What’s the image all about?
From Emptiness to Possible Possibility
to Something
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Allow me to go to the beginning,
whenever and wherever that might have been within some timespace
singularity. There is the C. S. Peirce tripod (Figure 1). Yes, a tripod. Why?
Because Peirce was a triadophobe—some might
say a triadomaniac—but we can’t dwell on this aspect
of Peirce (for further see C. Hookway, Peirce, Routledge,
1985). Again, why a tripod? Because of its three-dimensionality on a
two-dimensional plane (we live in a 3-D world but textuality
is limited to 1-D linearity on a 2-D plane).
Because its three legs afford a premonition of broken symmetry, having
evolved from a mere point or zero to one and then division, or two, and three. Because its legs can—syncopatedly,
when at their best—wobble and waver and flip themselves
around in fluid rather than fixed fashion.
In short, because it is a metaphorical image of what gives the
appearance of structure, yet it is process (in this vein, and if you find
yourself so inclined, you might give the enclosed article, SEMIOLOGY MEETS SEMIOTICS: A CASE OF LINGERING LINGUICENTRISM? a
click, as well as the ‘telegraphically’ suggestive powerpoint
displays, SEMIOTICA.PPT and SYNCOPATION.PPT).
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The tripodal image (Figure
2), in this manner, gives a hint of possibilities for future engenderment of signness. Or better, it gives a hint of possible possibilities, for there is not
(yet) anything at all. There is no more than passage—fluid as it were—beginning with zero, ‘nothingness’, or
‘emptiness’. Zero, like ‘nothingness’ or
‘emptiness’, is in C. S. Peirce’s words, the ‘initial condition, before the
universe existed’; it was not a state of pure abstract being. On the contrary it was a state of just
nothing at all, not even a state of emptiness, for even emptiness is something’
(Collected Papers [CP]: 6.215). As Shakespeare asks in Macbeth, nothing is, but what is not? Perhaps we can say that pure ‘is not’,
‘nothingness’, or ‘emptiness’, is ‘absolute nothing’, ‘absolute emptiness’, if
we can use language at all in this context.
It is like ‘pure zero’, ‘boundless freedom’ (CP: 6.215).
Zero is something you have to write to show that there
is nothing. But deep down we don’t
really like zero; it’s just the fill beside the integers, which are what’s
really important. Zero is the prose that
gives us a hint about what possibly might have been, or possibly will have been. It
is the pause that relaxes, before it puts things into action. ‘Things’ and ‘action’. Now we’re getting down to the nitty-gritty
real world of everyday living.
Mathematicians study zero as that which is devoid of numbers, but that
which can give rise to the engenderment of any and all numbers. Geometers study the ‘zero space’ that their
figures don’t occupy, and topologists study knots by exploring the spaces where
the knots are not. What is not in the knot
is more important than what the knot is,
for without the is not, there is no is, no knot.
‘Nothingness’. Like zero, when it changes, it vanishes into
something. ‘Nothingness’ is presumably
perfect, and thus not very interesting.
According to a current theory, the universe started with a perfectly
symmetrical virtual nothing, and then it became meaningful as something, or
better, as what is becoming something
other than what it was becoming. In this sense, contemporary physics tells us
that you can get something from ‘nothingness’, contrary to Lewis Carroll’s
White Queen, and to Shakespeare’s King Lear.
In fact, just as zero engenders all numbers, so also the original
‘nothingness’ contains the wherewithal for engendering everything.
In Figure 2, zero fades into the ‘empty set’ (the
noticed absence of something that was,
or in the future might be), and then
to a possibly possible singularity, Ö·, to a choice between one thing (+) and
its other (-), and to
mediation (y) of one
thing and its other as well as mediation of that selfsame mediator with
them. During this process, ‘emptiness’
morphed into mere possible possibility
and mediation of the implication of that possible
possibility by a mediator that is, itself, part of the process just coming
into the initial stage of becoming (for perhaps some insight on this topic in equally
‘telegraphic prose’, try clicking ZERO.PPT
and MEDIATION.PPT, if you wish).
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And why the Ö·? And the + and the -, or ±? The sign, Ö·, is
tantamount to the imaginary number, Ö-1, or to be
more explicit, ±Ö-1.
Just as the imaginary number is a possibility
that stands hardly a chance of becoming actualized
in the real physical world of concrete, practical everyday living, so also Ö· and some possibility (+) and that possibility’s counterpart (-)and mediation
(y) of both of them, can hardly become a
meaningful sign as long as they remain unactualized. But the beauty of possible signness, is that in many
cases—though by no means all cases—the possible
signness can enter into the process of signness-becoming. So much for possibilities (you might peruse MIDDLEWAY.PPT
first, and then NAGARJUNA.PPT).
How can signness-becoming begin? By drawing
a distinction that separates something from something else, + from -, right from
wrong, good from evil, and so on. Once a
distinction has been made, is whatever became and what didn’t become or
shouldn’t have become set in concrete?
Of course not. There is always
the possibility, from the third leg
of the tripod, by way of mediation,
or the ‘middle way’, of something else, something spontaneous, fresh, and new,
to begin its becoming.
Consider an oval and a line dividing one half of it from the other half
(Figure 3). We have something (A) and
something else (B), or A and Not-A, and the necessary line of demarcation
between them. But what is the line? Is it A?
No. Is it B? Negative also. But as Not-A it has something in common with
B: it is Not-A. And as Not-B it has something in common with
A: it is Not-B.
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In a manner of
speaking, then, it is both A (as Not-B) and B (as Not-A) as a result of this
sharing quality; and yet it is neither A nor B, for it is Not-A and it is Not-B. It
is both, contradictorily or inconsistently speaking, and it is neither,
incomplete, deficiently, or unfinishedly speaking,
because there is the possibility of
something else emerging from the line of demarcation (which, like any line,
geometrically speaking, it is made up of an infinity of infinitesimal points or
‘nothings’ or ‘emptinesses’, so to speak). In other words, the line is in a
two-dimensional sense tantamount to Ö·, as a visible or symbolic simulacrum
emerging out of ‘0 à Æ à…’, or
‘emptiness’, and the ‘empty set’ (for the pragmatic nature of the ‘empty set’,
you might click on IT.PPT). Just as a solitary point can give rise to the
becoming of a line, a line can give rise to the becoming of a plane, a plane
can give rise to the becoming of a cube, and a cube can give rise to the
becoming of a four-dimensional hypercube, so also the ‘semiotic tripod’ as possible possibility can give rise to
the becoming of signness
(for a study in interdimensionalities, see KLEINBOTTLE.PPT, GODELCOMPLEXITY.PPT, and NEWGODEL.PPT).
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Thus we have
the tripod as a model of signness-becoming fleshing out the three Peircean sign components (Representamen, Semiotic Object, Interpretant) (Figure 4), the
three categories of sign processes, physical world processes and mental
processes (Firstness,
Secondness,
Thirdness)
(Figure 5), and learning about signs, the world and the mind, and Peirce’s
three modes of discovery, from possibility
to actuality to provisional knowing, as seen in their corresponding images (Figure
6). Notice that in the latter two
tripods, Alethic,
Ontic, and Epistemic (Figure 7) are no more than
what is possible (possibly both true and false),
what is tentatively either true or false, and what is indeterminate (neither true nor false), for some alternative always stands a chance of emerging
into the light of day (these figures carry the implication of the ‘0 à Æ à Ö· à + à - à y à …n’
progression, the whole concoction of which might be in the Peirce sense labeled
‘cosmology’ (with respect to which you might entertain the notion of clicking COSMOLOGY.PPT).
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Notice, moreover, how the legs of the tripod mesh with
that which can become (creatively, improvisingly,
spontaneously) conjectured (or abduced (or abducted, through abduction) to appropriate Peirce’s third element of logic to
complement the classical logical terms, induction
and deduction) (Figure 8). What is conjectured, is, at the moment of the
conjecture, possibly both true and false. But, in the most
successful of possible worlds, it stands a chance of becoming a part or the
whole of a world version, that which might be conventionally considered under
no uncertain terms either true or false, even though as in the case of
any and all worlds version, it can be no more than tentative. It must be considered tentative, for knowing
is no more than provisional, for during some unexpected moment, some
alternative to an apparently irresolvable problem might be in the process of
emerging into the light of day.
Notice, in addition, that the central image appearing
at the initiation of this webpage begins, significantly, with the Yin-Yang
symbol, that ‘contradictory complementary coalescent’ liquid, flowing whirlpool
giving rise to all that is becoming something other than what it was becoming
according to Dao philosophy. Notice how
the two-way arrow leads from the Dao symbol to the tripodic
possible possibility of signness, and how
on the right side of the image we have the Dao centered symbol—significantly,
three-way rather than two way—of the becoming of signness, from Representamen or sign (R), to Semiotic Object (O), and to Interpretant (I).
And notice how the large central sphere offers a sense of the tripod in
terms of elongated ovals depicting Firstness, Secondness and Thirdness.
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Finally, notice how, in the large central sphere of
the image: (1) the solitary oval,
depicting Firstness, bears the idea of possibly both one alternative and
another alternative (+ and -), (2) the Secondness oval depicts either
one of the two alternatives or the
other one having been selected and a mark of distinction having been drawn in
order to honor the classical logical either/or
imperative intact, at least provisionally, and (3) the Thirdness
oval gives an idea that, in the long run, neither
the one alternative nor the other
alternative is capable of establishing carved in granite certitude and
indubitable knowledge, but rather, some other possible alternative might find itself seeping up from the
erstwhile mark of demarcation to bring about the emergence of something new
(see DAOWATER.PPT).
The sphere of Firstness can
be qualified as overdetermined,
since, given the virtually inexhaustible range of possible possibilities, at different times and places what would
otherwise be considered contradictory or inconsistent alternatives can find a
happy resting place within the sphere of Secondness. The sphere of thirdness
can be qualified as underdetermined,
since between one alternative and another one, and perhaps another one, and so
on, some hitherto unknown alternative might slither up to make its presence
known (for the set of terms, overdetermined and underdetermined,
and relevant Peircean terms, vagueness and generality,
and Gödelian inconsistency
and
In order to encapsulate this whole shebang, allow me
to suggest an all-encompassing image (Figure 9). It suggests a sign with subscripts ‘X-1’ and
its alternative, and another sign, with subscripts ‘X’, both of them having
emerged from ‘0 à Æ à + à - à Ö· à y’ as the possible possibility of signness. The two
signs in the oval are distinguished by a line of demarcation, which allows for
the emergence of one or more of a virtually unlimited number of overdetermined possibilities one of which might take the
place of one of the underdetermined signs that up to that juncture had been
considered qualifiable as legitimized knowing (you
might look at GALEANO.PPT and ONTHEFRINGE.PPT).
And we are back to the beginning. That is to say, we have journeyed from zero
to the empty set to the possible
possibility of signness
to signs becoming signs, and ultimately, if indeed we might wish to consider
ourselves more than mere finite and tenderly fallible human animals, we might
create for ourselves a sense of our having encompassed the entire universe of
signs, our world version and all other world versions to boot, in the past, at
present, and as possibly possible
future world versions. As such, we find
ourselves within the entire concoction of world versions and at the same time
it will be as if we were outside, holding this entire concoction in our
conceptual embrace. These world
versions, including and at the same time excluding ourselves, will be
comparable to George Spencer-Brown’s words in Laws of Form (E. P. Dutton, 1979, p. 105):
We may take
it that the world undoubtedly is itself (i.e. is indistinct from itself), but,
in any attempt to see itself as an object, it must, equally undoubtedly act so
as to make itself distinct from, and therefore false to itself. In this condition it will always partially
elude itself (in this vein, you might take another look at COSMOLOGY.PPT).
Thank you. I have genuinely appreciated your patience.
floyd merrell