Mathematics, critical thought and the problem of categoricals (again)

Jurriaan Bendien bendien at
Tue Jul 8 18:20:02 MDT 2003

Thanks again Les, I have a lot of things happening here, and cannot spend
the time on this I would like. Just a few brief notes meantime:

I consider that mathematics is an extremely important tool to dispell
so-called "magic" and myth in the irrationalist sense, where it needs to be
dispelled. Take for example an issue of emigration, which I am personally
concerned with at present. Good quantitative reasoning and research can
dispell a lot of prejudices and myths in this area, and be an effective
anti-racist instrument. Therefore I think that mathematics (and statistical
applications) can in principle help improve our very moral functioning and

On the other side, I consider also that you do need a certain amount of
"magic" in life to enjoy it, as long as it does not substitute for rational
thought, i.e. there are dimensions of life which are not rationally
explicable. It is well known that we can analyse a subject to death, but in
that case the subject ceases to be enjoyable. I am quite happy to analyse
certain social circumstances to death, if by doing so I kill them off, and I
am sure you can think of the type of thing I am talking about. I consider
that children can be cheated out of "magical" moments, which they are
entitled to experience and enjoy naturally, without patronising and
commercially-oriented interference.

I have personally often enjoyed the tricks of conjurers and jugglers, but
even if captivated by this, modern psychology also teaches us not to be
fooled in this area, and to search for a rational explanation behind the
apparent "wizardry" which shows how it is practically done. We may find, for
example, that the emperor has no clothes on. Or it may add to our
appreciation of the artistry involved in the conjuring act.

Beyond this, as Wittgenstein remarks, there is an irreducible and
unremovable "mystical" dimension to life. You could attempt to explain this
in terms of the fact, that the stimuli impacting on the human organism which
experiences them, are for the most part processed by the unconscious mind.
That is to say, we may as human beings not be as "rational" as we claim to
be, even if we are mathematical geniuses (and I am certainly not among
those, to the contrary). But it is a big leap from there, to the theorem
that human behaviour is mostly not rationally explicable or predictable at

My previous remarks about modelling complex systems really derive from this
simple idea: we can develop a quantitative logic so that we can manipulate
assumed variables abstractly in complex ways, and investigate their
behaviour under a variety of conditions. However, when we seek to apply our
quantitative logics to empirical experience, we are faced with the problem
that we need valid counting units. These valid counting units rely on
categorisations (groupings) of experience, and here I think it can be proved
beyond any doubt that many if not most of our categorisations are
conventions built up through thousands of years of human social practice.
Ultimately human experience contains dimensions which defy logical or
quantitative analysis, but even then we can ask what the probable magnitude
of these dimensions is.

Logically, this means for a simple example, that where one person observes 2
entities, another person may observe 3 entities, even although they observe
exactly the same thing. Take as an example a case where two people, call
them J and S, observe two other people, call them A and H. If we now ask
person J how many persons he observes in the set P and Q, he will say 2. But
if we ask person S the same question, she might say 3. We might inquire of
S,"but aren't you falsely including J in the set of A and H", sort of in the
corner of your eye, in your peripheral vision ? And S might well say, "no, I
just happen to know, or observe, that H is pregnant", and this observation
implies a categorisation of "persons", with which we may or may not agree,
or what Quine refers to in another way as specific "observation

Taking a slightly more complex example, consider the case where we wish to
count the number of family-based households, i.e. kinship groups within
households. In order to do this, we require a typology of families and a
typology of households.
For the vulgar Marxist, this may be a pathetic Weberian sociological
exercise, but in fact, it is a crucial aspect of scientific research of
relevance to economists, trade unionists and social activists, and this
scientific exercise reveals a great deal about what we are exactly talking
about when we talk about families and households. To pursue this sort of
research, critical inquiry is indispensable, and we get nowhere at all, by
denying the existence of social science or fomenting moral dogmas.

I believe this kind of insight is enormously important, including for the
understanding of the profundity of Karl Marx, as a creative thinker who
expertly "reframed" economic categorisations, in a searching and critical
way, in order to break through conundrums in the economic thought of this
time. It is all very well to invent complex quantitative models of economic
phenomena for example, but if the theoretical or categorical assumptions on
which these models are based are in some way counterfactual or
unsustainable, then it is still a question of "rubbish in, rubbish out", and
no matter what mathematical wizardry we let loose on the problem, we will
not solve it, until we have changed our categorisations or theoretical
assumptions. This is exactly what Marx was doing in settling account with
Feuerbach, in writing his theses.

An important dimension of the historical problem of human ideology is
likewise, that we are often not aware of the categories that we are
practically committed to, we assume them, take them for granted, we more or
less have to, if we wish to go anywhere and arrive at our destination in one
piece for example. It may take a great deal of scientific investigation to
establish whether or not these categories are arbitrary or not, and what the
limits of their application really are. One of the great problems of the
computer age is the overextension of categories and concepts, which are
applied to new areas to which they are not appropriate. And this generates
new forms of reification, the distortion of human experience by machines,
the human being as the slave or servant of machine-produced experience.
Conversely, our capacity to assume complexity increases, so that we may make
problems more complex than they really are, and this may serve ideological
purposes as well, by demobilising or paralysing human action. We may be
bamboozled by experts who imply a complexity which is not there.

If I may refer here again to the problem of socio-biology: this is a new
field stimulated by new sexual freedoms and biological research, the ability
of bourgeois society to recognise better the "natural animal" in itself and
the implications of that natural animal for profit-making. But in linking
biological phenomena to social phenomena, a whole series of new
categorisations have to be formed, a whole set of assumptions are made in so
doing (since we must assume something; the human brain certainly does). And
these categorisations may be arrived at in a speculative, shoddy way, just
as when I dress badly or raise my child badly if I had one. It may be argued
for instance that these categorisations are inherited through the genes,
that somehow they exist in the bedrock of the human brain, but in
"biologising" human existence, the social existence of human beings may be
mystified at the very same time.

Now why is this ? Because, in a society divided into social classes with
conflicting interests, ideological influences cannot be removed, and these
class contradictions simultaneously prevent scientific findings from
becoming correctly generalised. And therefore if class contradictions
intensify, the probability increases that scientific findings are distorted,
deformed and abused.
Even in the primary socialisation of a child, social inequality impacts on
the cognitive ability of the child, a point about which Andre Gorx wrote an
excellent essay (see Michel Bosquet, Capitalism and Everyday Life, Harvester

In my personal view, therefore, Frederick Engels's concept of scientific
socialism ought to be turned on its head: it is these days not so much a
question of making socialism scientific, but rather, that in order to pursue
genuinely critical and self-critical, scientific inquiry to the end, you
ought to be a socialist or Marxist, because only being a socialist or
Marxist draws your attention to the deeper and wider background of your own
scientific enterprise, the social, historical, and categorical foundations
on which it is based.

An anti-socialist would, no doubt, call this "propaganda" by the socialists,
and he would say, you do not need to be a socialist in order to acknowledge
the existence of social classes in history; "I can perfectly well
acknowledge their existence, but I will say, so what, there are just winners
and losers, that has always been so and always will be so". Point taken, but
the socialist, the radical, always take the controversy further, he asks (1)
how does it come about that there are winners and losers, what kind of
winning and losing are we talking about, what is the framework within this
occurs etc. (2) why is it that in your media you are systematically forced
to deny, distort, and obliterate large dimensions of human experience,
turning winning and losing into a mystery, including the mystery of the
rules which govern it ? (3) why is there so much uncertainty and
mystification about where the human species is coming from and where it is
going, even when we have all the tools and means at our disposal to find
this out ? (this theme is dealt with in Richard Sennett and Jonathan Cobb's
book, The hidden injuries of class; some people think this book is out of
date now in an era of sexual freedom, but I reject this view; Sennett's
subsequent book about flexibilisation of labour proves this).

Marx commented: "to be radical is to go to the root, and the root of man is
man himself". I had a discussion along these lines with a mathematician, and
his opinion was that the "root" referred to a penis, and that radicalism
could be proved only by applying this penis in a certain way. Since I failed
to do this to his satisfaction, he got annoyed, calling me "unmanly" among
other things.

I accept that there is an element of truth in his observation, but feminists
taught me very clearly that "manliness" does not inhere in phallocentrism.
My occasional clumsiness in the sexual field has little bearing on my
manliness or lack thereof.  For a balanced objective assessment, we must
therefore examine critically the categorisation of gender and sexual
practice, and sexual politics, both sides of the story. I do aim to do this
conscientiously, I have done it, but I am a human being, and I cannot very
well defend myself against a mass of people who seek to interfere in my life
against my wishes, disrespecting my life. All I can do is state my point of
view, and smash injustice. Only the most stupid, vulgar minds can equate
lying with sexual abstentionism. Since I get impatient with lies, my
attitude tends to be: if you lie, I abstain or go elsewhere. I realise it is
sometimes necessary to be receptive to "little girl lies" if indeed the
purpose is seduction, but I get impatient with it. As far as I am concerned,
the important thing is to know what you want, and to be certain about your
right to have it. Vulgar sexual insinuations, even if mathematically or
statistically presented, may only fudge the real problems that I am
concerned with, and want to be concerned with.

These notes are a prologue to another issue which I wish to pursue some time
in the future, namely the philosophical problem of universals, in relation
to the philosophy of praxis.



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