No More Learning

But this is clearly untenable, for the signs in a formula are even more undetermined when no one points out, by other means, what does each sign stands for, and thus the entire problem reappears out of the blue. By saying what do each sign stand for, we would not employ again undefined terms, unless we want to incur in another manifest, vicious circle. Mario Bunge himself later recognizes that: "But mathematical form alone won't tell us anything about the physical meaning of the formula". (1973, 30)
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C. W. Klimster raises another good objection against the procedure of leaving terms undefined, although he says 'concept' where the more appropriate thing to say would be 'word' or 'term': "I cannot accept this idea of understanding because it gives no assurance that we shall know how to apply the concepts in a new situation which may develop in the future" (Bastin,1971, 124). To put if briefly, I can carry out opera- tions the moment I am given a mathematical formula, but if I do not know what its signs stand for, I will be stunned the moment I meet a new situation; I will not know how to apply it. Stripped from meanings, the formula does not hold any relation at all with reality and it is im- possible for me to refer it to something.
Mathematics are conceptless; Hegel told us that determinations "were accepted without concept and often without any sense" (EPW, 259 A). This is the reason why I can execute operations like a machine when I am given a formula. Hegel states that with mathematics, the mind finds itself "in one activity that is the extreme alienation of itself, in the violent acti-vity of moving within the lack of thought" (WL I 208).
Those who say that they leave terms undefined, return sooner or later to what 'everybody understands for', but they do this tacitly. It happens here what Bunge says: "A physical theory is assigned a literal and ob- jective interpretation by assigning every one of its referential primitive symbols a physical object --entity, property, relation or event-- rather than a mental picture or a human operation" (1973, 119).
The intention to dispel away the subject is shameless. Bunge supposes that everybody understands what words such as object, entity, proper- ty, relation and event mean. But all people are far from understanding such things, and even if they did understand them in some cases, that can only occur in function of the subjects, as we will later see: "Giving names, that is easy, but a different thing is to understand" (GP I 241).
We will now raise three definitive objections against the resort of leaving terms undefined, which, unfortunately, is widespread among the rebellious, empirical sciences: they cannot know whether there is circularity and hence absolute vacuity and pettiness in their theory; they cannot know whether there is a contradiction or if they are mak- ing metaphysics instead of empiricism.
Bunge himself foresees the perils of this abyss when he demands the 'primitive independence' as the absolutely indispensable requirement for the axiomatization of a scientific system: "the basic concepts of an axiomatic system must be mutually independent, i. e. they must not be
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defined by others (In fact, if one of them were defined in terms of other basic concepts, it would not be a primitive concept)" (1973, 165).
It is amazing that Bunge closes his eyes before the evident fact that we would not know which, among two terms, is dependent and which one is derived and which one is logically previous if we do not know what each of them mean, that is to say, if we do not define them, which means to give up the farce of leaving terms undefined.
This is a devastating objection not only against Bunge but against all the alleged authors of the method of undefined terms. It is impossible to find out if we are defining A in function of B and B in function of A as long as we do now know the meaning of A and B, or in other words, as long as we do not define them.
It is impossible to exclude circularity if we do not make definitions; it is impossible to avoid that an entire system becomes a big tautology, a bunch of things that that does not affirm or deny any single thing. And this concerns not only scientists who want to leave terms undefined, but also those who explicitly refer to what 'everybody understands'; for if we do not make the meanings explicit, it is perfectly possible that what everybody understands by A is in function of what everybody understands by B and vice versa.
And there is something worse than circularity: contradictions. It is impossible to know if two terms are or not contradictory unless we know what they mean. Most of the times, what people feel tends to be metaphysical, and the only way to prevent that from happening in a particular case is, in fact, to look for the meaning of the term in ques- tion i. e. to define it.
According to acclaimed anthropologist Benjamin Lee Whorf, the native language is for the mind a metaphysical frame. Gary J. Millers summarizes thus this position:
According to this view, the language structure operates as a ready-made metaphysical framework through which the speakers perceive and concep- tualize. A person's language is his means of interpreting reality; it shapes his comprehension of the environment and supplies him with his definitions, categories, concepts, and perspectives. (Rossi et al. , 1977, 197).
We do not need to embrace another deterministic thesis of Whorf which posits that the preexisting scheme of language is unavoidable. It is possible to elude consciously the prejudices inherent to one's own
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native language. But precisely, for that purpose, we need to find out what the meaning of the concept is. For instance, if we set ourselves the goal of constructing an empirical science, the only way to investigate if a word is metaphysical and needs to be excluded from the system is to make its meaning explicit. To leave a term undefined is almost as set- ting oneself to construct a metaphysical system.
5. definitionS by decree
One used frequently to believe that each one of us can define his terms as he pleases, but this ruse has become today very fashionable among certain scientists in order to elude the obligation of investigating the meaning of words, an investigation which, as they can foretell, would necessarily lead them to the study of the knowledge of the subject. We are dealing here with definitions by decree, arbitrary definitions. One simply decides to understand by 'time' such thing and gets rid of trouble.
Let us get to the root of the problem. Every attempt to define tries to lead the comprehension of someone else, to the content which the defining person affirms to be the meaning of the word in question. That is what logicians call the definiendum; it would be what we called 'such thing' in our previous paragraph.
There are three possibilities in the arbitrary definitions: that the definiendum is another word, an empirical data or a fantastical image or object.
An example of the first modality is the one that we mentioned be- fore: I choose to understand by space a group of points and I get rid of the problem. Such a definition is null and void because point is defined in function of space, and the circularity does not bring any content whatsoever to the understanding of other people. Those who define by decree, obviously, will look as a definiendum a word that does not need to be defined in function of the term they are trying to define; but here lies the difficulty of this principle, in order to avoid circularity one needs two definitions which are not obtained by decree. As long as we do not have the true definition of A and the true definition of B, it is impossible to know if A is defined in function of B and vice versa. The only way to prevent the arbitrary definition from being null and void is to abandon the arbitrary definition and use a true definition. This objection settles once and for all the issue.
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But there is even more to this. In this first modality, what the arbi- trary definition does is simply to affirm the synonymy of two words; nevertheless, what is simply affirmed can also be simply denied. In order to make science we would have to demonstrate the synonymy. The only way, however, to demonstrate that two words are synonyms is to provide the true definition of each of them, not an arbitrary one. And here we come across with the same result: the arbitrary definition needs to be abandoned. I mean, of course, if we are really willing to make science.
We must notice that the solipsistic approach does not avoid this difficulty. He who defines by decree cannot be so obstinate as to say that he does not care about other human beings, and that the definien- dum is to him such thing and period. Science means universality, some- thing that is valid always and not only in a solitary act. Since he who affirms a synonymy performs a public deed, he needs to demonstrate his affirmation; otherwise, it can be denied without further trouble. Since all the consequences of the system would depend on the original definition, all the system would depend on the whim of someone who affirms or denies something. If they call that science, I am sorry to say this, but they have confused science with literature.
As we said in the first chapter, science demonstrates and Literature only affirms and leaves its truth to the taste of whoever wants to em- brace it. In that case what one affirms is a synonymy, and both such pseudo-defintion and the entire system are subject to the aesthetical or pragmatic whim of the author, its audience or anybody else. That is a literary essay. The only way to avoid it is to demonstrate the syn- onymy, but the only way to demonstrate a synonymy is to show the true definition of the two terms in question. Let us say here loud and clear that arbitrary definitions avoid the necessity of studying the sub- ject in order to avoid the true meaning of words, but one deliberately renounces thus to science and starts making literature.
And their resource would backfire at them if they assumed the romantic position of saying things like synonymy is only hypotheti- cal, everything is subject to further revisions, science never reaches an end, the last ideals are always far beyond our reach, and more stuff of that pathetic sort. On a general basis, this position is self-destructive, since there must be something true for a thing to be hypothetical; only in comparison to something else a thing can be labeled as such. But with the case we are dealing here, the hypothetical resort is particularly
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counterproductive, since 'hypothetical' is not something that can be either true or false, but something which can be either true or false and which is submitted to a test in order to see if it is true or false; it is impossible to submit something to a test if we do not understand what is going to be tested, i. e. if we do not define it with true definitions. The only way to find out if an apparently hypothetical synonymy is true or false is to compare the true definitions of the apparently synonymical words. This is the reason why this resort backfires at them; when a def- inition is hypothetical it necessarily demands that one looks for a true definition. What can be either true or false and is not tested is called uncertain, not hypothetical. Escapism reaches its utmost point by re- jecting the subject and grounding science on sheer uncertainties. One gives up thus science and true knowledge. Let us not make a big deal about this: to give up science means to avoid the study of the subject.
Arbitrary definitions, in their first modality, stumble upon another obvious difficulty. He who advances a term while defining another evi- dently needs to suppose that such term has a meaning by itself which is not susceptible of arbitrary definitions; otherwise, we would embark upon an indefinite process and, in short, no content would be brought to the understanding of other people. Arbitrary definitions essentially suppose other definitions that are not so. Therefore, since imaginary and empirical definienda are ruled out in this modality, one has to look sooner or later for the meaning of the appointed terms in the knowing subject himself. The same arbitrary definition refers sooner or later to the subject, provided that one does not want to embark upon an indefi- nite process. As Hegel says: "supposing and determining never reach the final goal" (JS 27).
"It has been made clear that indefinite progress belongs to the reflec- tion which lacks concept; the absolute method, which has the concept as its soul and content, cannot lead us there" (WL II 500s).
The second modality or possibility of the arbitrary definition is that the definiendum is an empirical object, a data effectively perceived as empirical by him who makes the definition. If the said person had the concept in question, he would simply give us a true definition and would not come up with the folly of making a dogma out of an ar- bitrary definition; but since he does not have it, he thinks that he can point out something with his finger and say 'I understand by definien- dum this'. As we can see, 'this' is, evidently, too particular; which is something that goes against his own interests. For instance, if he says
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'by animal I understand this', he does not mean thereby that being an animal is to be identical with his dog. It would follow from this that there would not be any other animals, for identity is always reciprocal. If being an animal is to be identical with this, other animals would not be animals because they are not this.
Aside from the question as whether or not individuality is an em- pirical data, when someone points out with his finger and says 'this', he aims at individuality. Therefore, this is not what the dogmatic per- son means to say; he aims at something more universal. He does not have anywhere to land his 'this' other than his own imagination, since he lacks the concept, which would be indeed universal, and the per- ceived data is too particular. Therefore, the most recurrent modality of arbitrary definitions is the third one.
"It is common in the empirical sciences to analyze what one dis- covers in imagination" (Rph 32 Z).
The comment of Hegel regarding the third modality is this: "But to remain in the phenomenon or in that which is produced in imagination for the ordinary cognition means to renounce both to the concept and to Philosophy" (WL II 435).
The image presented as a definiedum candidate is blurry most of the times in order to avoid being so particular and incurring in the same failure of the second modality. But it does not succeed. For instance, the man of the street, who does not have the concept of animal --even biolo- gists still dispute the definition of animal--, may be blurrily imagining a horse when he says that word. As blurry as it may be, however, it is a horse; should the meaning of animal were that one, it would follow that neither birds, fishes, microbes nor reptiles would be animals.
That is the failure of every arbitrary definition, for we saw that, if the definiendum is an empirically perceived entity, it becomes even more particular, and if it is a word, it does not actually define anything; it ends up alluding to true definitions which cannot be drawn without the study of the subject. Those are the only three possibilities there are.
Let us provide another example. As we saw in our last chapter, one does not ordinarily have the concept of human. Those who believe, therefore, that, instead of the concept, they have all singular persons before their eyes, only deceive themselves: they are only imagining something. A nebulous and vague image comes up to their minds. As vague as it may be, however, it is always too particular. They may be imagining a masculine figure, but that would rule out half of humanity
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from being human. If they imagine a thin person, that would exclude all fat individuals. Should they imagine a young man, all mature peo- ple would be discounted, etcetera.
In this regard scientists do not differ much from ordinary men. The physic who, avoiding the concept, pretends to define space as a group of points, probably imagines a certain group of black specks (not points) against a white canvas, for example, he may be imagining twenty-eight points nicely distributed, but we would rule out thereby the spaces that consist in a million points and the spaces whose twenty-eight points are distributed differently. And so it happens with everything.
One must notice that operationalism always falls in one of the three modalities of arbitrary definitions and fails, and that meditionism is also a mere species of operationalism. Although some specialists be- lieve to have the concept in question, it is obvious that they do not have it and that they are providing as definiendum a word, a fantasy or a sensible data; they become thereby targets of the objections we have raised. Let us put two examples: movement and time.
The arbitrary decree of operationalism about movement is the same to say as 'I understand by movement the fact that a body goes from one place to another'. They pretend to operationalize movement, since by means of Cartesian coordinates it is possible to identify and measure the two alluded spaces.
Before criticizing these definitions by decree, let us document its recurrent presence in the statements of contemporary physics. R. A. Serway says the following: "The movement of a particle is completely known if one knows its position in space at every moment" (1985, 28).
Let us give the floor also to Max Born, who, by the way, is very con- vinced of having the concept: "It is first necessary to subject the concept of motion itself to analysis. The exact mathematical description of the motion of a point consists of specifying at what place relative to the pre- viously selected coordinate system the point is situated from moment to moment. " (1962, 16)
And finally, Arthur Eddington: "Motion is generally recognised by the disappearance of a particle at one point of space and the appearance of an apparently identical particle at a neighbouring point. "
It is perfectly evident that movement does not consist in that. Although they say 'I understand by this. . . ' they are not understanding anything; they do not have the concept. Therefore, they are providing as definiendum a verbal expression, a supposed empirical data, or a fantasy. If a particle
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no longer existed in moment A and then begun to exist again in mo- ment B, there has been no movement or trajectory at all; the particle has not gone through the intermediate space; it is false to say that by knowing two positions one knows the movement. By measuring time and using coordinates, physics may determine two points in space and two moments in time, but they can only infer the existence of move- ment as such, and that will occur when they add the adequate premises in which the word movement appears for the first time, premises that are not only very dubious but completely gratuitous as well. The idea of movement is added from the outside; the operationalist device does not get a grip of movement; at the most, it gets only its effect: the new position of the particle. One of the completely gratuitous premises ad- vanced thereby is that we are dealing with the same particle, something of which no empirical observation can bear witness, since identity is not an empirical data but a metaphysical and speculative lucubration without parallel. Another premise is that the intermediate space is con- tinuous, an untenable thesis as our third chapter will show. Another premise is that a new position of the particle can only explain if there has been any movement, but should that be the case, movement would be a mere explicative entity introduced from the outside by the specu- lative mind in order to provide an account of empirical phenomena. If the mind introduces something whose meaning is not the empirical phenomenon itself, then it must define what it introduces so that we understand it and the mind knows what it is speaking about; therefore, every operationalistic definition by decree is accessory, for they need to define movement: the spirit reappears again as though the operational- ists had not said a single word.
In the famous 'tunnel effect' all physics agree (cf. EB, 23 717, 2) that it is impossible that the particle has been in, or went through, the in- termediate space, for the particle would have there negative synergic energy and imaginary speed, which is simply absurd. It simply occurs that the particle was first in a Y place and later on in a Z place, but there has not been any movement. To affirm the contrary would not only contradict the fundamental principle of modern physics which states that nothing unobservable exists; it would be to affirm a physical im- possibility.
The definition by decree of Serway, Born and Eddington and all physics do not get at all a grip of the concept of movement. They pro- vide us as definiendum a word or a group of words, or a fantastic image.
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But we have shown that no definition by decree achieves its aim of giv- ing meaning to words without studying the knowing subject.
Another famous case is the decretory ingenuity of Einstein when he says: "one understands by 'time' the position of the minute hand of a watch in the most immediate proximity of an event" (1971, 40).
It is obvious that there is no concept here, for sooner or later one would have to define watch, and one would evidently say that it is a ma- chine to measure time, or in either case, one would say something else in which the word time reappears, and thereby we would be immerged in an absolute circularity. At the end of the day, nothing would have been defined; there would not be any concepts whatsoever. Bridgman even mocks that circularity by suggesting that a watch should be de- fined as a machine that adapts to Einstein's laws. One wonders how serious did Einstein take his own apparently empirical definition when one reads this letter of him quoted by Dyson Freeman: "People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion. " (Dyson 1979, 193).
There is no doubt that other physical definitions of time are circular. For example, some physics say that one only needs to define 'day', which they believe to be something very concrete. They affirm thus that a day is the lapse of time that goes between two successive sun- rises. But they cannot define lapse or the concept of 'successiveness' without mentioning time. If there is something which is clearly impos- sible to be defined without reference to the subject, that thing is time, as we will later see.
If someone says 'I take by time this' what happens is that he remains with this and forgets about time. This is a valid objection against all ar- bitrary definitions and exhibits them once and for all as illusions, since no knowledge is possible if the data designated by the expression 'this' is actually time as long as we do not know what the word time means, that is to say, as long as we do not have a true definition.
In other words, I cannot understand someone when he says 'I take by time this'. I can understand this, but not time. That person does not understand what he/she is saying. In order to understand his/her phrase we would need to know what time is. But then the arbitrary definition would be unnecessary. The arbitrary definition is an essen- tially unintelligible locution. It does not constitute a public act because it is essentially unintelligible. It is a subjective and whimsical act. It falls outside the realm of science.
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There is a more widespread ruse than arbitrary definitions (and which is even more traditional) employed in order to avoid the study of the object. It is the superstition Locke and the Scholastic Philosophers called the theory of abstraction, according to which concepts have their origin in sensation. Few errors in the history of thought are easier to refute than this one; however, it remains attached to the minds of those who do not dare to make a simple reflection. What is striking is that Plato crushed that belief, once and for all, more than twenty-five cen- turies ago:
"Why, on what lines will you look, Socrates, for a thing of whose na- ture you know nothing at all? Pray, what sort of thing, amongst those that you know not, will you treat us to as the object of your search? Or even supposing, at the best, that you hit upon it, how will you know it is the thing if you did not know? (Meno 80 D)
Hegel says that thus: to make a generalization "it is indispensable to know what it deals with. " (NH 259)
In other words, in order to make a generalization one needs before- hand the concept; in order to abstract the aspect in question one needs beforehand the idea that allows us to focus on that aspect. But then, the concept does not have its origin in sensation; it existed beforehand in the mind because it is the condition of possibility of all the so-called process that leads to the abstraction of the concept from the empirical data.
"To hit the mark with the substantial, one needs to carry along the knowledge of it. Sensation does not know what the substantial is, just as the hand does not (know) what color is. " (VG 259).
The object has one thousand characteristics and aspects. Even the person with the most recalcitrant prejudices must recognize that not everyone have in their minds a determined concept; but how could some- one focus his attention on the aspect that is indeed pertinent and leave aside the irrelevant ones, so that it produces in him the concept in ques- tion, if he does not know beforehand what it is about? And if he knows it, he already has the concept; the causal contribution of sensations comes in late. What could one look for if one does not know that?
That does not mean that ideas are innate, as if children were con- scious of them from the beginning. The spirit needs to develop and take gradually conscious of itself; concepts only stem from self-
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consciousness. "The exterior is only an impulse for the spirit to dis-
play itself" (GP I 471).
The spirit, of course, is in itself undetermined, it is the concept that exists for itself; its development is to reach awareness. The determinations that it produces and takes from itself cannot be called innate. This development must be provoked by something exterior; the initial activity of the spirit is reaction; only thus it acquires knowledge of its own being. (GP III 211).
When that superstition says concept, it imagines an empirical impres- sion (v. g. green), not a concept. For that reason they think it is obvious that that impressions could not be caused by anything else than sensa- tions. But concepts are not that. A spatial figure is not a concept. The entire theory of abstraction is based on a confusion of concepts with the images of fantasy. In order to dissuade their defenders, one would only need to remind them, for instance, that the concept of triangle is a completely different thing than the image of triangle: the image is always very much particular; sometimes we imagine our triangle as a white line against a green screen, sometimes as a black line against a white screen, sometimes we imagine it bigger and sometimes smaller; sometimes we imagine it as an equilateral triangle with its vertex pointing upwards, sometimes as a triangle rectangle with a cathetus over its vertical. On the other hand, the concept of triangle is always the same and it is universal.
One of the essential aims of our next chapter will be to show how concepts are shaped by self-consciousness; the task of our present chapter is to make the reader see how useless are all the efforts made to avoid the study of the subject, one of which is the theory of abstraction. Let us see how Hegel reformulates our central argument against it:
When the unthinking consciousness declares observation and experience to be the source of truth, what it says may well sound as if only tasting, smelling, feeling, hearing, and seeing were involved. It forgets, in the zeal with which it recommends tasting, smelling etc. , to say that it has no less essentially determined the object of this sensuous apprenhension, and this determination is at least as valid for it as the sensuous apprehension. [. . . ] What is perceived should at least have the significance of a universal, not of a sensuous particular. (PG 185)
Had they not determined something, they would not know where to draw their attention. That determination is a concept, and a concept is
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