Reply to Julio Huato - Formalisation, Maths, Dialectics, Marx, I

Jurriaan Bendien bendien at tomaatnet.nl
Mon Jul 14 09:22:50 MDT 2003


Hi Julio,

Another whopper... I suppose I should be thankful to you. Here is another
whopper for you, and I ain't talking hamburgers.

You wrote:

The 'mathematics' or the 'formalization' doesn't come later.  Formalizing is
just another name for theorizing.  We light up our practical clash with the
world by formalizing, doing empirical work, formalizing, doing empirical
work...  Is there direction in the formalization?  Well, that depends on the
practical task, which determines the object of inquiry.  Formalization may
lead to generalize or to deepen into the particulars, or to both.  It
depends on the practical needs.

Me:

I do not quite agree with your idea that formalising is just another way of
theorising, and I will tell you why. In order to formalise logically or
mathematically, you must have something to formalise in the first place,
some variables or factors deemed to be important, and through formalisation
you want to explore how those variables are related and what the
quantitative implications are. The question I have chosen to focus on in my
discussions with Les Schaffer, is "where do these variables or factors come
from, where does the data you seek to manipulate come from" ? This problem
is as old as the pre-Socratic philosophers, if not older (because it arises
in human practice even before they get round to philosophising). And it is
clear, that to identify and collect these variables, you need an original
act of conceptualisation which is prior to mathematics and prior to logic,
or at any rate outside it, external to it. In other words, you need to
import some empirical content, some research questions, some categories, in
order to be able to formalise something and to explore the implications of
what you have formalised. It is true, that once you have made some
assumptions, the model you devise can generate new insights which help to
develop theory, I do not deny that at all. I am just saying that in
constructing the model for starters, you are already using some
categorisations, assumptions, conceptual distinctions or background theory
which are themselves not exclusively a product of formalisation processes.
So, when people are baffling us with quantitative and logical wizardry, we
are quite entitled to inquire critically into the ultimate assumptions of
their reasoning processes, at least some of which they have imported from
somewhere, and which are not internal to those reasoning processes. But what
typically happens is, that the model that is built up is itself mistaken for
a theory, but it is indeed a mistake, because it is a theory of which at
least some premises or assumptions may not be made explicit or which may be
conveniently regarded as "trivially true". And this is extremely important,
because it might be exactly those "hidden premises" in the argument which
are decisive to the validity of the theory. They may not be known; we may be
mesmerized by the elegance and rigour of the logical systems we have
devised, which give total confidence in our own position. But our logic and
mathematics may really be only a Maginot defence line (this is a system of
fortifications originally devised to defend the French border against German
attack, which according to the Von Schlieffen strategy was simply bypassed,
through an offensive routed via a relatively defenseless Holland and Belgium
into the North of France). This is why I insist strongly that formalisation
cannot substituted for, or completely equated with formalisation processes.
I think that Louis and Les would agree with me about that, because having
professional experience with programming, they know that in order to write a
programme to execute a set of tasks and produce certain results, you require
some original conceptualisation of what those tasks are, you need some
theoretical background to identify discrete tasks and how they fit together,
in order that you may be able to write your programme. And the processes
involved here are not simply logical in the formal sense. In fact, a
programmer said to me once, "programming is an art, some people just have
the knack, some people don't, even although they are extremely logical
people". The "art" resides precisely in an creative act of conceptualisation
and the ability to refer to a rich store of associations which enable you to
specify which methods of formalisation and which logical steps are most
appropriate and efficient. This conceptualisation process involves analogies
and metaphors, in other words, mental associations and symbolisations drawn
from the human culture in which you live and in which you were formed.

YOU:

Do we need -- as you say -- a "dialectical theory" to have "a method" to
develop "the premises" so that we can undertake a "mathematical
formalization" the right way?  That's too long a chain in my view.  I think
of cognitive dialectics as this back and forth between induction and
deduction, between 'empirical work' and 'formalization.'

ME:

See my comments above. I do not think you necessarily need a dialectical
theory, I just think that in your creative act of original
conceptualisation, you are forced to think dialectically anyhow, even if you
do not know it. All that dialectical theory might do, is make the
dialectical stratagems in your think more explicit, that is all. There is,
according to logicians, a hell of a lot more to logic than simply induction
or deduction, in fact, there are literally hundreds of logics possible, and
we do not even know what the limits of logic and mathematics are. I have
already made that point earlier, because I said that our ability to
formalise is limited only by our ability to conceptualise something clearly.
You can formalise dialectical processes to some extent, but if you do that,
then in so doing you leave the terrain of dialectics, precisely because you
have formalised it. What I am suggesting is that in practice you use both
dialectics and formal logic, even if you think you are only applying formal
logic.
All that dialectical theory aims to do, is to make the processes involved in
dialectical thinking more explicit. But can we say, that Shirikov provides
the definitive description of dialectics ? This is absolutely ridiculous, we
are dealing here with a bureaucratic attempt at thought control in the guise
of fostering a better philosophy of science.

YOU:

But isn't dialectics also ontological (the way the objective world moves)?
It must be.  Otherwise (forgive my functional way of arguing) this cognitive
interaction would not be necessary and it would not lead to practical
success.  Objective dialectics is what underlies the back and forth between
empirical work and formalization.  That is why no formal system can be
complete or absolutely decidable.  The dialectics in the objective world
appears into theoretical systems in the form of 'paradoxes' or
'contradictions.'

ME:

Well, what Engels was really trying to do in his speculations about the
Dialectics of Nature was to trace out the implications of dialectical
thought more rigorously in terms of the materialist conception of history.
If it is possible for people to think dialectically, then, he reasons, this
must ultimately reflect the fact that reality has dialectical properties.
And if reality has dialectical properties, than the relationship between
human beings and the world in which they live must have dialectical
properties. But because human beings have emerged and originally evolved
from amoeba within the world they now inhabit, it must be the case that the
natural universe itself has dialectical properties, because otherwise we
would not be able to think or act in dialectical ways in our behaviour. But
this last premise cannot ultimately be logically or empirically proved
beyond all doubt, it is a metaphysical theorem, in exactly the same way that
the theorem that mathematics contains universal, objective truths is a
metaphysical theorem

YOU:

Whether the formalization is 'mathematical' or 'discursively logical,'
depends on the subject matter and on the state of 'mathematics' and 'logic.'
  I usually think of mathematics in a tautological (dialectical?) way, as
"mathematics is what mathematicians do."

ME:

Not quite. There is overlap between formal logic and mathematics, but
mathematics contains the concept of number which allows quantitative
permutations of logical operators, whereas ordinary formal logic does not of
itself contain the quantitative aspect beyond terms such as ""less than" or
"greater than", "belonging to the set of X or Y", "excluding this, or
including that" and so on. But at a certain point, formal logic merges into
mathematics because formal logic is forced to refer to the quantity of
implications of its own application. Formal logic is more tautological than
mathematics in a sense, because mathematics can operate quantities, but
nevertheless logical formalisation can make explicit implications of the
adoption of particular assumptions which constitute new knowledge, and which
are not tautological other than in the sense that they are necessarily
implied by the inferential system. The imperative of dialectical theory is
"let us get more rigorous about the metaphors, analogies and symbolisations,
in other words the deep structures of thought which originally inspire
mathematical and logical systems."

YOU:

At least in the fields of economic analysis that I'm most familiar with, my
impression is that mathematics has swallowed logic to a large extent.  With
a suitable definition of mathematics (which is compatible with the practice
of the mathematicians as I observe it), logic appears to me as a subset of
mathematics.

ME:

I would regard mathematics, formal logic, and dialectical theory as
semi-autonomous but overlapping fields of inquiry.

YOU:

A model, by the choice of premises, is already theory in the sense you use
the term.  When economists build models, they are building theories.  Given
the constraints imposed by the state of our 'logic' and 'mathematics,' why
would one choose some assumptions and not others if one doesn't think those
assumptions are the ones that best reflect the essential characteristics of
a phenomenon?  (A functional argument again.)  If the deductive structure of
the model doesn't reflect those characteristics, only by chance we'd get
good results.

ME:

Well, I still disagree, because a theory has a different purpose from a
model. A scientific theory makes claims about the true nature of the object
of that theory, which exceed the claims made by an associated set of models,
because the theory rationally explains the assumptions which a model must
take for granted in order to explore their implications more precisely.
So, anyway, the reasoning is in reality most often of the following type: my
background theory tells me to expect that if X occurs, then Y will occur,
but now I have found that Y does not occur, but instead Z occurs. This is
puzzling, and now I want to know whether this peculiar result is due to a
faulty assumption in my theory, or due to a facet of experience which the
theory has ignored or fails to explain. In order to do this, I want to get
very precise about what I am talking about, and consider the implications of
different ways of looking at the problem. So I build a model which could
explain the link between X and Z, which runs counter to what I expected,
namely that Y would be consequent on X. I ask myself, "what could explain it
?" and then I methodologically adopt some assumptions which could explain
the X-Z connection, and explore their logical or quantitative implications.
This may not the way in which the reasoning appears, formally speaking, to
the outsider, but that is what is going on for me. The problem however is,
that the model, itself devised to explore the implications of the theory
with some new ideas aiming to resemble the real situation better, may import
assumptions which are really incompatibe with the theory. This is a quite
legitimate procedure, if we are honest about what we are doing, after all,
we have a genuine puzzling phenomenon, and we do want to resolve it somehow,
we just try a few things to see what would possibly explain it. But the
problem is that the assumptions we are importing, may not be fully explicit
or clear, they may be hidden or unstated, precisely because the purpose of
the model is to develop or apply theory to some new puzzling phenomenon. I
agree, it is often difficult to tell theory and models apart, to clearly
separate the two, but that is precisely the problem I am referring to...

YOU:

Formalizing is theorizing.  'Presenting' is spelling out the deductive
structure that goes from the premises to the conclusions.  And this
deductive structure is a formal system.  The conclusions are to be compared
with the observable facts and -- more generally -- with our practical
experience.  (More on conclusions below.)  And the cycle goes on and on.

ME:

I agree formalising is part of theorising, but it is not the whole of
theorising, because formalisation always relies on a set of premisses, and
the question then is where those premisses come from ? And those premisses
cannot ultimately be the product or result of formalisation. This is
precisely what Marx is concerned with all the time, and he is looking for
non-arbitrary ways to import his premisses.

YOU:

There is nothing here that gives us the answers ready made.  The struggle
shifting and expands our subject matter continuously.  As we try to extract
the answers, we refine our methods, and we go on an iterative interplay
between 'empirical work' and 'theorizing.'  Everything -- and I mean
everything -- is moving.  There is no universal algorithm.

ME:

There may be a universal algorithm, but I have no way of knowing that a
priori, and I may never know that, in fact it may exist but it may be
impossible for human beings to grasp it anyhow.

YOU:

I insist, theorizing is reducing.  It is extracting the signal out of the
noise.  The acceptable cutoff point between signal and noise depends on the
depth and scope of our practical needs and -- I guess -- the level of
empirical complexity our brains can accept when making decisions.  The
conclusions of a deductive structure have to be calibrated to that level of
empirical complexity as well.  When I do grocery shopping, the level of
empirical complexity that my brain requires to decide whether to put
something on the shopping cart or not is pretty low and my wife has to write
a list for me, in some cases detailing the size and color of the can, etc.

ME:

Well yes, a theory seeks to reduce complexity to a manageable level in order
to make it comprehensible. The two tools which the human brain offers for
this are stimulus discrimination and stimulus generalisation. A cognitive
discrimination process says, this stimulus is different from, is discrete
from, separate from other stimuli. A cognitive generalisation process says,
this stimulus is like, or analogous to, or similar to, or associated with
other stimuli. All living organisms have this ability for stimulus
discrimination and stimulus generalisation, so all living organisms are able
to theorise in some primitive sense. The aim of theory is to establish a
determinate relationship between our consciousness and our experience of a
world which exists external to us in a comprehensible way. But at the
highest level, theory seeks to portray the whole of human experience in a
determinate way. And this is where, as Marx notes humorously, Hegel fell
into the illusion that human history is merely the objectification of the
Idea. But this error that Hegel makes in trying to invent a logic that
explains life, the universe and everything, is a quite common error, because
it is very common for people to impute to or project categories and
relationships they have devised in thought on to the world in a way which
suggests that those categories and relationships actually exist in the
world, that they have an objective, mind-independent existence. Marx argues
that the fethistic, reifying consequences of the market economy actually
encourage this process. Capitalist activity appropriates an object out of
the natural world, analyses it in its constituent elements, separates out
those elements, reassembles those elements in a profitable way, and then
generates a new product which modifies the natural world. But in the
process, the real relationships between consciousness, human beings and the
world they live in may be inverted, distorted or deformed. The "reduction"
which the analytical and subsequent synthetical process involves, may in
fact generate a massive distortion of human consciousness, or at least a
massive modification of human consciousness, which annihilates sociality and
historicity, the species relation between people and between people and
nature.

YOU:

Theorizing is something like computing a 'statistic' -- i.e., a complex
function -- of the 'chaotic concrete' by which we squeeze the 'abstract laws
of motion' out of it, and then use 'logic' and 'mathematics' to derive (with
'intermediate links' if required) conclusions that are verifiable by
observation and practical experience.  We push the theoretical deductive
structure all the way down to the level of empirical complexity we require
to deal with our practical tasks.

ME:

Even in computing a statistic, we must theorise in a manner which goes
beyond any statistical theory. I used to do it for a living. Computation
refers to a calculation or an inferential process, but to get that off the
ground, we must import some numbers, data, empirical content. Marx's method
starts off with the data and the interpretations of that data, in order to
arrive through abstraction at a few simple concepts, which form the basis
for the reassembling of the interpretations and the data in a coherent,
rationally organised theoretical structure. This is not just empiricist
modelling, it is theorising, dialectical theorising (see Jindrich Zeleny,
The Logic of Marx).

YOU:

An issue is whether there are social phenomena so complex that there is no
way to reduce them to a manageable theory.  The Keynesian tradition in
economics emphasizes this case.  A phenomenon such as 'long-run investment,'
a crucial link in the reproduction of a modern capitalist economy, is in
Keynes' General Theory, chapter 12, not amenable to theoretical reduction
because it is -- as Duncan Foley puts it -- a 'self-referential' process (an
endless loop in an algorithm).  (John Paramo accused me of 'economic
reductionism' because -- perhaps -- he doesn't think that all theorizing is
necessarily 'reductionism.')  But Marxism is not nihilism.  We are driven by
practical needs.  We may even use a ballpark approximation to a 'solution.'
In immediate political decisions, we may use our intuition -- or some
quick-and-dirty trial-and-error decisions rules.

ME:

The first question which you always must ask in this situation is: where
does the complexity I detect originate from, what sort of complexity is it ?
Does it (1) inhere in external reality, or does it (2) inhere in my
perception of external reality with a certain consciousness, or does it (3)
inhere in the way in which I am inserted into the world, my specific
relationship with the world ?
If it inheres in reality, then you must simplify, you must find a principle
of economy (cognitive efficiency), set priorities in tackling it. If it is
an artifact of your own consciousness, you must self-critically reflect on
the conceptual distinctions you are making, which actually may generate a
lot of useless complexity. If it inheres in the way in which you are
inserted in the world, you must re0-examine your relationship with the
world, and alter it. In a popsong by Crosby, Stills, Nash and Young called
"Our House", you have the line "now everything is easy 'cause of you", in
other words, what previously seemed enormously complex and difficult has
become easy because a new relationship with the world has becomes
established.

YOU:

So I think of it more along Lenin's "concrete analysis of the concrete
situation," except that I think of it as requiring a clear articulation with
Marx's most polished results (which happen to be higher abstractions because
that's where he left things).  Either the abstract layers of Marx's critic
of political economy are valid or not, helpful or not.  And if they are
invalid, their refutation needs to be explicit.  As you say, how come he
foresaw with such accuracy the tendencies of capitalism?  (See, you also
give functionalist arguments.)  That _must have_ something to do with his
'theory' (even if still highly abstract) and his 'method.'  But, agreed, we
shouldn't confuse his presentation with what he actually did.

ME:

When Lenin is talking about "concrete analysis of the concrete situation,",
what he is referring to is the relative place and limits of theorising.
Theorising may lead to higher and higher forms of abstraction which lead
further and further away from living reality. Or theorising may lead to more
and more specific applications of theory in lived experience. Lenin is
saying, at some point we have to cut through the crap and say we able able
to understand this situation we are dealing with and change it, and we must
not be distracted by theorising which becomes so nuanced and abstract that
it loses any real relationship with its object, becomes divorced from its
object, and becomes divorced from practical applications and practical
experience. This is very easy to do in mathematics and logical theory.

[ end Part I ]





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