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<p class=MsoNormal align="center"><b><span style='font-size:16.0pt;font-family:"Times New Roman",serif'>
Kant </span></b><i><span style='font-size:16.0pt;font-family:"Times New Roman",serif'>is
to</span></i><b><span style='font-size:16.0pt;font-family:"Times New Roman",serif'>
Gödel <i>as</i> Hegel </span></b><i><span style='font-size:16.0pt;font-family:
"Times New Roman",serif'>is to</span></i><b><span style='font-size:16.0pt;
font-family:"Times New Roman",serif'> Turing<br>
</span></b><span style='font-family:"Times New Roman",serif'>
<br>
- Adriraj Talukdar, Swagato Saha</span><b><span style='font-size:16.0pt;
font-family:"Times New Roman",serif'><br>
<br>
<br>
<br>
<br>
</span></b><b><span style='font-family:"Times New Roman",serif'>Foreword:</span></b><span
style='font-family:"Times New Roman",serif'> <i>This marks the beginning of a
consolidated effort and requires the reader to be somewhat familiar with the
work in previous issues, or better still, directly with the theories and the
theorists concerned. This is something we will be coming back to in future
issues as well, from time to time, until we are convinced otherwise that the
formula is wrong. <br>
We have each decided on a category of our choice that we believe best describes
the formula. As such, there is a shared premise although it may not be all that
apparent to begin with.</i> </span><b><span style='font-size:16.0pt;
font-family:"Times New Roman",serif'><br>
<br>
<br>
</span></b><b><span style='font-family:"Times New Roman",serif'>Part 1 </span></b><i><span
style='font-family:"Times New Roman",serif'>(by Adriraj Talukdar)</span></i><b><span
style='font-family:"Times New Roman",serif'>: </span></b><b><span
style='font-size:16.0pt;font-family:"Times New Roman",serif'><br>
</span></b><b><u><span lang=EN-IN style='font-family:"Times New Roman",serif'>Mind,
Machine & More:</span></u></b><b><span lang=EN-IN style='font-family:"Times New Roman",serif'>
</span></b><span lang=EN-IN style='font-family:"Times New Roman",serif'>What
came first, a chicken or a chicken’s egg? Well, one way to answer this is that
chickens emerged from some ancestor species and they laid eggs before chickens.
But the question then will be – was it a non-chicken egg that gave birth to the
first chicken or was it a non-chicken that laid the first chicken egg? In other
words, the problem is to identify what is a chicken’s egg – an egg laid by a
chicken or an egg from which a chicken will emerge? Any answer to this question
is simply a case of fixing a definition. And this riddle, I might say, only is
established once in our notional order, the circularity of chicken and egg is
established. In fact, a question can be asked only within an already fixed
language or episteme and in different epistemes the answer can be different. It
is not to say that there is no one truth, but that answers can be formulated in
different ways, depending on the course of discourse.</span></p>
<p class=MsoNormal><b><span lang=EN-IN style='font-family:"Times New Roman",serif'>Formal
Knowledge:</span></b><span lang=EN-IN style='font-family:"Times New Roman",serif'>
For unambiguous answer to any question, one must first state the question
unambiguously. That is why, in any field of study, a basic form of language is
to be determined. It is also required to begin with a least number of
assumptions, namely the axioms of that formal language. A formal system ensures
that with the primitive rules and axioms, any statement within that language
can be derived in a definite method, independent of individual understanding.
Philosopher Immanuel Kant elucidated how human mind understands the world with
the help of a formalism innate in our mental faculties. He said that we cannot
reason in void. Our senses perceive sensible data and then the data is
synthesized in our minds to form our knowledge. But then, this synthesis
requires a set of rules a priori in our mind, namely the synthetic a priori.
Kant categorised statements in two ways. (i) Statements in which the subject
contains already the predicate is called an analytic statement (e.g. - a
quadrilateral has four sides) and a statement that is not analytic is synthetic
(e.g. - cats have four legs). (ii) A statement whose truth is not required to
be proven by experience is called a priori (e.g. - A red flower is not
colourless) and a statement which is true by experience is called a posteriori
(e.g. - That rose is red). It is easy to see that analytic a posteriori
statements cannot exist. For Kant judgement is not only about purely formal
statements, but logic encompasses general thinking as well. But Kant says that
our knowledge cannot go beyond the horizon of our sensible or rational
possibilities. That is there is a possibility that some knowledge about the
Real is always inaccessible and incomprehensible to us.</span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif'>Kant
also accounts for statements considered to be infinite judgement. As opposed to
the statement “rose is not red” the statement “rose is non-red” is not just a
negation of a predicate, rather it poses rose among infinite possibilities of
everything non-red. Here philosopher G.W.F. Hegel looks at infinite judgement
in a different way. Instead of positing it just as opposed to both affirmation
and negation, Hegel looks at a dialectic development of logical propositions.
The affirmation “individual is general” (e.g. – I am someone) fails to give a
mere complete picture gives rise to its negation – “individual is not general
i.e., particular” (e.g. – I am not anyone). But the negation also fails to be
sufficient and thus sublates onto an infinite judgement – “individual is
individual”; where the individual in predicate has elevated to a general
category itself (e.g. – I am who I am). Thus, for Hegel negation of negation is
not simply back to affirmation, but a more developed judgement.</span></p>
<p class=MsoNormal><b><span lang=EN-IN style='font-family:"Times New Roman",serif'>Incompleteness
and Turing Machine:</span></b><span lang=EN-IN style='font-family:"Times New Roman",serif'>
Given a formal language and a statement in that language, is there a definite
method to decide if that statement is true or not? Such questions are known as
decision problems or Entscheidungsproblem, first posed by Hilbert. The answer
is no. Kurt Gödel first proved that given any formal language rich enough to do
arithmetic of natural numbers, there exist statements that cannot be proven
from the axioms of that language i.e., there are no ‘definite method’ to decide
the truth or falsity of such statements. But what is meant by a ‘definite
method’? Alan Turing tried to define such a method. Since we are dealing with
formal statements, it is not that a human mind using its intuition and
innovativeness tries to tell the truth. Rather the solution must be done by
finite, mechanical steps. Turing proposed such machines (called today, Turing
machines) that can use finite atomic moves and all the steps can be chalked on
a finite table (called a table of behaviour). Although the proposition is
theoretical, it is not the case that the machine cannot be made physically, the
point being to have a definite effective method. Turing used the example of a
teleprinter that can move left or right and can read, write and remove finitely
many symbols or a human who performs one atomic step at once (today one
computer programme can be considered a table of behaviour for a Turing
machine). Given enough time a Turing machine can go on for infinitely many
steps. Turing defined a problem to be computable if such a definite method can
be found on the table of behaviour of a Turing machine dealing with this
problem. </span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif'>Turing
also gave a way to encode the tables of behaviour of Turing machines in
‘description numbers’. Since a Turing machine can use finite many symbols in
finite many moves, one can represent Turing machines by finite many symbols and
likewise enumerate them. He showed that there are countably many Turing
machines enumerated with respect to their description number. Turing gave
simple argument using Cantor’s diagonalisation that no Turing machine can exist
that can decide if a description number is satisfactory. Suppos<span
style='color:black'>e, such a machine exists. Then it can find the nth digit of
the description number of nth machine change it and assign it to the nth digit
of description number of a new machine. This new machine then has a description
number different from all existing machines and thus reaches a contradiction.
Following Gödel, Turing proved this way that there exist problems that are not
computable.</span></span></p>
<p class=MsoNormal><b><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black'>Intuition and the Oracle:</span></b><span lang=EN-IN
style='font-family:"Times New Roman",serif;color:black'> According to Gödel’s
theorem there are mathematical statements that are true but formally
unprovable. Gödel notes that human mind can however determine by intuition the
truth of these unprovable statements. Turing here introduced ordinal logic
where such true Gödel statements can be added to a formal system recursively so
that the system tends toward completeness. Turing proposed an abstract concept
of Oracle machines that by some way determines even an undecidable problem in a
single step. Turing suggested that the oracle machine indeed is a Turing
machine but with an extra configuration. Turing clarifies that this oracle use
is not mechanistic, it is an opaque entity that just delivers the answer.
Turing compares this to the role of human intuition. But unlike an abstract
model of Oracle machines our intuition does not simply states truth value in a
step. Turing was well aware of that<span style='background:white'>. Turing
showed how his argument for the incompleteness of Turing machines could be
applied as well to oracle machines.</span></span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black;background:white'>Gödel’s second incompleteness theorem showed that
no formal system rich enough to do arithmetic of natural numbers can prove its
own consistency. Turing proved that no Turing machine can determine if its
description number is satisfactory. Here one key thing to notice is that both
of them bring self-reference as the rising point of incompleteness. When we
represent a formal system in its own language, we see this representation to be
an undecidable problem. But is not it where our intuition differs from a formal
system? Human mind is capable of thinking about itself as well.</span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black;background:white'>A Turing machine translates a logical problem to
an arithmetic problem. Then the goal is to prove or disprove the statement –
“The consistency statement of this system is true.” It has been proven by
Alfred Tarski that arithmetical truths cannot be defined within arithmetic.
This is because notions like “truth” are not translatable into such formal
setup. But our intuition does not only use language like a machine, it
constructs and acts with the meanings of notions as well.</span></p>
<p class=MsoNormal><b><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black;background:white'>The Form is The Content:</span></b><span
lang=EN-IN style='font-family:"Times New Roman",serif;color:black;background:
white'> Following Kant, Gödel formally proves that there is incompleteness in
logic that is there are always truths unknowable to a formal system. Turing
tries to subvert this problem, but to do so he proposes an abstract oracle
machine which finally in a black box keeps its mechanics unknowable. The
problem can be traced in how such formalisms are structured. First, they begin
with some assumptions and axioms and then a set of rules are defined so as to
act upon the relations between objects in these systems. But human mind is not
just a machine following rules. And to look for answers outside logical system
is to undermine logic which should encompass general thinking as well. So
instead of formalism constructed with propositions and their mechanistic
derivation, we can look into judgements, particularly infinite judgements that
follows a dialectic development rather than our conventional logical systems
that are simply static and mechanistic. A judgement that is not just playing
upon symbols and syntax, rather really deals with the semantic or content and
does not treat form and content in isolation is going to be the formalism to
properly encounter the logic of human mind. Turing himself notes that human
intuition is not a machine that is just disciplined. That is humans behave on
their own capacity.</span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black;background:white'>Suppose we say, mind is a machine. But we have
seen that how mind disagrees in action from general machines that is to say the
negation is implied, mind is not a machine. Then following infinite judgement,
we can see how the category of machine is unable to contain mind insofar that
mind demands to be elevated to a category of its own. Mind is mind.</span></p>
<p class=MsoNormal><span lang=EN-IN style='font-family:"Times New Roman",serif;
color:black;background:white'>Look at the most developed AI’s today. The best
they can do, being fed more and more training data, is to mimic human behaviour.
In no way can we say they actually “behave” that way. <br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
</span></p>
<p class=MsoNormal><b><span style='font-size:16.0pt;font-family:"Times New Roman",serif'><br>
</span></b><b><span style='font-family:"Times New Roman",serif'><br>
Part 2</span></b><span style='font-family:"Times New Roman",serif'> <i>(by
Swagato Saha)</i><b>:</b></span><b><span style='font-size:16.0pt;font-family:
"Times New Roman",serif'><br>
</span></b><b><u><span style='font-family:"Times New Roman",serif'>Temporality
of Logic:</span></u></b><b><span style='font-family:"Times New Roman",serif'> </span></b><span
style='font-family:"Times New Roman",serif'>This shall serve in many ways as a
continuation of <i>‘Erasure of Categories’</i> (2<sup>nd</sup> Issue/Cogito),
particularly in its consideration of ontological implications of the same.
Under the current category (Temporality of Logic), I hope to rationalize some
of this, besides charting a couple of alternate directions. <br>
The basic theme of categorical erasure seems to be that, given a category
posited as a universal; its rational constituency, its completeness is
eventually ruptured in the face of newer categorification(s). That is, beyond
its limit, the universal fails to assume within, or to dissolve inconsistencies
in its categorical space. In the domain of Chemistry, this translates to the formation
of the multitude of molecular categories, from the (supposedly) ontically prior
atomic category (Electron Density, let’s say). However, as was mentioned
before, the obvious slippery slope to easy Nominalism (Universals do not exist)
is to be avoided here. <i>In other words, a certain defence of Universality is
in order.</i><br>
Or, to render this point more explicit, consider Hegel’s critique of Kantian
formalist ethics as harbouring an empty room for subjective content – ‘Do your
duty’; since it says precisely nothing about what duty is or what it ought to
be, and requires the subject to assume ‘responsibility’ for this evaluation, it
cannot but appear as a rather insincere Universalism. However, for Kant, this
emptiness is what characterises the transcendental subject; and the associated
semantic space thereof. That is, Kant appears to be fully aware of the latent
formlessness of his injunction, and as the first philosopher of modernity
proper, we may say, provides the inaugural gesture of modern subjectivity. <br>
As such, subjectivity is the radical rejection of ‘false universals’. As Zizek
remarks, the major philosophical revelation of modernity is that ‘there is no
Big Other’. There is no ulterior guarantee of eventual reconciliation of Truth
& Meaning. Zizek goes on to suggest that this gives us a formula for
obscurantism today, as this very insistence on reconciliation – if Freud
inflicts a certain radical epistemological break in his exposition of psychic
mechanisms, then Jung is its obscurantist counterpoint. Or, consider New Age
appropriations of Quantum Physics nowadays, that attempt to domesticate its
paradoxes within everyday ontology.<br>
Nonetheless, how are we to defend Universalism? Is it proper to defend it even?<br>
For Kant, it is beyond pure Reason to bear a decisive verdict on questions of
existence – for it is then we are caught in, what Kant calls, ‘dynamical antinomies’.
Along these lines, an acute condensation of all of Transcendental Philosophy is
to be found in Chomsky’s passing remark – “Real is an honorific term.”<br>
And therefore, post-Kantian realists (starting from Fichte) must wage war on
this typically transcendental silence on the question of existence. For
Nietzsche, it is violent disposition (power relations) at the heart of all interaction;
for Schopenhauer, it is pain at the heart of existence; for Marx, it is the
reality of economic-relations and productive drives; or to go back; for
Descartes, it is thought in and as radical skepticism that is the condition for
existence; or for the naturalist (or even, proponents of Lebensphilosophie), it
is the ever-present vital matrix of Nature that preexists all; and finally, for
Plato, the universal order of Ideas necessarily preexists the multitude of
particular material bodies.<br>
What they all variously and equally seem to mobilise is the notion of a ‘Real’,
a gesture that preexists ‘Representation’- the form, in order to enact this
post-Transcendental Realist break. <br>
Think about newborns or really small children in social gatherings. Unable to
speak, it is only through their gestures that we can come to know anything
about them. I’ve always imagined such children as feeling somewhat
uncomfortable at the center of all attention – not that they do not
(narcissistically) enjoy it from time to time. And while people tend to relate
to the child affectionately, it seems as if we lack the proper predicates in
conversation; that is, there is a distance between what the child (actually,
intentionally) does and how it appears to us or what we understand thereof to
be its action. So, even the most nominal gesture ends up as unnecessarily
emphasized and gawked at, whilst perhaps more urgent calls for attention on the
part of the baby are lost in translation. In any case, there is this mystery
about the predicates that correspond to what the subject (baby) does. <br>
In a similar vein, much of the controversy surrounding universals among
(post-Kantian) Realists, is about deciding on the appropriate predicate. That
is, the universal predicate is the basic founding gesture of existence. And
thus, any defence of Universalism entails the formation of a universal
predicate.<br>
It is my conviction that we have a reasonable candidate for this – with respect
to 20<sup>th</sup> century cognitivism – Computation. <i>(Computation as
Universal Predicate)</i><br>
<br>
To steer into ontological waters, consider Plato’s scheme – there is an
eternal, immutable order of ideas, trans-historical by its very nature;
comprised purely of Universals. Against this, we have a multitude of material
bodies comprising the more transient, plastic order of existence, that can only
hope to variously distort Ideals to interact with the same. That is, the
singular, universal Ideal against the multitude of differentiated, particular
material bodies – consequently, <i>difference</i> arises out of the
instantiation of the Ideal as a particular material entity, <i>between
Universal and Particular</i>; and, <i>between Particulars</i> as distinct
entities, each describing unique, characteristic distortions.<br>
An exemplary element of this idealist topos, as it’s typically conceived of in
discourse, is Logic. Doesn’t our traditional notion of Logic describe precisely
this atemporal kernel, that variously manifests and directs the phenomenal
interplay of changing material substrates that it acts upon? Consider, in
foundational theories of mathematics, the formalist-logicist worldview (Hilbert
- Russell/Frege, respectively). Despite obvious theoretical differences, both
camps are generally expected to agree upon the privileged status of this kernel
(which Plato may have called ‘agalma’). Frege, in fact, was openly critical of
the Kantian noumenon.<br>
Or, so proponents of substrate-independent Consciousness might claim, that
Consciousness is to Body, as logic is to operand, as software is to hardware. <br>
How are then we to respond, as avowed materialists, on the question of Logic?<br>
A step seemingly in the right direction, variously informed by Hegelian and/or
materialist dialectics, would be to conceptualise the immanent Temporality of
Logic itself. <br>
In ways, Hegel comes off as more of a formalist than Kant – afterall, as Hegel
says, Kant has too much of a soft spot for the thing-in-itself, whereas, Hegel
is primarily concerned with Appearance. This is reflected of course in his
famous ‘All that is Real is Rational, all that is Rational is Real’, and in his
inversion of the traditional question of Metaphysics (How to move to Essence
from Appearance?) to instead ask ‘How is Appearance possible?’. That is, it is
not Hegel’s purpose to forego Kantian epistemology to pre-critical realist
ontology (of the Spinozan kind) – the basic epistemological thought-world
relation remains very much the core of his speculative project. Along lines of
categorical erasure, Hegel stands for the speculative positing of a Universal
which unfolds so as to undermine itself, via the logic of coincidence of
opposites, or as radical self-deployment as its own Particular. <br>
This simply means that (what Kant calls) Pure Reason has to open itself up to
pathological contingencies – the same way a physicist, for example, though
sound in his reasoning, simply cannot deduce (a priori) the outcome of
interactions among cellular organelles. Or, to return to Kantian Ethics – it is
as if a certain necessity for subjective engagement is inscribed into the very
form of the ethical doctrine, which can only ever be meaningful when the
subject assumes and fills out its empty content. <i>As such, the Hegelian form
describes a certain transformational logic, </i>(comparable perhaps in ways to
Kantian infinite judgement)<i> using which it must posit its own content.</i> (These
are conditions that the universal predicate, previously discussed, must
satisfy.)<br>
Let us imagine a slightly different ontological schematic now. As Lacan
observes (from Aristotle’s square of oppositions), <i>‘the Universal does not
exist; it insists.’</i> Without Plato’s Universal Ideal, of course the
multitude of matter remains undifferentiated. It is only against the backdrop
of an imagined (parallactic, to use Zizek’s categories) ‘ideal’, can <i>difference</i>
be recognised <i>between a Particular and the failed Universal</i> wherefrom it
came; and as such, no essential difference can be surmised between Particulars.
<br>
For Hegel, Being is no longer associated with Unity or the One, as it was in
traditional metaphysics, beginning with Parmenides. It is this impossibility of
the One to fully coincide with itself that results in the proliferation,
manifold instantiation of the One as its own Particular. As a result, there is
a certain necessity for (what Kant calls) pathological contingency within the
form of Reason (here, Logic) itself. In ways, this implies a radical break with
traditional Rationalism where a certain deductive completeness of the
categorical space is presupposed. <br>
To put this in psychoanalytic perspective, there is a name for this necessity
of contingency – object petit a (object cause of desire). Incidentally, this
mutualism between German Idealism and (Lacanian) Psychoanalysis is the
discovery of Zizek (and the Slovenian School). Already, we see, there is a
minimum of temporality inscribed in this schema. <br>
<i>Multiplicity arises as a result of the failure of One to coincide with
itself.</i><br>
<br>
There is a deeply consequent parallel here, between Hegel’s mobilization of
contradiction and Freud’s notion of the Symptom. Far from pathological
disturbances and peripheral formations or anomalies, both Freud and Hegel seem
to argue for the constitutive role of Contradiction/Symptom, both in terms of
how Reality is structured (ontological aspect), and how thus we are able to
grasp it in our finitude (epistemological aspect). This is a decidedly
post-Kantian move which posits the antinomy of Pure Reason as situated in the
Kantian noumenon itself. <i>As such, for Freud (and Lacan, and Zizek), analysis
does not concern the interpretation of a Symptom; rather, “…it is
interpretation to the Symptom.”</i><br>
<br>
Kant, who basically sets the coordinates for modern epistemology, posits the
thought-world relation at the heart of philosophical thought. Consider the
following question, variously taken up by 20<sup>th</sup> century physicists,
perhaps most comprehensively by Wigner – How is it that mathematics, (in some
sense) a fiction of the human mind (thought), can provide such precise and
powerful descriptions of natural phenomena (world)? In this, we may detect a
certain critical distance towards pre-critical ontology and Principle of
Sufficient Reason (Spinoza/Leibniz; PSR) – that is, while it may be possible to
rationally account for the way things appear and exist, there is in a way the
ominous possibility that we remain confined to our circle of (false) representation
in it all, eternally in the trails of Descartes’s Demon. Consistency does not (necessarily)
imply Existence. Much in the way that Gödel critiques the formalist school in
terms of self-reference, in Kant, we find the complete articulation of (transcendental)
Reason that can thus critically reflect on its own ‘conditions of possibility’.<br>
However, this raises other concerns – does every ‘new’ question, every critical
encounter, every contingency within a particular episteme, boil down to a consideration
of and eventual reconciliation with its conditions of possibility? So, in
response to a question such as ‘Is there metaphysical free will, or is the
universe causally determined?’, one can only elucidate, reflect on the
epistemic constellations that would even allow for the formulation of such a
question, instead of answering it. Any attempt to answer such a question
implies a collapse to Kantian antinomies. In other words, Kant has no definite
formula for Change – whether it exists, and if it does, are we able to grasp
it?<br>
<i>{An instance of this transcendental logic pushed to its extreme is Derrida’s
deconstruction. As Zizek critiques, deconstructionists want to desperately
fashion out routes for ‘rhetorical distanciation’, to enforce a separation
between the speaker and what’s spoken, in order to therein emphasise the infinite
potence of the medium of language (as the ‘condition of possibility’ of
discourse). It is along these lines, that the likes of Zizek & Alain Badiou
advocate a move beyond the linguistic turn in Philosophy. }</i><br>
Kant was fully aware of this problem, particularly when he considers the
prospect of historical-moral progress in his ‘Conflict of Faculties’, where
upon arduous reflection, and inspiration in the form of the French Revolution,
he nevertheless affirms this notion of progress. (Not to mention, this is where
Hegel intervenes with his notorious ‘Aufhebung’.)<br>
And so, we are required to conceive a formula for Change – a rewriting of
history books, a rewiring of conditions of possibility. And as it so happens,
we have a prospective candidate in the category of ‘Emergence’, to realise this
shift. In the sense, the question of Emergence insists beyond reflections on
conditions of possibility. <i>It retroactively grounds itself.</i><br>
<br>
Contemporary perspectives on Emergence, even within Natural Science, largely
conform to – what Chomsky calls – ‘Phylogenetic Empiricism’. Consider P.W.
Anderson’s formula for Emergence apropos ‘More is Different’. One has to ask
here – ‘Does every Difference imply More-ness/Less-ness?’, and, ‘Is More always
Different?’. If the answer is yes on both counts, that is, if Anderson’s logic
is pushed to its prescribed limit, it simply means there is no room for ontogenetic
difference in this schema. In other words, it still has this pre-Gödelian
picture of a happy formalist who rejects the irreducible nature of mathematical
structures, and looks to account for the existence of the same through formal
variations. It is however required here, that we think of a different formula
for Emergence, one which takes into account its ontogenetic effects, namely as
‘The One is Different’. This obviously refers to the irreducible nature of
mathematical structures, that is, One as Number is (irreducibly) different than
One as Vector; or in a similar vein, (ontogenetic) Emergence reflects Hegel’s notion
of the barred universal in and as the fundamental, paradoxical non-coincidence
of the One. <br>
<br>
A number of dubious consequences follow this obfuscation of the ontogenetic
dimension in contemporary theories/interpretations of Emergence. What ought to
spark immediate suspicion is the strict opposition between the two positions on
this question – we have people who reject Emergence as being ‘unscientific’ or
‘semi-scientific’ at best, and – people (a large number of them chemists,
incidentally) who take it to be something so extremely routine and self-evident,
that it’s impossible to step out of it, as it were, and ponder its conditions
of possibility thereof. <i>The old ill-fated Coincidence of Opposites at work
again!</i> <br>
The first section of which I am critical, decidedly opposed to Emergence,
favours reductionism in some shape or form. However, and to put it in Freudian
terms, the second section supposedly favouring Emergence, which for them is a
near tautology, nonetheless operates from a position of disavowal. That is, it
still involves a faulty blurring of the lines, a papering of cracks, a
mystification of foundational questions raised by the ‘hard problem’ of
Emergence, so that it appears trivial as ‘not even wrong’.<br>
<i>(It’s kind of like when students try to convince themselves they basically understand
what’s being taught and that it’s all repetition, when they really don’t and though
it’s really not.)<br>
</i><br>
Okay, but where in all this does Computation show up?<br>
There is a well-documented crossing of paths of Wittgenstein and Turing, when
the latter happened to attend one of the former’s lectures on Foundations of
Mathematics at the University of Cambridge, in 1939. There were brief exchanges
that appear highly insightful, even more so when put in context. Wittgenstein,
who wasn’t especially fond of the Incompleteness Theorem, nonetheless was a bit
more receptive towards Turing’s Theory of Computation. It appears, that though
Turing’s verdict on Hilbert’s Decision Problem is strictly correlative to Gödel’s
‘Kantianism’, Wittgenstein insisted on a minimal separation of the two
categories despite their obvious resemblance, possibly down to how computation
pertains to real-time physical processes, whereas one might claim Mathematics
doesn’t. Further, this seems like an appropriate characterization, bearing in
mind Wittgenstein’s mathematical anti-Platonism. <br>
However, the icing on the cake would be Turing’s surprising interjection when
Wittgenstein seemingly suggested that contradiction in a formal system isn’t
inherently problematic. “But bridges would collapse.” – says Turing (I
paraphrase). <br>
This strangely brings us back to consider afresh the epistemological question –
how is it that mathematics can provide such precise descriptions of nature? –
except, with an additional twist – what would a nature corresponding to an
inconsistent formal system look like?<br>
<br>
To go back to the 3-charge constellation previously discussed (Erasure of
Categories), much in the way that Nature in its <i>(‘reified’)</i> steady state
appears transparent to us, it seems we have a proper understanding of ‘formal
systems in equilibrium’ – however, imagine a system where one or more of its
constraints have been lifted or modified such that it stops being formal, akin
to the displacement of the central charge – the suggestion is that
‘perturbations’ of this sort allow for the analysis of what we may call <i>‘Almost
Formal Systems’</i>. As in, it’s not the case that we have a total operational
breakdown, but on the contrary, insightful variations, deviations that can in
some sense be regulated and put to proper use.<br>
In Darren Aronofsky’s Pi, there is this scene where a computer, going tragically
haywire trying to get to the end of a non-terminating non-repeating pattern as
it’s been programmed to do, hysterically collapses and as it does collapse,
provides (in its dying breath as if) the very sequence the protagonist was
after. Like in Citizen Kane’s ‘Rosebud’, or the classical (albeit somewhat
misleading) understanding of the Unconscious (as a reservoir of lost meaning
that fails to surface in rational spheres), or of course Jean Piaget’s notion
of ‘Cognitive Disequilibrium’ as pedagogically formative, ‘Almost Formal
Systems’ appear to echo the common theme of dispositional mental states. And to
pursue this metaphor to the end, one might even include in this line, the
chemist’s probing of excited states as possibly explaining reaction mechanisms
or general ground state molecular properties (not that these are mental acts,
of course). <i>There is no temporality in equilibrium.</i><br>
This line of inquiry seems particularly crucial to me, keeping in mind Turing’s
later efforts to think of Natural Philosophy as rooted in Computation. In ways,
this accentuates the separation that Wittgenstein did insist on, and as such<i>,
we are required to regard Computation in an altogether different light as a
natural phenomenon, and so as our de facto universal predicate.</i> For Turing,
all effective natural mechanisms are (by some standard) computable. Now, a
momentary reflection on this suggests there are, or at least, appears to be a
number of non-computable natural mechanisms. Take the simple case of formation
of molecules from atoms. Following Turing’s line of thought, in such cases we
are required to consider the possibility that the ‘natural logic’ of such a
mechanism eludes us yet. In other words, the fact that we arrive at such an
algorithmic impasse reveals something about the essential nature of the
unsolved problem. (This is comparable to Hegel’s category of ‘negative
determination’, and already in post-Kantian territory. <i>So, the fact that our
minds might fail to conceptualise some aspect of the world is a property of the
thing in itself. This is the essential shift in the theoretical perspective on
the thought-world problem.</i>) <i>(‘Non-computability’ As ‘Symptom’)</i><br>
And we are required to think of a kind of Computability that is responsive thus
towards instances of Emergence, it involving the articulation of such a
deadlock, to begin with. It remains to be seen if ‘Almost Formal Systems’ offer
any real insight in this direction.<br>
<br>
<i>(To be continued in a later issue…)</i><br>
<br>
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