Formalism, Truth and War
Dear list members,
It seems to me that a major problem underlying the ancient unsolved
("western") problem of "objective" truth is the ("western") schism
between "art/culture" and "science/mathematics". I am therefore
interested to know if, and how, this problem manifests itself (or is
treated) within other cultures.
A recent serendipity as a result of switching on the BBC world service
-was the remark that "(western) christianity" has evolved the concept of
"faith" which is absent in other religions -which are, instead, based on
the observance of ritual with an absence of specific dogma which must be
believed or proven in order to participate. Unfortunately, I missed the
remarks which lead up to this.
Since the discovery of non-Euclidean geometry around 1860, the
"sciences" -in the general sense of intellectual systems of thought
working with (relying on) systems of "formal" proof -have been involved
(via Rutherford, Einstein, quantum physics, chaos theory, etc.) with
questions which were previously intuitively dealt with within the "arts"
(i.e. non-formal traditions of thought) but have recently been
re-introduced into "cultural" theory (as a result of scientific
discoveries) and (as far as I can see) been completely misunderstood.
It seems to me that "science" (via relativity) is able to deal with
"subjectivity" in a pragmatic and valuable way (i.e. mapping between the
representations increases scientific knowledge) -while "culture" has
succeeded only in confusing itself (via relativism) and postmodernist
dogma which indeed reduces everything to a single "duh!".
Clearly, the situation is made more complex by the inherent belief
(within "western" philosophy") that there is indeed only one "truth" and
so the rest must be "subjective" falsity. It is this (unconscious)
assumption which reduces the (sorely needed) potential plurality of
postmodernism to monolithic (neo-fascist) intellectual autism.
As far as I can see, a "formal" system has a series of "axioms" (basic
assumptions) -plus a system of rules to transmute these assumptions (or
to derive new statements from them) -which eventually leads to a set of
"theorems" which are considered "True" within the system.
One is only allowed to operate within the system in terms of explicit
rules -so "formality" seems to be primarily associated with "becoming
explicit". In an "informal" way we could perhaps say "formality" is
concerned with the "development of form"!
Another characteristic of "formal" systems -is that "axioms" and
"theorems" are generally interchangeable -so two different systems are
possible which are (presumably) congruous.
Yet another important characteristic of "formal" systems is a result of
their basic "tautology" -i.e. statements are "true" only within the
"context" of the system. Attempts to "de-contextualise" are therefore
extremely dangerous. Unfortunately, de-contextualisation is is the basic
conceptual technique which underlies "abstraction" -which in turn is the
most successful (male(?)) conceptual tool within the "western"
intellectual tradition. It should therefore be obvious that the process
of "abstraction" may well be the secret of "western" intellectual
success -but it is also the reason for the inherent confusion within
that same tradition -simply because the original "context" is always
destroyed and with this loss of knowledge regarding the underlying
(formal) system we have also loose all understanding of the origin,
derivation and limits (validity) of the concepts we use so freely.
However -perhaps the most important characteristic of "formal" systems
is (despite the beliefs of those on the "cultural" side) the fact that
the "axioms" upon which the whole system is based are completely
Because "formal" systems are explicit -anybody who applies the rules
consistently will (presumably) produce an identical result to any other
person -independent of their position in time, space or social status.
So we have the bizarre (within the context of western philosophy)
situation of an "objective truth" hidden within a purely "subjective"
I suppose the easiest way to explain/resolve this (pseudo(?)) problem is
to consider the axioms, derivation rules and theorems of a formal system
as representing the construction of a "conceptual space". The direct
result of applying individual rules could then be seen as being
concerned with (defining) the (local) "geometry" of the space -while the
more general characteristics of the system would be concerned with
(defining) the (global) topology of the conceptual space generated by
the axioms and derivation rules.
I suspect that "objectivity" can therefore only exist within the context
of a "formal" system (as a product of the system -and a "validity" which
is limited by it).
So we have a situation where "objective" truth is possible -but is
limited to a "conceptual space" firmly located within the metaphorical
"black hole" of "Theory". It would appear that "truth" can be found -but
is of no practical value.
However, this is presumably not strictly true -because an understanding
of the implications (theorems) derivable from the axioms does represent
"objective" knowledge regarding the "topology" of the hypothetical
"conceptual space" constructed by those axioms!
Now we have only the problem of mapping this knowledge into a pragmatic
To do this we need to rely on the ancient technique of "analogy" -i.e.
If this situation/context is congruous with that conceptual space -then
if we do X we will produce Y as a result (as predicted by our
Obviously, this "Pragmatic" approach can only result in a "negative"
proof -i.e. if it doesn't work then we can assume that our previous
assumptions were unsatisfactory -but we still cannot safely assume that
the situation is indeed (fully) congruous with our "concept/image/model"
Perhaps the best strategy to deal with this problem of "negative proof"
is to (pragmatically) apply a wide range of different solutions to the
same situation in order to explore the congruence between the different
"topologies". This is surely the theory behind Heglian dialectics and
the practice which makes "discussion" so useful (if approached fairly)
when dealing with (complex) problems. The "mapping" between different
conceptual spaces (or representations) is what I refer to as
"relativity" -which is clearly more (pragmatically) effective than
"nihilistic" relativism (duh!).
If the theory being sketched out here is at all functionally valid then
it should be clear that a "tension" between "theory" and "practice" is
both inevitable and essential. It should also be obvious that we need
conceptual diversity -just as much as we need bio-diversity.
Furthermore, we may remark that if "formality" is (primarily(?))
concerned with making things explicit (because the more "explicit" they
are the more congruent any attempt to "reproduce" the system will be)
-then art (being concerned with the materialization of concept) is a(n)
(informal) formal system (i.e. is a movement towards "formality").
Artistic and cultural systems may also be considered as being concerned
with the application, exploration and development of "aesthetic" axioms
(i.e. "arbitrary" assumptions which are generally "emotionally
satisfying" -but may also be introduced "just for fun").
Artistic and cultural systems are therefore essential
ontological/epistemological tools which enable us to explore the
topology of the space within which we (individually and collectively)
One may therefore suspect that it is only the total degradation of
respect and understanding for "formal" (and legal) systems within
"western" art and culture (also reduceding "art" to a meaningless pomo
game) that could explain how it is possible for the president of the
richest country in the world to declare a "War on Terrorism" without any
apparent consideration of what this term might actually mean -and that
others can offer support for the bombing of one of the poorest countries
in the world in the name of "freedom" and "democracy" in an apparent
escalation of the war which has now made it an American "War against
Trevor Batten <www.dma.nl/batten>