Australian General Semantics Society Inc. (AGS)



Some Publications by AGS Members and Associates

"Mathematics as Psychologics"

Milton Dawes

 In our high school introduction to Math, understandably, we are not taught to think of Math. as also Psychological and Psychotherapeutic Tools -- Tools we can use to gain some Knowledge and Understanding, of our Knowledge and Understanding of ourselves, others, and the World.

Among the most powerful ideas the human mind has come up with, are the notions of "Variable, Functions, and The Calculus".  In his Epistemologic, Meta-Psychologic book "Science And Sanity", Alfred Korzybski referred to the Calculus as The Logic of Sanity, involving "

A study of a Continuous Function by following its history by indefinitely small steps:" as a way to understand and deal with problems.In a World of Continuous Functions (Think. "Changing Relationships")...In a world where every 'thing' has a history...In a world of "Variables" (Think of words and anything, based on the different meanings and values we give, as "Infinite Valued Algebraic Semantic Variables"). In such a World. We can apply The Method of The Calculus as a Supreme, Psychological, Psychotherapeutic, Critical Thinking Standard and Guide...A Scientific Tool...A Tool we can use to help us resolve our problems at personal, cultural, national and international levels. (As a Psychological and Psychotherapeutic Tool. There are "No numbers or equations involved".)

We live in a world of changing relationships (Continuous Functions) and other Variables. As individuals, as continuous functions...We are in changing relationships with time, ourselves, others, changing environments, language, and the culture that we inhabit and inhibits us. 'Things' (occurrences, happenings, goings on), exist as continuous functions of time, themselves, other things, and so on. That we live in a world of changing relationships is usually forgotten when addressing problems. There is a tendency, usually based on a "One cause one effect paradigm", I call it our "Algebraic Menace", when we forget situations, problems, etc, as "Semantic Variables", and "Continuous Functions" (changing relationships). Wouldn't we be better off resolving our problems thinking "Multi-Causality, and Multi-Consequences, than "Thinking based on "One cause one effect"??

I find this a little funny...but also disconcerting: In our elementary algebra problem-solving (Y = 3X): We give X a value to solve the problem. (We can give X any value we choose. In life situations, the different semantic values we give to the variables of our problems, and our non-acceptance of this as legitimate, normal and natural, often add to our problem.

Also. As a Function of Time, Itself and other variables -- While we are busy, occupied in exploring the roots of a problem, describing the problem, setting up committees, discussing plans, etc: The "Problem" (not a noun, but a verb) as a continuous function of time, is often, not only changing due to interrelated and interacting goings on...But in its own activities as a goings on, and as a continuous function: The problem is also a problem creator, creating other problems. In addition to this: Our Knowledge and Understanding sometimes become "Constants"...In their blocking our accepting and gaining further Knowledge and Understanding that could help us resolve our problem!

In applying The Method of The Calculus: Since we do not know and cannot know...If, When, That, we have taken the last step in our explorations -- We can assume that our Knowledge, and Our Understanding, will be Conditional, Provisional, Incomplete, and Uncertain. And also. If Our beliefs are functions of our Knowledge and Understanding...Our beliefs will also be provisional, incomplete, and Uncertain!!!
Imagine trying to solve a high school algebra problem when the variables you started with kept changing...and creating their own variables!!! (Reminds me of A Canadian National Film Board film where a fellow is trying to sit on a chair that kept moving away whenever he tried to sit on it. (I forget the name of the film.))

Remembering that we are dealing in a world of continuous functions, changing variables, and emergence of more variables, can help us better manage problems.
BTW. We as Individuals, are also Continuous Functions of Time, Ourselves, Others, and Goings on. We are not Constants.

So what are those involved in so effectively solving mechanical, scientific, electric, electronic, etc., problems, doing? Our politicians, and ourselves could learn a bit from them about solving problems. I would guess that the Method of the Calculus (but with numbers and equations) is involved.

Comments welcome!
Milton Dawes

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