From the Tree to the Labyrinth (94 page)

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).

16

The Definitions in Croce’s
Aesthetic

It may seem odd to include a critique of Benedetto Croce’s
Aesthetic
in a collection of essays devoted to the history of semiotics and the philosophy of language. But, apart from the fact that the full title of Croce’s work
(The Aesthetic as the Science of Expression and of the Linguistic in General)
¹
entitles us to speculate on what “linguistics in general” might mean for Croce, the present chapter will deal for the most part with the lack of precision of the definitions on which the
Aesthetic
is founded. In a volume that opened with a critique of the most venerable model of definition (the Porphyrian tree)—whose inability to define we attempted to demonstrate, but to which we must at least grant an almost heroic effort of logical rigor—we feel duty bound to examine a theoretical work which undermines its own project through the dramatically approximate nature of the definitions it pretends to provide.

Rereading the
Aesthetic
today, we encounter a number of ideas that have become part of received wisdom, as well as the record of a series of battles lost from the outset. Among the latter, this is not the place to tackle the indefensible equation between aesthetics and “linguistics in general,” a paradox of such proportions as to call for a separate treatment of its own.
²
What seems to me more urgent is an examination of Croce’s theory of intuition, not just because this is the first topic the work addresses, but because with it Croce intends to lay the cornerstone of his entire system.

1. The book’s incipit asserts that knowledge takes two forms: it is either intuitive or logical, and, consequently, knowing means producing either representations or concepts. But, after passing in review several traditional woolly notions regarding the nature of
intuition,
Croce confronts the problem himself, not by definition but by example: “the net result in the case of a work of art is an intuition” (p. 2). The procedure would be incorrect if it was Croce’s intention to demonstrate what art is, taking the notion of intuition as his starting point; but in fact his intention is to demonstrate what intuition is, taking as his starting point the experience we have of art. Even in this latter case, we would simply have gone from example to antonomasia, if it were not for the fact that the antonomasia in fact conceals an absolute identity.