To accept this would be to rule out
intellectual
work, and that would confirm that one does not have the general concept of work, which was the only thing at stake here.
Hegel Was Right_nodrm
In other words, although it does not approach to or go away from any other thing, God would see that object moving.
The idea according to which the absolute space is the sensorium Dei goes back to Henry More, and in a certain way, to Pierre Gassendi. But we must take into account that in times of Newton everybody believed that movement was something absolute. And they still think the same thing, all those who have neglected relativity in order to remain attached to the myths of common-sense. Since the times of classic physics, Hegel disproved that belief with the mere analysis of the idea of movement:
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 50 Hegel was right
"Ultimately, it is absolutely clear that movement as such only has meaning and existence in a system of many bodies, and by the way, many bodies which stand in reciprocal relation according to different determinations" (EPW 269A).
For the same reason, Hegel rejects the first law of Newton: "a recti- linear infinite movement is a void mental monster; because movement is always towards something" (GP II 193).
Moreover, Hegel holds that the physics of his times would have avoided those phantasmagorias if they had taken the time to read well Aristotle: "Aristotle shows that the void suppresses movement [. . . ] In movement the body --as distinct-- is a positive relation, not towards nothing. " (GP II 185).
And a little before that point in his book, he says: "Aristotle deals then with the void space, an ancient question for which Physics still cannot find a solution. They could do that if they read Aristotle, but for them thought and Aristotle are things which have absolutely no existence in the world. "
Already with his commentary on Zeno, Hegel had explained the relativity principle of movement: "And this is also true: that movement is definitively relative. " (GP I 315).
In order to reject the notions of absolute space and time as unsci- entific, Hegel did not have to wait until Michelson's experiment: he only needed to realize that those were mere abstractions. Evidently, an abstraction cannot pretend to have the same status of reality: "The word absolute has often no other meaning the word abstract; thus, abso- lute space and absolute time are no other thing that abstract space and abstract time" (EPW 115A).
We have displayed these quotations in order to show that the link between modern physics and Hegel's philosophy is not fortuitous. Our author already knew how unscientific and ungrounded it is in Physics to project as real something not observable.
2. a baSic principLe
Before venturing into the refutation of the different ways out that have been invented to avoid the study of the subject, we beg the reader to consider the following reflection as fundamental, for even though it is obvious in itself, it has been neglected during the last centuries.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 51
If a word does not have an empirical meaning, the origin of the con- cept in question cannot be sensation, and hence it is necessary to look in the subject itself both for the origin and the meaning of it.
For all what follows in this book, the above reflection is essential.
It cannot be stated that the origin of such a concept is sensation, for the simple reason that the origin would have to be an empirical data, but precisely no empirical data corresponds here to the concept.
For example, the concept of 'point', in which definition enters the idea of unextendedness, could have not been caused evidently by any sensible data or by imagination, for every empirical data is extended and every image of fantasy is extended as well; consequently, the ori- gin and the meaning itself of the concept 'point' should be looked for in the subject.
On the other hand, all sciences use at least some concepts whose meaning is not empirical. The science that raises fewer doubts in this regard is Physics, but apart from the example I just mentioned, we already saw that Margenau listed only some of the few concepts which are not empirical: mass, energy, charge, force, wavelength, strength, potential, probability, amplitude, crystal, magnetic field, atom, photon, electron, meson. (1978, 98)
The following text of Hegel deals with Mathematics, but it mentions several terms employed by Physics as well:
Other mathematical determinations such as infinite, relations, infinitesimal, factors, potencies, etcetera, have their true concept in Philosophy itself; and it is wrong to believe that Philosophy should extract and take them borrowed from Mathematics, where they are accepted without concept and often without any meaning at all; these concepts must wait until Philoso- phy gives them their sense and justification. (EPW 259A)
It seems evident to me that none of these terms have an empirical origin.
Einstein, the most acclaimed physic of our century, goes far beyond Margenau. His forceful statement should not be so zealously hidden away from the public by the apologists of the empirical sciences:
And let us say this in regard of the historical development. Hume clearly understood that certain concepts, for instance, that of causality, cannot be ex- tracted from the material of experience by logical methods. Kant, convinced
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 52
Hegel was right
of the indispensable character of certain concepts, considered them --just as they are selected-- as necessary premises of any kind of thought and dis- tinguished them from concepts of empirical origin. But I am convinced that such differentiation is mistaken and does not approach the problem in a natural way. From a logical point of view, all concepts, even the closer ones to experience, are free constructions, just as the concept of causality, which was the starting point of the dispute. (Schilpp, I 1969, 12).
According to Einstein, not only some concepts of Physics but every single concept lacks an empirical origin.
3. what everyone underStandS?
That being said it is now of primal importance to take this into account. More often than not, one believes to 'know' the meaning of a certain word, because one thinks that the meaning is a determined empirical data which is easily observable. But in the cases that the word being considered does not have an empirical meaning, it would be unjusti- fied to suppose, without further investigation, that 'we know what it means'. It is by no means true that we already 'understand' its meaning; we may be imagining something, but that image is not the meaning in question, for imagination can only contain combinations of empirical impressions and accumulate the data provided by the senses; however, if the concept does not have an empirical meaning, no empirical im- pression or combination of them could provide it. Let us go back to the above mentioned example. There are some people who believe they know what the meaning of the word 'point' is; but what they imagine is a speck, not a point; if it were unextended, as it should be to be a point, they could not imagine it. As a matter of fact, they do not know what the word point means; they do not have the concept.
We must look for the meaning and for the concept in the knowing subject.
Let us put another example. In the context of discussion of modern pluridimensional, non- Euclidean spaces, a great number of mathema- ticians and physics do easily away with the problem by saying that space is a group of points. However, since they do not know what a point is, this so-called definition lacks any kind of meaning. The situa- tion gets even worse if they try to define point, for they will irremediably
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 53
say that it is an unextended part of space. They define point in terms of space, and they define space in terms of point. The circularity of this argument is manifest. We do not gain any knowledge by means of this procedure, and clearly, one will notice that these people do not know what they are speaking of.
Here is where what we were discussing occurs: they ease themselves by believing that the meaning of the word space is a certain empiri- cal data that is easily verifiable. An opponent would probably answer to this objection something like 'you are not going to deny that I am looking at the space between my body and the wall in front of me'.
Of course, I will deny this. What this person is seeing is the wall in front of him. Space as such is not observable; it is not an empirical data. Since it is not an empirical data and they do not know how to pro- vide it with meaning by other means, they do not know what they are
speaking about.
One brief digression: if modern physics boasts their rejection of
non-observable entities, one wonders why they keep speaking of spaces, let alone pluridimensional ones. The only justifiable criterion would be the 'necessary factor to explain observable data'. But we will see in our fifth chapter what the Science of Logic has to say about those explicative intended factors.
It is the right time to do away with a false way out. Scientists will admit that many concepts do not have an empirical meaning, and yet they say that they are inferred from empirical data. I do not deny here the logical legitimacy of the inference in question; but it is obvious that, in order to infer certain concepts, we must first need to know what they mean. Precisely, in this case, the meaning does not coincide with any empirical data, for it is necessary to infer it since the meaning is not an object of empirical experience; if it was an empirical data, we would not have the need to infer it. In some of the premises of the inference process, one of these concepts --which are not derived from empirical experience-- appears suddenly: How is it possible to handle it if we do not know what it means? What it seemed to be a way out only makes more acute the need to look in the knowing subject for the origin and the meaning of concepts.
We do not need here to stop for long in order to examine another way out which is identical to the previous one. According to this po- sition, there are some things that are not empirical in themselves but only in their effects. God and the soul also have sensible effects, but that
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 54 Hegel was right
is not enough to know what those terms mean. The question is not about their empirical effects: what is here discussed is if the entity itself to which its causality certain effects are attributed is empirical or not. Although we do not put into question the legitimacy of such attribu- tion, it is impossible to know which entity they are speaking of as long as we do not know the meaning of the word they designate it with. Moreover, to judge if the said entity can be the cause of such effects, we need to understand beforehand the word that designates it. The fact that the said entity could have or not such effects does not make us know what the meaning of the word in question is.
Now, he firstly hinted and then explicitly said that, more often than not, the men of the street or the scientist do not know what they are speaking of; they do not have the concept; they do not understand what they are saying. It sounds severe, but it should not offend any- body because this is not any kind of truth: it is a truth that it is urgent to straighten out despite its harshness. "To know what one says is much more unusual as what one thinks, and one is very unjust by calling severe the reproach of not knowing what one says" (BS 249); "ordinarily, one calls concepts that which is nothing more than a reverie" (WL II 281).
Given that everybody is able to use a certain term not only in private but in a conversation or in a discussion with others, they think that be- cause of that they understand it and that they have its corresponding meaning, when in fact they only have an image product of their fan- tasy. For instance, as we have previously demonstrated, it seems that common people do not have the concept of 'point'; however, it is obvi- ous that we can all use the word point very skillfully. The same happens with the word space, whose meaning is ignored even by physics.
Let us put an entirely different example: the word 'work'. We all commonly use it without any mayor trouble. Nevertheless, I dare not only all workers but economists and labor lawyers as well, to define 'work'. I have not yet found anyone who has the concept of it. Everybody supposes that they understand this word, but some imagine a certain manual activity (v. g. , a man digging a whole with a shovel) and others imagine a still man performing a certain intellectual activity. The most common thing to happen is that each person imagines something re- lated to their own trade or profession.
One only needs a handful of insisting questions to dispel any at- tempt to define work. Is effort, for instance, something essential for an
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 55
activity to be called work? On the one hand, if one answers affirma- tively, then the really skillful expert who enjoys his own professional efficacy and performs his job without fatigue would not be actually working despite the fact that his productivity is superior to that of the majority; on the other hand, if one answers negatively, the millionaire swimmer, who is in his own private pool trying to beat the crawl Olym- pic records, would be working, --which is an utterly absurd premise.
Does work, in order to be that, need to produce something? We come across here with the physiocrat theses which posit that nature is the only one that produces more than what it plants, and that work only modifies and does not produce things. According to Physics, nothing in fact is ever produced, because the existing matter in the universe does not increase nor decrease. And even leaving this aside, it is obvi- ous that the work of fishermen does not produce anything; they only collect fish from the sea. The same goes for miners and harvesters. Should one person argue that by working one produces exchange value and not something material, that person would confirm in the first place that the majority of people do not know what work is, for evidently, almost the largest part of humankind does not know what exchange value is, and the few who say they do, frequently do not know it. In the second place, it would turn out that a group of workers, who produced a great stock of merchandize which did not find demand in the market and ended up rotting out, would have not worked at all.
Does it lie in the essence of work to modify an object or a material substance?
To accept this would be to rule out intellectual work, and that would confirm that one does not have the general concept of work, which was the only thing at stake here. In the second place, and this carries even stronger consequences, the distinction between work and consumption would disappear, for consumption also modifies things. And in the third place, since the fishers, the miners and the harvesters do not modify but only transport matter, it would turn out that the activity they perform is not work. And it would be ridiculous to say that the only thing that matters is the changing of the place in question, for then the thief would be performing a job, with the same right to social remuneration as the workers in the fabrics. In addition, the dis- tinction between work and rest would disappear, for he who goes out to take a walk changes the place where his clothes are in.
The result is here the same as in regard to space and point: he who believes to comprehend and know the meaning of a certain word by
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 56 Hegel was right
using it skillfully deceives himself. What he has is an image "for ordi- nary life does not have concepts but only imaginations" (WL II 357). And this image is not the meaning of the word in question, because it is too particular and because other people have a completely different image in their heads when they use the same word.
From this follows that the resource employed sometimes by scien- tists in order to elude the obligation of defining a term is completely mistaken. It is an appeal that is based on what 'everybody understands for. . . '. But it is false that everybody understands. This resource does not lead to the concept nor does it make the scientist in question know what he is talking about.
There would also be a more immediate objection: if everybody un- derstands it, then why don't they say it?
Before examining the next escapist resource it is convenient to state that recent experimental psychology confirms entirely Hegel's observa- tion in the sense that no one should be offended when told that he does not understand and even lacks the concept in question. Let us quote textually the acclaimed author of the treatise Concept Learning, psycholo- gist Earl B. Hunt, although his terminology is not the same as Hegel's:
Conceptual classification may be contrasted with another type of classi- fying behavior called discrimination learning. In discrimination learning, objects are classified on the basis of directly perceived properties such as physical size or shape. The usual explanation for discrimination learning is that the sensory features of any stimulus are matched to what is already remembered of these features, and that the learner ? s response becomes associated with them. The response thus classifies the stimulus. In discrimi- nation learning, subjective representations of immediate and past stimuli seem directly to indicate concrete, physical features (in contrast to the more abstract nature of concept formation). (EB 22, 897, 2).
While human beings popularly are called abstract thinkers, many of the classifications people make clearly seem to be concrete discriminations. Indeed, people may use the same term either in a discriminative or con- ceptual way. A child uses the term policeman in discriminating a man in distinctive uniform, while a lawyer may have a concept of a civil servant charged with enforcing criminal codes. (EB 22, 898, 1)
In this example, the professional studies of the lawyer would have lead to the acquisition of the concept, while the child, a typical example
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 57
of what Hegel calls 'ordinary life', proceeds by means of this association of empirical features called imagination: but the child and the lawyer em- ploy the same word and use it skillfully. It becomes obvious that using a word skillfully does not imply by any means that we have the belong- ing concept and that we understand. Let us repeat this with Hegel: "To know what one says is much rarer than what is thought" (BS 249).
What Hunt has summarized for us is the result of a large series of experiments. Nevertheless, it is evident that animals also learn how to discriminate and yet they do not have concepts. If we distinguish between science and technique, between knowledge and skills, it be- comes obvious that mere empirical discrimination is enough for ani- mals to possess a series of techniques which in many cases are more refined than ours. As we will later see, the technical success boasted by our empirical sciences does not demonstrate by any means that these disciplines understand.
4. Leaving termS undefined?
It is likely that the writers of treatises who leave some terms undefined refer to what "everybody understands". It is likely because, if they were not referring to this, their readers and hearers would have their mind in blank after reading or hearing those terms, they would not have any- thing to hold on to, and they would not know how to cling on to the signals they receive. Although the scientist does not make his reference explicit, his audience notices the reference to what 'everybody under- stands'. However, since they do not have the concept, the words are not actually referring to anything.
Mario Bunge claims that undefined terms "are not therefore obscure or undeterminate, since they are specified by a number of formulas" (1973, 9).
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)
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 58 Hegel was right
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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 59
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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 60 Hegel was right
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.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 61
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.
The idea according to which the absolute space is the sensorium Dei goes back to Henry More, and in a certain way, to Pierre Gassendi. But we must take into account that in times of Newton everybody believed that movement was something absolute. And they still think the same thing, all those who have neglected relativity in order to remain attached to the myths of common-sense. Since the times of classic physics, Hegel disproved that belief with the mere analysis of the idea of movement:
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 50 Hegel was right
"Ultimately, it is absolutely clear that movement as such only has meaning and existence in a system of many bodies, and by the way, many bodies which stand in reciprocal relation according to different determinations" (EPW 269A).
For the same reason, Hegel rejects the first law of Newton: "a recti- linear infinite movement is a void mental monster; because movement is always towards something" (GP II 193).
Moreover, Hegel holds that the physics of his times would have avoided those phantasmagorias if they had taken the time to read well Aristotle: "Aristotle shows that the void suppresses movement [. . . ] In movement the body --as distinct-- is a positive relation, not towards nothing. " (GP II 185).
And a little before that point in his book, he says: "Aristotle deals then with the void space, an ancient question for which Physics still cannot find a solution. They could do that if they read Aristotle, but for them thought and Aristotle are things which have absolutely no existence in the world. "
Already with his commentary on Zeno, Hegel had explained the relativity principle of movement: "And this is also true: that movement is definitively relative. " (GP I 315).
In order to reject the notions of absolute space and time as unsci- entific, Hegel did not have to wait until Michelson's experiment: he only needed to realize that those were mere abstractions. Evidently, an abstraction cannot pretend to have the same status of reality: "The word absolute has often no other meaning the word abstract; thus, abso- lute space and absolute time are no other thing that abstract space and abstract time" (EPW 115A).
We have displayed these quotations in order to show that the link between modern physics and Hegel's philosophy is not fortuitous. Our author already knew how unscientific and ungrounded it is in Physics to project as real something not observable.
2. a baSic principLe
Before venturing into the refutation of the different ways out that have been invented to avoid the study of the subject, we beg the reader to consider the following reflection as fundamental, for even though it is obvious in itself, it has been neglected during the last centuries.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 51
If a word does not have an empirical meaning, the origin of the con- cept in question cannot be sensation, and hence it is necessary to look in the subject itself both for the origin and the meaning of it.
For all what follows in this book, the above reflection is essential.
It cannot be stated that the origin of such a concept is sensation, for the simple reason that the origin would have to be an empirical data, but precisely no empirical data corresponds here to the concept.
For example, the concept of 'point', in which definition enters the idea of unextendedness, could have not been caused evidently by any sensible data or by imagination, for every empirical data is extended and every image of fantasy is extended as well; consequently, the ori- gin and the meaning itself of the concept 'point' should be looked for in the subject.
On the other hand, all sciences use at least some concepts whose meaning is not empirical. The science that raises fewer doubts in this regard is Physics, but apart from the example I just mentioned, we already saw that Margenau listed only some of the few concepts which are not empirical: mass, energy, charge, force, wavelength, strength, potential, probability, amplitude, crystal, magnetic field, atom, photon, electron, meson. (1978, 98)
The following text of Hegel deals with Mathematics, but it mentions several terms employed by Physics as well:
Other mathematical determinations such as infinite, relations, infinitesimal, factors, potencies, etcetera, have their true concept in Philosophy itself; and it is wrong to believe that Philosophy should extract and take them borrowed from Mathematics, where they are accepted without concept and often without any meaning at all; these concepts must wait until Philoso- phy gives them their sense and justification. (EPW 259A)
It seems evident to me that none of these terms have an empirical origin.
Einstein, the most acclaimed physic of our century, goes far beyond Margenau. His forceful statement should not be so zealously hidden away from the public by the apologists of the empirical sciences:
And let us say this in regard of the historical development. Hume clearly understood that certain concepts, for instance, that of causality, cannot be ex- tracted from the material of experience by logical methods. Kant, convinced
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 52
Hegel was right
of the indispensable character of certain concepts, considered them --just as they are selected-- as necessary premises of any kind of thought and dis- tinguished them from concepts of empirical origin. But I am convinced that such differentiation is mistaken and does not approach the problem in a natural way. From a logical point of view, all concepts, even the closer ones to experience, are free constructions, just as the concept of causality, which was the starting point of the dispute. (Schilpp, I 1969, 12).
According to Einstein, not only some concepts of Physics but every single concept lacks an empirical origin.
3. what everyone underStandS?
That being said it is now of primal importance to take this into account. More often than not, one believes to 'know' the meaning of a certain word, because one thinks that the meaning is a determined empirical data which is easily observable. But in the cases that the word being considered does not have an empirical meaning, it would be unjusti- fied to suppose, without further investigation, that 'we know what it means'. It is by no means true that we already 'understand' its meaning; we may be imagining something, but that image is not the meaning in question, for imagination can only contain combinations of empirical impressions and accumulate the data provided by the senses; however, if the concept does not have an empirical meaning, no empirical im- pression or combination of them could provide it. Let us go back to the above mentioned example. There are some people who believe they know what the meaning of the word 'point' is; but what they imagine is a speck, not a point; if it were unextended, as it should be to be a point, they could not imagine it. As a matter of fact, they do not know what the word point means; they do not have the concept.
We must look for the meaning and for the concept in the knowing subject.
Let us put another example. In the context of discussion of modern pluridimensional, non- Euclidean spaces, a great number of mathema- ticians and physics do easily away with the problem by saying that space is a group of points. However, since they do not know what a point is, this so-called definition lacks any kind of meaning. The situa- tion gets even worse if they try to define point, for they will irremediably
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Why the subject? 53
say that it is an unextended part of space. They define point in terms of space, and they define space in terms of point. The circularity of this argument is manifest. We do not gain any knowledge by means of this procedure, and clearly, one will notice that these people do not know what they are speaking of.
Here is where what we were discussing occurs: they ease themselves by believing that the meaning of the word space is a certain empiri- cal data that is easily verifiable. An opponent would probably answer to this objection something like 'you are not going to deny that I am looking at the space between my body and the wall in front of me'.
Of course, I will deny this. What this person is seeing is the wall in front of him. Space as such is not observable; it is not an empirical data. Since it is not an empirical data and they do not know how to pro- vide it with meaning by other means, they do not know what they are
speaking about.
One brief digression: if modern physics boasts their rejection of
non-observable entities, one wonders why they keep speaking of spaces, let alone pluridimensional ones. The only justifiable criterion would be the 'necessary factor to explain observable data'. But we will see in our fifth chapter what the Science of Logic has to say about those explicative intended factors.
It is the right time to do away with a false way out. Scientists will admit that many concepts do not have an empirical meaning, and yet they say that they are inferred from empirical data. I do not deny here the logical legitimacy of the inference in question; but it is obvious that, in order to infer certain concepts, we must first need to know what they mean. Precisely, in this case, the meaning does not coincide with any empirical data, for it is necessary to infer it since the meaning is not an object of empirical experience; if it was an empirical data, we would not have the need to infer it. In some of the premises of the inference process, one of these concepts --which are not derived from empirical experience-- appears suddenly: How is it possible to handle it if we do not know what it means? What it seemed to be a way out only makes more acute the need to look in the knowing subject for the origin and the meaning of concepts.
We do not need here to stop for long in order to examine another way out which is identical to the previous one. According to this po- sition, there are some things that are not empirical in themselves but only in their effects. God and the soul also have sensible effects, but that
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is not enough to know what those terms mean. The question is not about their empirical effects: what is here discussed is if the entity itself to which its causality certain effects are attributed is empirical or not. Although we do not put into question the legitimacy of such attribu- tion, it is impossible to know which entity they are speaking of as long as we do not know the meaning of the word they designate it with. Moreover, to judge if the said entity can be the cause of such effects, we need to understand beforehand the word that designates it. The fact that the said entity could have or not such effects does not make us know what the meaning of the word in question is.
Now, he firstly hinted and then explicitly said that, more often than not, the men of the street or the scientist do not know what they are speaking of; they do not have the concept; they do not understand what they are saying. It sounds severe, but it should not offend any- body because this is not any kind of truth: it is a truth that it is urgent to straighten out despite its harshness. "To know what one says is much more unusual as what one thinks, and one is very unjust by calling severe the reproach of not knowing what one says" (BS 249); "ordinarily, one calls concepts that which is nothing more than a reverie" (WL II 281).
Given that everybody is able to use a certain term not only in private but in a conversation or in a discussion with others, they think that be- cause of that they understand it and that they have its corresponding meaning, when in fact they only have an image product of their fan- tasy. For instance, as we have previously demonstrated, it seems that common people do not have the concept of 'point'; however, it is obvi- ous that we can all use the word point very skillfully. The same happens with the word space, whose meaning is ignored even by physics.
Let us put an entirely different example: the word 'work'. We all commonly use it without any mayor trouble. Nevertheless, I dare not only all workers but economists and labor lawyers as well, to define 'work'. I have not yet found anyone who has the concept of it. Everybody supposes that they understand this word, but some imagine a certain manual activity (v. g. , a man digging a whole with a shovel) and others imagine a still man performing a certain intellectual activity. The most common thing to happen is that each person imagines something re- lated to their own trade or profession.
One only needs a handful of insisting questions to dispel any at- tempt to define work. Is effort, for instance, something essential for an
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activity to be called work? On the one hand, if one answers affirma- tively, then the really skillful expert who enjoys his own professional efficacy and performs his job without fatigue would not be actually working despite the fact that his productivity is superior to that of the majority; on the other hand, if one answers negatively, the millionaire swimmer, who is in his own private pool trying to beat the crawl Olym- pic records, would be working, --which is an utterly absurd premise.
Does work, in order to be that, need to produce something? We come across here with the physiocrat theses which posit that nature is the only one that produces more than what it plants, and that work only modifies and does not produce things. According to Physics, nothing in fact is ever produced, because the existing matter in the universe does not increase nor decrease. And even leaving this aside, it is obvi- ous that the work of fishermen does not produce anything; they only collect fish from the sea. The same goes for miners and harvesters. Should one person argue that by working one produces exchange value and not something material, that person would confirm in the first place that the majority of people do not know what work is, for evidently, almost the largest part of humankind does not know what exchange value is, and the few who say they do, frequently do not know it. In the second place, it would turn out that a group of workers, who produced a great stock of merchandize which did not find demand in the market and ended up rotting out, would have not worked at all.
Does it lie in the essence of work to modify an object or a material substance?
To accept this would be to rule out intellectual work, and that would confirm that one does not have the general concept of work, which was the only thing at stake here. In the second place, and this carries even stronger consequences, the distinction between work and consumption would disappear, for consumption also modifies things. And in the third place, since the fishers, the miners and the harvesters do not modify but only transport matter, it would turn out that the activity they perform is not work. And it would be ridiculous to say that the only thing that matters is the changing of the place in question, for then the thief would be performing a job, with the same right to social remuneration as the workers in the fabrics. In addition, the dis- tinction between work and rest would disappear, for he who goes out to take a walk changes the place where his clothes are in.
The result is here the same as in regard to space and point: he who believes to comprehend and know the meaning of a certain word by
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using it skillfully deceives himself. What he has is an image "for ordi- nary life does not have concepts but only imaginations" (WL II 357). And this image is not the meaning of the word in question, because it is too particular and because other people have a completely different image in their heads when they use the same word.
From this follows that the resource employed sometimes by scien- tists in order to elude the obligation of defining a term is completely mistaken. It is an appeal that is based on what 'everybody understands for. . . '. But it is false that everybody understands. This resource does not lead to the concept nor does it make the scientist in question know what he is talking about.
There would also be a more immediate objection: if everybody un- derstands it, then why don't they say it?
Before examining the next escapist resource it is convenient to state that recent experimental psychology confirms entirely Hegel's observa- tion in the sense that no one should be offended when told that he does not understand and even lacks the concept in question. Let us quote textually the acclaimed author of the treatise Concept Learning, psycholo- gist Earl B. Hunt, although his terminology is not the same as Hegel's:
Conceptual classification may be contrasted with another type of classi- fying behavior called discrimination learning. In discrimination learning, objects are classified on the basis of directly perceived properties such as physical size or shape. The usual explanation for discrimination learning is that the sensory features of any stimulus are matched to what is already remembered of these features, and that the learner ? s response becomes associated with them. The response thus classifies the stimulus. In discrimi- nation learning, subjective representations of immediate and past stimuli seem directly to indicate concrete, physical features (in contrast to the more abstract nature of concept formation). (EB 22, 897, 2).
While human beings popularly are called abstract thinkers, many of the classifications people make clearly seem to be concrete discriminations. Indeed, people may use the same term either in a discriminative or con- ceptual way. A child uses the term policeman in discriminating a man in distinctive uniform, while a lawyer may have a concept of a civil servant charged with enforcing criminal codes. (EB 22, 898, 1)
In this example, the professional studies of the lawyer would have lead to the acquisition of the concept, while the child, a typical example
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of what Hegel calls 'ordinary life', proceeds by means of this association of empirical features called imagination: but the child and the lawyer em- ploy the same word and use it skillfully. It becomes obvious that using a word skillfully does not imply by any means that we have the belong- ing concept and that we understand. Let us repeat this with Hegel: "To know what one says is much rarer than what is thought" (BS 249).
What Hunt has summarized for us is the result of a large series of experiments. Nevertheless, it is evident that animals also learn how to discriminate and yet they do not have concepts. If we distinguish between science and technique, between knowledge and skills, it be- comes obvious that mere empirical discrimination is enough for ani- mals to possess a series of techniques which in many cases are more refined than ours. As we will later see, the technical success boasted by our empirical sciences does not demonstrate by any means that these disciplines understand.
4. Leaving termS undefined?
It is likely that the writers of treatises who leave some terms undefined refer to what "everybody understands". It is likely because, if they were not referring to this, their readers and hearers would have their mind in blank after reading or hearing those terms, they would not have any- thing to hold on to, and they would not know how to cling on to the signals they receive. Although the scientist does not make his reference explicit, his audience notices the reference to what 'everybody under- stands'. However, since they do not have the concept, the words are not actually referring to anything.
Mario Bunge claims that undefined terms "are not therefore obscure or undeterminate, since they are specified by a number of formulas" (1973, 9).
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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 60 Hegel was right
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.
