"YOU ARE Semantically Confused!"
If those are not fightin' words, they ought to be, for they are a serious accusation to all of us who are interested in our ability to think clearly and accurately.
Their seriousness is not lessened by the fact that all too often the phrase really means that its user feels that his opponent is obviously and unmistakably wrong, but that no sufficiently crushing argument to annihilate his wrongheadedness seems to be available at the moment.
Then too, it is unfortunately true that the accusation may just possibly be valid; the situation which the phrase "semantically confused" purports to describe actually does exist. We may, literally, "not know what we are talking about." Possibility of difficulty of this sort arises as soon as we leave the point-at-it level of reference. We have these troubles because we cannot break down the notoriously slippery higher order abstractions into their more explicit lower level components, among other reasons.
All these things are particularly true of the social sciences and of psychological matters. They are much less true in the physical sciences.
In our dealings with the physical universe for the last three hundred years or so, we have learned pretty well how to keep away from major complications of this nature by applying two principles.
The first of these is that we can talk meaningfully only in terms of directly measurable quantities, or other quantities which we can derive from these explicitly. The prime example of this is the ether. Einstein's thinking destroyed this concept, as to physical utility, merely by showing that if his postulates were justified we could never devise any means of detecting the existence of the ether. We are still at liberty to use this concept, if we choose, but we now do so after having been warned that we have no way of ensuring that what we say will have any meaning.
The second principle is based upon the fact that our minds appear to be like a rather poor juggler: one can keep no more than two or three things, at the most, in the air at any one time. Just as soon as we try to trace out the effects of several causes operating simultaneously, just that soon are we in danger of confusion, unless we use some sort of symbolism which will more or less automatically systematize things for us.
To cite an authority on this point, contradicting as it does the common notion that we should be always very much aware of what we are doing, let us quote Alfred North Whitehead, the eminent mathematician, logician and philosopher. What he has to say is directly in point:
In the very early days of the physical sciences, it rapidly became evident that the customary symbolism of words was neither brief nor perspicuous enough to do the job that had to be done. With this discovery began the mathematization of the physical sciences which is still proceeding successfully today. Repeated efforts to apply this second principle in the same form to the social sciences and to psychology have often been made in the past. Most of them have had no particularly outstanding successes over more conventional methods, however.
This may very well be because the second principle alone is not enough, but needs the aid and guidance of the first; and it is only comparatively recently that the realization of the importance of talking only in terms of observable quantities has begun to enter deeply into the thinking of those concerned with these sciences.
Today, however, there seem to be some extremely good reasons for hoping that the simultaneous application of both these principles will soon permit clearer and more valid thinking about some of our chief causes of semantic confusion than has ever before been possible. This new revolution of thought started in the field of biology, but has rapidly spread into sociology.
It began as an attempt to produce a mathematical physics of the living organism, which would stand in the same relation to conventional biology as does mathematical to experimental physics. Very great advances have already been made in this field; N. Rashevsky, one of the pioneer workers in mathematical biophysics, in revising his standard text on the subject, found it necessary to enlarge the contents of the volume to the extent of making it several times larger in size, and he apologized in the preface because he was compelled to abbreviate the discussion of much of his material far beyond the point of maximum intelligibility.
The first spilling-over of the new subject was directly into psychology, that is, into a consideration of the neural apparatus by means of which we think. At this point the new science enters into intimate relations with cybernetics. The success of the attempts to rationalize biology also soon echoed by application of the method to sociological thinking. It seems probable that we can see here most clearly the relation of these new methods to the problem of avoiding "semantic confusion."
As an example, let us consider now the concept of freedom. In the normal course of events, such a discussion leads almost immediately to definitions and to disputes about the validity of the definitions. Much of this no doubt arises from varying connotations of the terms in the minds of the disputants.
Within a short time we may expect to hear: "You are semantically confused!"
Let us see what the mathematical approach through observable quantities may be able to do for us in this unhappy situation. First of all, we ourselves have a job to do: So broad a notion as that of freedom has many aspects, and we must decide in advance which of them we wish to discuss. Our mathematics cannot do that for us, nor can we expect it to do so. We can demand, however, that once we have settled this point for ourselves, the symbolization take over from there.
One possible content of the concept "freedom" concerns itself with economic freedom, that is, with the amount of time which we must spend in getting our living. This seems a comparatively simple aspect; let us discuss it first. Of course, we must first define the symbols which we shall use. We shall define them verbally here, but we must try to do so in such a manner that the quantities they represent are unambiguous and are directly and objectively measurable.
For this purpose, let us take the symbol W to mean the maximum amount of physical labor which an individual can perform per unit time. We may not know, nor be able to measure what this is at the moment, but it seems clear that it is a quantity measurable directly by some objective means.
Let us take the symbol w to denote the actual physical work performed by the individual to provide himself with the necessities of daily life. Again this quantity is directly and objectively measurable, at least in principle.
Various objections may arise at this point; it may be said, for example, that the work done will vary from day to day. To this the answer can be made that we can then speak of the average amount of work, obtained by observation over a sufficiently long period. It may be objected that the definition of the symbol w begs the question, that we do not know what the "necessities of life" are; but a very broad answer, which indicates the general way of meeting such objections, is available to this. We merely reply that we are speaking of a given individual, and we can find out what the necessities of life are, for him, by observing just what is required to keep him alive and no more.
Given these two very simple things, W and w, then, we may now propose the following definition of "economic freedom":
F e = (W-w) / W
It is easily seen that this does the right sort of thing, at least qualitatively. If the individual under discussion must do the maximum work of which he is capable to gain the necessities of life, W = w, and his economic freedom is zero.
For the present, we shall let this particular way of regarding the concept of freedom rest here, except to remark that if we wish to know more about F e in any particular case, we should have to observe that it depends upon other things than those we have mentioned explicitly in this simplified and purely illustrative example. For instance, the quantity w will depend upon the productivity and the means of distribution of the society in which the given individual lives. However, this gives rise to no essential difficulty; a more complete study would require that we determine such things about the society in order to specify w, and hence F e would vary with them, but there is no order to specify w, and hence F e would vary with them, but there is no reason why we could not apply the same type of approach to these.
It may be added that this has already been done to some extent by those working in this field, and there exists a mathematical theory which shows us how w varies with the class in society to which the individual belongs, under rather broad assumptions as to the structure of that society.
Just for the sake of showing that this general way of thinking applies to a somewhat more complex type of "freedom," let us look at a rather different aspect of that concept. Our previous definition of freedom concerned itself only with the proportion of an individual's total possible work per unit of time, which was necessary to provide him with subsistence. However, our guinea pig can do in his free time, as a further measure of his freedom. Since we shall here be considering the activities which he pursues, let us refer to this aspect as "activity freedom," to distinguish it from the previous case.
We must say something at once about the society in which our test case lives, but in order not to restrict ourselves any more than we have to, let us merely specify that this society makes a certain number, n, of activities possible to its members, and that all these activities are equally available to all those living in that society. It is true that this is not very realistic; however, we must creep before we can walk. Again, the simplification is the cause of no essential difficulty, and more detailed analyses have already been carried out elsewhere.
However, though all these activities may be available, the individual we are studying will not care for all of them. Let us say he likes m of them, and therefore dislikes the remainder, n - m, in number. For present purposes, it is not essential that we say anything about exactly how these m activities are chosen from the entire list; let us merely say instead that there is some number, M, of ways of actually choosing them (*).
It is also necessary for us to say something about how many other individuals of this society share his liking for exactly these activities. To avoid unnecessary complexity, let us assume that these likings are distributed among the individuals entirely at random; that is, for a given activity and a given individual, it is just as likely as not that it will be an agreeable activity for him. (It is quite possible to arrive at valid conclusions for other, more complex distributions, but the mathematics quickly gets more messy, and for the purposes of illustration the simplest assumption is here the best.)
On the basis of this assumption, it would be easy to prove that a fraction, 1/M, of all the members of that society will like exactly m particular activities, and those alone; let us merely accept this statement without proof.
We shall now have to think about the proportion of the time during which our individual comes into social contact with others. If the average number of individuals per unit area of the earth's surface in the region where our guinea pig is -- that is, the population density in that general area -- is denoted by N, he will come into contact with others with a
(*) For the benefit of those who may be curious about it, the formula which connects M with n and m is as follows:
M = nEm=1 ( (n) (n-1) (n-2) ... (3) (2) (1) ) / ( (m) (m-1) (m-2) ... (3) (2) (1) (n-m) (n-m-1) ... (2) (1) )
frequency of aN per unit time, where a is some constant fraction less than one, depending on such things as means of communication and other considerations external to this discussion.
Now for a few more symbols: Let us call by the name T the average fraction of unit time which our individual spends in contact with others. We shall take the symbol t to mean total time in contact with others. Then it will be true that t=aTN.
Now if we use the symbol Tf to mean free time, the proportion of the total time which our individual has entirely to himself, we can say at once that Tf = 1 - aTN.
Now, finally, bringing "activity freedom" into the discussion, we see that by our definitions, during the time Tf, our individual can do entirely as he pleases, if and only if he is with others who enjoy the same activities. Under the assumption of random distribution of preferences, t/M may then be spent in activities of his own choice, which he holds in common with others.
Now let us define Fa, activity freedom, as the total proportion of time during which he is able to pursue activities pleasing to him. Then we find that:
Fa = Tf + t/M = 1 - ((M-1)/M) a T N
There are several conclusions which may be drawn from this relation; however, it was here introduced primarily to illustrate a more complicated method of derivation than that of the first example, and to show a second definition to be possible. We shall therefore merely remark that a glance at the form of the expression resulting for Fa shows that this type of freedom decreases as the population density, N, increases!
These are just illustrations, of course, and are considerably simplified, but they do show that even so slippery and notoriously difficult a concept as that of social freedom may be handled easily by appropriate mathematical tools, if only we are careful to restrict our thinking to observable quantities.
It is also true that the approximations made in these derivations are certainly no worse than those of weightless springs, inextensible and perfectly flexible ropes, and perfectly rigid bodies of mathematical physics, which have contributed so much to our present control over our physical universe.
Perhaps this way of removing "semantic confusion," both actual and merely alleged, will do as much for our control of our social environment, if we are wise enough to try it -- and if we have time left in which to do so.
THE END
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