MATHEMATICS
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 2020 ▶ |
| Object type | Epistemology, ontology or semantics |
A general overview of its relation to systemics.
According to A. KORZYBSKI: “From the point of view of general semantics, mathematics, having symbols and propositions, must be considered a language. From the psychophysiological point of view, it must be treated as an activity of the human nervous system and as a form of the behaviour of the organisms called humans” (1933, p.250).
KORZYBSKI considered mathematics “…a limited linguistic scheme, which makes possible great precision and coherence — but at the expense of such extreme abstraction that its applicability has, in certain ways to be bounded” (D. BÖHM and F. David PEAT — 1987, p.8).
The same point was made by B. RUSSELL, who admitted that mathematics offers the appearance of truth because it is not saying what it is talking about: a comment that was echoed by A. EINSTEIN (see above).
In the same vein, K. BOULDING wrote: “… mathematics in any of its applied fields is a wonderful servant but a very bad master: it is so good a servant that there is a tendency for it to become an unjust steward and usurp the master's place” (1970. p.115).
All this justifies G. WEINBERG's caveat: “A degenerative disease sporadically afflicting the general systems movement is hypermathematisis: the generation of grand, sweeping and valid mathematical theories — often called ”general systems theories“ — which are as sterile as a castrated mule… because they can be applied to anything and thus to nothing: but they are doubly sterile because they are undistinguishable — on a mathematical level — from productive theories” (1975, p.68).
Mathematics, as a language, must necessarily take forms in accordance:
l. With the neural organization of the brain, still quite imperfectly known.
2. With the nature of the problems of which that brain becomes aware, as mental part of an observer. This is the reason why nonlinearity observed in complex systems tends to generate new mathematical tools.
This explains why new mathematics emerges frequently in synchrony with a new awareness of some class of hitherto undiscovered phenomena.