Posted:

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

arbitrary!

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"

arbitrary system!

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

application:

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

"theoretical" space).

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"

of it.

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)

live.

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

Civilization".

("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

arbitrary!

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"

arbitrary system!

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

application:

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

"theoretical" space).

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"

of it.

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)

live.

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

Civilization".

Yours sincerely,

Trevor Batten <www.dma.nl/batten>