit.

In other words, our perception is not mathematical but ingenuous, just as our perception of the supposed movement of the sun is ingenuous and not astronomical. Zellini (1980: 44) reminds us that the existence of a threshold of observability is a postulate both of physics and of the psychology of perception.

Zellini also appeals to Hume: our imagination must be capable of reaching a minimum beyond which we cannot conceive of further subdivisions. We can speak of the thousandth or ten-thousandth part of a grain of sand, but (apart from the fact that we cannot see it—which from the point of view of perception is no small matter) we can’t even imagine it except with the same dimensions as the grain of sand itself: “The idea of a grain of sand is not distinguishable, nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas.”

“Put,” said Hume, “a spot of ink upon paper, fix your eyes upon that spot, and retire to such a distance, that at last you lose sight of it; ’tis plain, that the moment before it vanish’d the image or impression was perfectly indivisible” (Treatise of Human Nature, I, 2, 27) At a certain point, the spot will become invisible, because it is too far away, but when it is on the point of disappearing, it will still be visible as a punctual and indivisible minimum. As is the case for the ideas of the imagination, an ultimate conceivable term is given for our sense impressions, whereby we go directly from nothing to a minimal perceivable reality not resolvable into smaller parts.

Hume might have added that—while it may be true that under the microscope the same ink blot would reveal a universe of bacteria that made it look like a painting by Kandinsky—from the point of view of our perceptual abilities, it is a black spot, nothing more or less.

If it can be granted that for Peirce the Ground is what I referred to as primary iconism, let us bear in mind that the Ground is an element, a marker, a quality that is (for whatever reason) being isolated and considered in itself. By whom is it isolated? Potentially isolable, it becomes isolated when a subject isolates it, from a certain point of view, and at that point it becomes the terminus a quo of an inferential process, in an upward and not a downward direction—toward the series of relationships, in other words, that bind that spot to me and to my perceptual interests, not toward the series of the infinite possible decompositions of the spot itself.

This, it seems to me, is exactly what happens when Peirce tells us that we feel the blackness of the ink as Firstness. It is possible that—to be able to recognize that what strikes our senses is a quality of blackness—the brain deep down performs an immense number of successive operations. I also agree with Paolucci (2005) that, for the empirical concept of dog as well, the Kantian intellect may make use, not of images, but of a flowchart. But, aside from the fact that the brain too, as a computational machine, must come to a stop at a certain point in order to be able to transmit “blackness,” at the level of conscious perception we are not aware of that additional fractalization. There is a threshold on this side of which we perceive or sense “black” as Firstness, primary iconism (or whatever you choose to call it), and that is the starting point for our all subsequent inferences.

Commenting on Hume, William James (1987: 1061) declared: “Either your experience is of no content, of no change, or it is of a perceptible amount of content or change. Your acquaintance with reality grows literally by buds or drops of perception. Intellectually and on reflection you can divide these into components, but as immediately given they come totally or not at all.”

Zellini also cites Wittgenstein (Notebooks, 18, 6, 15):

If the complexity of an object is definitive of the sense of the proposition, then it must be portrayed in the proposition to the extent that it does determine the sense. And to the extent that its composition is not definitive of this sense, to this extent the objects of this proposition are simple. THEY cannot be further divided.…

What I mean is: if, e.g. I say that this watch is not in the drawer, there is absolutely no need for it to FOLLOW LOGICALLY that a wheel that is in the watch is not in the drawer, for perhaps I had not the least knowledge that the wheel was in the watch, and hence could not have meant by “this watch” the complex in which the wheel occurs. And it is certain—moreover—that I do not see all the parts of my theoretical visual field. Who knows whether I see infinitely many points?

Let us suppose that we were to see a circular patch: is the circular form its property? Certainly not. It seems to be a “structural” property. And if I notice that a spot is round, am I not noticing an infinitely complicated structural property?…

A proposition can, however, quite well treat of infinitely many points without being infinitely complex in a particular sense.⁸

Let us attempt a paraphrasis in terms of perception. The complexity of a quale, if it is definitive of the meaning of a perception or a perceptual judgment, must be present and recognized as pertinent to the perception insofar as it determines the meaning of the perception. And to the extent to which the further segmentability of the quale is not definitive for this perception, to the same extent that quale is simple or primary. It is valid as Firstness and there are no pertinent inferential processes below its threshold.

To conclude (seeing that I began with Saint Thomas), I would like to quote Nicholas of Cusa: “Only in a finite fashion is the infinite form received,” Of Learned Ignorance, II, 11).

Originally written for the miscellany Studi di semiotica interpretativa (Paolucci 2007), which collected the contributions presented at the Scuola Superiore di Studi Umanistici of the University of Bologna during the academic years 2004–2005 and 2005–2006. [Translator’s note: Quotations from Kant and the Platypus are from the translation by Alastair McEwen (Eco 2000).]

1. See Peirce, Collected Papers (1931–1958)(hereinafter “CP”) 1:307: “any feeling must be identical with any exact duplicate of it,” and therefore the icon is a likeness, not in the sense that is like something else, but because it is the phenomenon that founds any possible judgment of similarity, without being able to be founded by it. This also explains my choice of the perhaps misleading term, “primary iconism.”

2. Claudio Paolucci recently suggested (in a private communication) that “obviously the burning sensation produced by the coffeepot is a Firstness for Peirce too, i.e., ‘the emergence of something new.’ Except that in Peirce Firstnesses ‘do not spring up isolated; for if they did, nothing could unite them. They spring up in reaction upon one another, and thus in a kind of existence’ ” (CP 6.199). The emergence of the Firstnesses through their being opposed to one another (Secondness) starting from the regularity of the habit (Thirdness) for Peirce is an event (CP 6.200), i.e., a singularity, a point at which something occurs.… In this way the spontaneity of Firstness, whose irregular and singular nature Peirce underlines (CP 6.54), turns out to be nothing other than an infinitesimal deviation from the law and from the regularity on whose basis it is produced (CP 6.59). Peirce calls habit, or Thirdness, this very regularity starting from which it is possible to generate the singular spontaneity of the Firstnesses in their opposition to one another (Secondness).… In other words, somehow, the very spontaneity of the event, of the emergence of something new (Firstness) is nothing but the habit of a regular series (Thirdness) which differentiates itself at certain given points: the singular emerges from the regular from which it detaches itself as a consequence of an instability effect.… In this way, since, as Peirce says, Firstnesses do not occur in isolation, the feeling of pain that emerges in the example of my morning coffee (Firstness) is a quality that emerges from a background of experiential habits (getting up in the morning, picking up the coffeepot, putting it on the burner, not turning the gas up too high, placing the coffeepot in just the right place: a whole syntax of habits and regularities of everyday experience). So the sensation of pain (Firstness) arises against a background of habits (Thirdness) that did not imply it (it is not regular to encounter pain in the breakfast scenario) and pain can only arise in opposition (Secondness) to this background of habits. So, even on the cognitive level, we find the pattern of the Logic of Relatives: on the basis of a series of regularities and habits that define the laws of my morning breakfast (Thirdness), a tendency to be distinguished from it may be created, out of which something new emerges, something for which the regularity of the local system does not make allowance. Firstness is an event of this kind, which arises in opposition (Secondness) to a regular background of Thirdness.”

3. Varzi (2005) returns to themes previously discussed in Smith and Varzi (2000: 401–420). [Translator’s note: The Phantom Blot is a Walt Disney character (Macchia Nera in Italian). He is an archenemy of Mickey Mouse and first appeared in the comic strip Mickey Mouse Outwits the Phantom Blot by Floyd Gottfredson in 1939.]

4. [Translator’s note: The quotation from Varzi’s article appears in the original Italian in Eco’s text.]

5. Nevertheless, with reference to the Phaedrus, in which Plato recommends that we divide being into species “according to the natural formation, where the joint is, not breaking any part as a bad carver might” (Benjamin Jowett trans.), Varzi reminded us that, if all boundaries were the product of a conventional decision, then our knowledge of the world would be reduced to a knowledge of the maps we have drawn of it (an example of the total substitution of facts by interpretations). But, without postulating a totally realistic solution (according to which the world presents itself to our experience already prepackaged into objects, events, and natural properties), he cited my proposal (from K & P) as a compromise solution: though in different cultures veal may be carved in different ways (so that the names of certain dishes are not always translatable from one language to another), it would be very hard to think of a cut that offered at the same time the end of the snout and the end of the tail. Even if there were no one-way streets in the world, there would still be no-entries, in other words objective limits to our ability to organize the content of experience.

6. Originally published as “Questions concerning Certain Faculties Claimed for Man,” Journal of Speculative Philosophy (1868) 2, 103–114].

7. At this point we might be tempted to open up another can of worms: Why does one thing attract my attention at the expense of another? But reconstructing a theory of attention in Peirce lies beyond my capabilities, and beyond the scope of this chapter.

8. English translation: Wittgenstein (1961: 63e–65e).