Logic
We had to multiply the examples of real dialectic in rigorous analy- sis of the terms, because both scientists and superficial commentators believe that in Hegel the transition from one concept to another is ca- pricious and of a literary kind.
We had to multiply the examples of real dialectic in rigorous analy- sis of the terms, because both scientists and superficial commentators believe that in Hegel the transition from one concept to another is ca- pricious and of a literary kind.
Hegel Was Right_nodrm
" (WL.
I 182).
This is why Hegel can conclude: "quantity is the truth of quality itself" (WL I 333). What seemed to be limit turns out to be null within the spirit, which is the only realization that goes deep down into the bottom of the entity.
Looking at things more closely, we see that the quality is the discon- tinuity, while the quantity is the continuity, and we saw that continuity and discontinuity are identical. In the same way, its multiple qualita- tive characteristics make that spirit a compound entity; and the nullity or indifferent character of such limits is what makes the spirit simple. We are always in the same dialectic of identity and distinction.
All this could only be denied by someone capable of assigning to the concept of qualitative an empirical meaning, a meaning different than the one contained in the alluded definition; but nobody is capable of doing that. It should be evident that there is nothing as qualitative as the spirit's characteristics, and that the origin of the concept of quality is self-awareness. The idea as whether something can stop being what it is could have only been formulated around the unmistakable iden- tity of the spirit. There is content: the individuality, which has in the spirit its true meaning. On the contrary, to call qualitative something material is always a tautology that says nothing. Let us think in this hollow inanity: the green, if it is not longer green, is no longer what it was. Evidently, this is an extrapolation: we are projecting towards the outside of the spirit's unmistakable identity, as if this could have in the material some meaning.
It should be evident that there is nothing as qualitative as the spirit's characteristics. And yet, the spirit dominates the limitations (every de- termination is limitation) and is still the same not just in spite of them, but in and because of them, because the identity only has sense between one 'same' in certain character and that 'same' in other character. Hence,
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 192 Hegel was right
they are quantitative for if they change it keeps being what it is. And the truth of quality is quantity.
Let us move to another example of antinomy that is shorter but no less interesting: the intensive and the extensive. This contrast is not the same between continuous and discrete. The continuous or discrete resides in the very quantity and lack of limit. The extensive or intensive drives our attention to the limit, to the determination of the stub or extremity, which allows us to speak about the quantity (amount) that is not important for the continuity or discretion because a magnitude is con- tinuous or discrete before reaching the limit although this may never be reached.
The reader will agree with us in that common people talk about the extensive in contrast to the intensive with a sensational ease, as if the definition was not necessary because 'everybody' knows what these concepts mean everybody knows what are opposed to.
Supposedly, the elements that constitute the extensive magnitude are exterior to each other: if we say one hundred meters, every meter stands apart from the other ninety-nine meters. In opposition, the in- tensive magnitude pretends that the last element, the stub or extrem- ity --ordinarily called degree-- is the only one that exists, and the others are absorbed by it. If we say 'forty degrees', one supposes that the twelve and the thirty-five degrees do not exist, or that they have been absorbed by the forty degrees. The extensive magnitude is mul- tiplicity, while the intensive magnitude, apparently, does not have multiplicity in itself but is rather a simple determination. It is easy to see that we are in the same dialectic of the one and the multiple, the simple and the compound. The origin has to be the subject's re- flection over himself, but this time we will not insist on it; it is enough to show that the antinomy or contraposition is more imaginary than real.
The mere fact that the sound of a high tone, which is intensive, con- sists in a bigger number of vibrations per second, which is extensive, raises enough suspicion. In the same manner, when the physic talks about a higher degree of temperature, he actually refers to the height of the mercury's column, which is extensive. The suspicions are con- firmed if we analyze the concepts.
Even if we talk about an extensive magnitude, each number we pro- nounce absorbs the numbers smaller in the same sense in which the degree supposedly absorbs the smaller degrees. By mentioning a small
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extensive magnitude --five meters, for instance--, it is possible that the imagination will figure that it is seeing the four extended meters just besides the fifth one, but if I say 2,728,585 meters, it is false that the fantasy imagines all those meters extended out along each other; they have been absorbed by the biggest, even though we are dealing with an extensive magnitude. The decisive factor should be the concept and not an imaginary figuration that can be present or not.
On the other hand, the absorption of the intensive is not a real absorp- tion. When I say forty degrees, the word forty supposes that thirty-nine is distinct from forty, and that thirty-eight is distinct from thirty-nine, and the same until we reach the unit, but it means that they are outside from each other, that they are external to each other; without that im- plicit journey, the forty could not represent an amount or quantity, but only an element that exists by its own. In order to signify a determined quantity, it is necessary that the thirty-nine is something distinct, and that would apply to the thirty-eight and so on indefinitely. We can- not say that they are exterminated or absorbed; each one maintains its own different meaning and exteriority in relation to the others. What appeared to be simple is, in fact, not the case: "as indifferent to the dif- ferently determined intensities it has within itself the externality of the amount; and so intensive magnitude is equally essentially an extensive magnitude. " (WL. I 217)
After Hegel's death, Physics has made a big fuzz about the dis- tinction between heat and temperature. But even assuming that this distinction is real, what is truly necessary is to re-think if that coin- cides with the distinction between extensive and intensive. This is a typical case in which the scientists, without examining the meanings, use the first couple of existing words for two entities that seem dis- tinct to them. Furthermore, it is possible that we are not dealing in this case with realities which are empirically verifiable, but with one reality that has been postulated as subjacent in order to explain the existence of the other; and it is possible that both have been postulated in or- der to explain the empirical phenomenon of the varying height of the mercury column. Soon we will see the Hegelian critique against those supposedly explanatory entities.
As a last example of true working dialectic let us mention the effec- tive solution to one of the most seemingly irreducible and unsolvable antinomies, namely, the antinomy between necessity and freedom, with which even Kant did not know what to do. About it Hegel says:
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Or take an example from a higher sphere: We say that man has freedom; the opposite content is necessity. 'If the spirit is free, then it is not subjected to necessity': and then the oppositum: 'His will, thought etcetera is determined by necessity, hence he is not free'; and they say: 'one excludes the other'. In such opinions the contents are taken as mutually excluding, as if they did not constitute something concrete. But what is true is the union of the two opposites; we have to say that the spirit is free in its necessity and only therein has freedom [. . . ] What is easier than to fix the concrete is always to say that necessity excludes liberty and vice versa (EGP 116).
We indicated (III, 10) that nobody can give an empirical meaning to the word necessity. Hence, the origin of this concept can only be the reflection of the subject on itself. But the only necessity that we know by reflection and self-awareness is the imperative imposed to us whether we like it or not. That moral imperative, however, is the one that makes us free for the first time by providing us a responsibility that generates self-awareness; only in the moment of being addressed by obligation and in the response to that obligation man becomes truly free. Before that, he was only an animal. "In duty the individual frees itself for substantial freedom" (Rph 149). "Like ethicity, true freedom consists in that the will does not have subjective and egoistic ends but only those of universal content" (EPW 469 A).
Not only due to its terrifying practical consequences, but also from the rigorously analytic and theoretical point of view, it has been a giant mistake to conceive liberty as a negative issue, as the lack of something. One deducts from this that man is free by nature, that all the primi- tive human groups are free since the beginnings, for if freedom does not consist in something positive that has to be acquired, man posses it by the mere fact of existing, without the need of conferring himself anything. One sees in that conclusion how big such a mistake is, for man evidently is not born free; during his first years he lacks freedom in the exact way little animals do. In regard to this point of unequalled importance we could not present a testimony more unexpected than that of Rousseau:
What is meant by a virtuous man? He who can conquer his affections; for then he follows his reason, his conscience; he does his duty; he is his own master and nothing can turn him from the right way. So far you have had only the semblance of liberty, the precarious liberty of the slave who has not received his orders. Now is the time for real freedom; learn to be your own
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the italics are added).
That this is said by the greatest panegyrist of the natural man is something the reader should not disregard.
I repeat: if liberty consists in not having, if liberty is a form of nothing, anybody has it. It is easy for the natural man to come to the world equipped with something that consists of nothing. In fact, things are the other way around: "freedom has to be essentially affirmative" (WG 775).
To define liberty the way Hobbes does, as the absence of impedi- ments, is totally circular and lacks content. Hobbes pretends to give the word liberty a physical and empirical sense, and evidently confuses 'being free' with 'being loose', like if the wild pig in the jungle was free just because he can go anywhere. But the word impediment does not have the empirical meaning that Hobbes would like it to have. If it is a current physical motion, it is indeed an empirical data the fact that a jail impedes it; but then one should affirm that I am free in so far I physically and effectively move myself (and nobody sets impediments on me). If I deliberatively decide to meditate at ease about my issues, Hobbes has to affirm that I am not free because empirically, there is no motion without obstacles . Surely what Hobbes wanted to say is that I am free if I can move myself without obstacles, even if I do not actually move myself. What he would say is that freedom consists in the capacity of being able to move oneself. But we have made evident (III, 9) that 'can' and 'being able' are not empirical data; the only way to give meaning to those words is by means of self-consciousness, and the meaning that we perceive there is not a mere possibility or an in- compatibility of terms, but a positive capacity: the power of the spirit of giving itself different determinations. The only meaning possible for the word can is self-determination of the subject, the free will that Hobbes wanted to put sideways by means of his attempt of configur- ing a physical meaning.
In addition, it is obvious that even in political life the lack of physical impediments would be useless if the subjects were not psy- chologically free. Huxley and Orwell have showed this clearly. If the victim is drugged, the captors do not need chains or fences. And more efficient than drugs is the systematic disappearance of knowledge in education, culture and information, which means to say, the systematic
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disappearance of concepts. Man is free insofar he thinks, insofar he has distinct points of reference than those monoidetic stimuli that ir- remissibly motivate the animal. Only he who has awareness is free.
The absence of physical impediments only has sense in function of the psychical liberty and it depends on that, for only in function of the second is possible to give meaning to the first.
If freedom is not something negative, if it does not consist of a lack, Rousseau's quote acquires an extraordinary relevance: going against his dogmatic apriorism of a natural goodness --which made him famous--, Rousseau honestly recognizes that freedom consists in the genuinely moral act that overcomes the natural tendencies and acts even against them. The demagogy that makes fun of us in front of the great audience by ridiculing 'monastic' asceticism and praising a 'happi- ness' that as we will see (VI, 2), no one can define is out of the question. That sort of people can remain with their triumph. What we are deal- ing here with is truth. Kant demonstrated the trueness of Rousseau's intuition. And Hegel sums up concisely the Kantian analysis:
Formerly, the so-called theory of happiness prevailed in the practical; morality was grounded in impulses; the concept of man and the way in which he had to realize his own concept was conceived as happiness, as satisfaction of his impulses. Kant demonstrated correctly that such thing is heteronomy, not autonomy of reason; being determined by nature is not freedom (GP III 334).
In the cases in which the course of action is decided not by the self but by an extern impulse one cannot speak of autonomy or freedom: the action is heteronomous.
"Man is not autonomous because movement begins in him, but rather because he has the power of stopping the movement and thereby to break his own immediacy and naturalness" (VG 57).
The spirit is what he makes of himself, not what impulses make him be. This is why we said (III, 2) that "liberty is the only true thing in the spirit" (VG 55), and that: "the only determination of the spirit in which all the other ones are contained is his freedom" (NH 58). In the first chapter we pointed out: "The natural is rather what the spirit must suppress" (GP II 107).
The necessity that is produced by the moral imperative identifies it- self completely with freedom. And only in that moment is understood
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the meaning of necessity and liberty. The abstract intellect was the one that separated and isolated them, and in doing that it made them unintelligible; that abstraction was the cause of the antinomy; in con- crete, that is to say, in the spirit, these two concepts do not contradict each other; on the contrary, they have the same meaning.
2.
Logic
We had to multiply the examples of real dialectic in rigorous analy- sis of the terms, because both scientists and superficial commentators believe that in Hegel the transition from one concept to another is ca- pricious and of a literary kind. For Hegel, on the contrary, "all logic consists in this" (WL II 495).
The logic consists in the 'it follows'. Everything else is accessory. Logic consists in this question: With what right is one concept inferred from another? With what right can one deduce a proposition in which the subject has a predicate another than the one he originally had be- fore? How can one justify the transition from one predicate to another, which is evidently a transition from one concept to another?
In the light of the above, it is enormously disquieting that scientists and philosophers do not realize the total revolution that Hegel intro- duced in this science, upon which the scientificity of all sciences de- pend, in spite of the fact that he specifically warns that the Aristotelian logic is useless and that he, Hegel, is founding the real logic:
The syllogism in the fashion of the abstract intellect --which is the one ren- dered by the traditional logic form-- has the meaning of a content joined with a different content. In contrast, the syllogism of reason has the content that the subject, etcetera, is joined to himself; the syllogism of reason is that some content, God etcetera, is united to Himself by means of distinguishing itself. This identity constitutes the essential element of the speculative con- tent, of nature's syllogism of reason. Aristotle is, therefore, the founder of traditional logic; his forms correspond only to the relation between finite to finite; truth cannot be understood under such forms (GP II 241).
The real logic is based on what this chapter has underlined: one concept 'follows' from another because they are not understood separately. The logical necessity is the exigency that a concept has meaning and is understood.
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The implication between the concepts is what traditional logic as well as set logic ignore. But that implication is what allows a real in- ference of something new, of something that effectively increases our knowledge and is not tautologically reduced to what was said: what was said does not 'follow' because we had it already. For instance, the well-known syllogism: 'All men are mortal, Socrates is a man, therefore, Socrates is mortal', does not teach us anything in the conclusion, for what it said was already stated in the first premise. The first premise could have not been stated had we not known that the content of the conclusion was true. Such reasoning does not make us wiser.
In contrast, the logic of Hegel begins with the concept of being, and because of the exigency of providing this term with a meaning, it leads us (cfr III, 3) to a new content: the activity of giving determinations to oneself. Being and existing can only consist in that. That really does increase our knowledge. The inference can be denied only by he who is able to provide the word being with another meaning, but we saw already that such thing is impossible.
We saw (III, 4) what happens with the initial concept of substance: it is not understandable that something can exist in itself if it doesn't give to itself the determinations of its existence; and then pass from the substantial content to the subjectivity content.
Tautology is the way-out of the abstract intellect that does not un- derstand. When it comes to understand the concepts, our knowledge actually increases.
The only path that fixational logics can go through in order to avoid becoming sheer tautologies is the hypothetical syllogism. I call here hypothetic not only the syllogism that has that explicit form, but also every syllogism in which one of the premises is taken as truth and is not demonstrated. This occurs extremely often, for the common logician thinks that, if every premise must be demonstrated, the syllogism con- tained in the demonstration would also need premises that need to be demonstrated, and so on indefinitely. When that happens the common logician takes a secure path and assumes some of the premises.
The point has a pivotal importance for the very concept of scientificity. Science is concrete and demonstrated knowledge; otherwise, one can 'choose' to accept it, just like the worldviews which are continuously advanced by pasquinade writers. Although the individual scientists is allowed to suppose some things because the life of a person has some limitations of time and energy, science as such cannot suppose anything;
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its obligation is to demonstrate. But if common logic replies that the premises of its syllogisms should not be demonstrated, what they are in fact telling us is that science does not exist, or, if anything, a very funny and easy thing to do. One can embrace any thesis, as arbitrary as it may be, for one does not need to demonstrate the premises that ground such thesis.
The traditional syllogism is a deceit. It simulates to demonstrate the propositions, but in the end it leaves them as uncertain as before, because its truth depends on the truth of the premises, precisely that which is left aside.
One can make a big mess which is apparently true because it is ex- pressed in conditional terms that are formally valid. But knowledge does not advance a single step by this procedure, since we do not know if the conditions are met or not. It would be a mental game with no relationship to reality and truth.
How was it possible that essayists and the users of traditional logic did not realize that, if premises are uncertain, concepts themselves are also so.
Indeed, one can build up a perfectly correct syllogism in which all the concepts are uncertain. In that case, we may ask: Where are they taken from? How can we know their meaning? And more importantly: How can we know that they correspond to reality?
The desire of obtaining some judgments by empirical experiences is, of course, an illusion. The judgment is never 'given'. The allegedly empirical judgment does not identify itself with the empirical data. Despite that they call it observational, the allegedly empirical presup- position consists in words, while seeing or touching does not consist in words but in shudders of the diverse parts of the nervous system. The basic and observational propositions is only an interpretation of sen- sible data, highly questionable because it is constituted by concepts, and no concept as such has empirical meaning, as we have repeatedly demonstrated. In order that logic starts working "what is perceived must have at least the meaning of a universal" (PG 185); and in fact "for us the object can be nothing else but our notions of it. " (WL I 15); "the syllogisms with which one demonstrates are concepts formed by the subject" (GP III 280).
It is then when, with all its virulence, the problem of demonstrating premises indefinitely is posited, for it depends on the concepts. Some certainty has to be the condition of possibility of science; otherwise,
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 200 Hegel was right
one would have to define science as the 'uncertain', and there would be no distinction between it and ordinary knowledge, and hence science would not exist.
Let us repeat the question: how do we know if concepts capture reality or not? It is evident that the famous 'correspondence between mind and reality' has to consist in the 'identity between the mind and reality'. Hegel says: "Only in thought exists the true correspondence between the objective and the subjective: that is myself" (GP II 165).
There cannot be any separation between the spirit and the concept of spirit; there can be no distinction there, and in fact, there is not any. We saw before (III, 1) that the spirit consists in knowing itself. "The first thing one has to do when it comes to the concept is to quit believing that the concept is something that we have, something that we have in ourselves [. . . ] What we call soul is the concept; the concept as such becomes existing and is the spirit, the self-consciousness" (PR I 220).
In this is myself there is certainty as whether the concept adapts to reality or not, as whether the concept captures reality or not. What we have expressed in our previous chapters demonstrates that all concepts stem from the concept of the spirit. As Hegel says, "the knower [. . . ] has in its concept the whole essentiality of the objective world" (WL II 438). We have demonstrated that it is an illusion to define reality indepen- dently from the subject (II, 7), and that 'out of thought' is an expression lack of meaning.
The relations and interferences between concepts --in which logic consist-- are only then possible because all of them point towards the same reality: the spirit. Besides, that is what judgments affirm: that one is the other. Without Hegel's contribution, logic today faces a dead end: it deals with tautologies or with unjustifiable synthetic judgments.
By way of appendix, one should notice that set theory is a desperate attempt of evading the concept, by making everything visual, spatial and imaginary. It figures that, if an object is a part of a certain set of objects, and that set is the part of a larger set, it is a logically justified step to affirm that the object in the first set is also a part of the second one. It figures that in this 'it follows' one does not employ any concept whatsoever. But it is primal to state that --despite the opposite figu- rations--, when the set logician says 'the set of metallic objects' he is neither pointing out with his fingers to all the metallic objects, nor is he imagining them, nor he manages that we imagine them. Consequently, there is no such set. If we understand him it is because we both have
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the concept of a metallic object. The extentionalist does not have before him the set of metallic objects in imagination, in empirical perception or in the mind: the only thing that he has before him are concepts. And to affirm that a certain material object forms part of a concept is preposterous.
How can one know whether x belongs to set A, when we do not understand the word by which one is trying to encompass set A? It is not true that someone can designate by means of this word certain set of objects, for we do not know to which object --among the many ones there are in the world-- this word is referred. To designate is not a re- lation that exists between the word and the belonging objects without the intervention of the knowing subject.
Since the set logicist does not have before him either set A or B, if he is truly referring to them it is due to the fact that he has in mind the two belonging universal concepts, and the relationship between the both sets of which he speaks is a relation between concepts. Now, there can be no other thing between concepts as relations of content; any other relation between them would be a mere metaphor. But the relations of content are precisely those which are studied by the Hegelian logic.
3. force
In the fourth part of this present chapter we will show the most pervasive critique that has ever been done to the natural sciences, which is con- tained in the work titled The Science of Logic. Natural science disciplines had not attended to such devastating critique, not even after Einstein and Quantum theory, although in some way, both Relativity and Quan- tum physics confirm what Hegel said. Nevertheless, it happens that the intellection of the above mentioned work depends on understanding the message from, what Hegel calls, the second book, the essence book, in which the concept of force is so paradigmatic that deserves to be ex- amined by us in full detail. That second book is the one which contains the explicative concepts, in contrast to the merely descriptive ones; but among the explicative ones, force, according to Hegel, is 'the most no- table one' (GP III 84), while Hegel warns that it is not actually a concept but a certain 'mental way', certain 'way of thinking'.
It is true that General Relativity with its realm wants to delete from the world of Physics the gravitational force which is the key to
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 202 Hegel was right
the great Newtonian construction. During the eighties many physi- cists, following Einstein's example, pretended to delete every force by spaces formed up to eleven dimensions. But, in the first place, we will soon see that the Hegelian critique of force is perfectly valid against any other concept of explanatory intention. And in the second place, physicists continue e to speak carelessly about forces despite of Einstein and his imitators. Raymond A. Serway still enumerates as fundamental --besides gravity -- the electromagnetic force between charges, the strong nuclear force between subatomic particles and the weak nucle- ar force (1985, 72). In general, atomic physics draws explanation with forces as if nothing had ever happened: e. g. Rittenhouse (EB 14, 330,2), Ziman (EB 14,340,1), Cuninghame (EB 14,361,1). And one speaks even about the "London Forces" which are applied between the molecules (EB 23,690 ,2) and the Van der Waals force is appealed to explain the liquids and solids formation (EB 14,377,1). The four forces that Serway enumerates appear to continue unperturbed on their explicative task: cf. Rosenfeld (EB 28,252) and Brown (EB 25,819).
One does not have the slightest idea when people like Rosenblueth say nowadays that science does not pretend to explain the phenomena. The concept of strength can only have the aim of explaining and nothing more. At least the discipline to which Newton dedicated his life never pretended anything else. On the first page of his principal work Newton identifies physics with the force science: "the rational mechanics will be the science of movements that shall result out from any sort of strength, and from the strengths required to produce any sort of movement" (1977, 1).
Newton was not so much impressed by the attack that Leibnitz for- mulates against him on its fifth letter to Samuel Clarke, according to which those forces are not in any way different from the scholastic's 'hidden qualities', by means of which it is tremendously easy to explain any phenomena: e. g. if a liquid tastes acid, then that can be explained by the hidden quality called acidity. That is the way Newton's explanations are: if the apple falls down to the ground, that can be explained by a certain attraction force whose single definition is to be the movement's explanation that is intended to be explained. It is like ancient medicine: if an ill person suffers melancholy, then that can be explained by the melancholic fluids.
Hegel says that it was Newton who "contributed the most" (GP III 231) to the inclusion of those brilliant explanations to Physics. But
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This is why Hegel can conclude: "quantity is the truth of quality itself" (WL I 333). What seemed to be limit turns out to be null within the spirit, which is the only realization that goes deep down into the bottom of the entity.
Looking at things more closely, we see that the quality is the discon- tinuity, while the quantity is the continuity, and we saw that continuity and discontinuity are identical. In the same way, its multiple qualita- tive characteristics make that spirit a compound entity; and the nullity or indifferent character of such limits is what makes the spirit simple. We are always in the same dialectic of identity and distinction.
All this could only be denied by someone capable of assigning to the concept of qualitative an empirical meaning, a meaning different than the one contained in the alluded definition; but nobody is capable of doing that. It should be evident that there is nothing as qualitative as the spirit's characteristics, and that the origin of the concept of quality is self-awareness. The idea as whether something can stop being what it is could have only been formulated around the unmistakable iden- tity of the spirit. There is content: the individuality, which has in the spirit its true meaning. On the contrary, to call qualitative something material is always a tautology that says nothing. Let us think in this hollow inanity: the green, if it is not longer green, is no longer what it was. Evidently, this is an extrapolation: we are projecting towards the outside of the spirit's unmistakable identity, as if this could have in the material some meaning.
It should be evident that there is nothing as qualitative as the spirit's characteristics. And yet, the spirit dominates the limitations (every de- termination is limitation) and is still the same not just in spite of them, but in and because of them, because the identity only has sense between one 'same' in certain character and that 'same' in other character. Hence,
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 192 Hegel was right
they are quantitative for if they change it keeps being what it is. And the truth of quality is quantity.
Let us move to another example of antinomy that is shorter but no less interesting: the intensive and the extensive. This contrast is not the same between continuous and discrete. The continuous or discrete resides in the very quantity and lack of limit. The extensive or intensive drives our attention to the limit, to the determination of the stub or extremity, which allows us to speak about the quantity (amount) that is not important for the continuity or discretion because a magnitude is con- tinuous or discrete before reaching the limit although this may never be reached.
The reader will agree with us in that common people talk about the extensive in contrast to the intensive with a sensational ease, as if the definition was not necessary because 'everybody' knows what these concepts mean everybody knows what are opposed to.
Supposedly, the elements that constitute the extensive magnitude are exterior to each other: if we say one hundred meters, every meter stands apart from the other ninety-nine meters. In opposition, the in- tensive magnitude pretends that the last element, the stub or extrem- ity --ordinarily called degree-- is the only one that exists, and the others are absorbed by it. If we say 'forty degrees', one supposes that the twelve and the thirty-five degrees do not exist, or that they have been absorbed by the forty degrees. The extensive magnitude is mul- tiplicity, while the intensive magnitude, apparently, does not have multiplicity in itself but is rather a simple determination. It is easy to see that we are in the same dialectic of the one and the multiple, the simple and the compound. The origin has to be the subject's re- flection over himself, but this time we will not insist on it; it is enough to show that the antinomy or contraposition is more imaginary than real.
The mere fact that the sound of a high tone, which is intensive, con- sists in a bigger number of vibrations per second, which is extensive, raises enough suspicion. In the same manner, when the physic talks about a higher degree of temperature, he actually refers to the height of the mercury's column, which is extensive. The suspicions are con- firmed if we analyze the concepts.
Even if we talk about an extensive magnitude, each number we pro- nounce absorbs the numbers smaller in the same sense in which the degree supposedly absorbs the smaller degrees. By mentioning a small
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extensive magnitude --five meters, for instance--, it is possible that the imagination will figure that it is seeing the four extended meters just besides the fifth one, but if I say 2,728,585 meters, it is false that the fantasy imagines all those meters extended out along each other; they have been absorbed by the biggest, even though we are dealing with an extensive magnitude. The decisive factor should be the concept and not an imaginary figuration that can be present or not.
On the other hand, the absorption of the intensive is not a real absorp- tion. When I say forty degrees, the word forty supposes that thirty-nine is distinct from forty, and that thirty-eight is distinct from thirty-nine, and the same until we reach the unit, but it means that they are outside from each other, that they are external to each other; without that im- plicit journey, the forty could not represent an amount or quantity, but only an element that exists by its own. In order to signify a determined quantity, it is necessary that the thirty-nine is something distinct, and that would apply to the thirty-eight and so on indefinitely. We can- not say that they are exterminated or absorbed; each one maintains its own different meaning and exteriority in relation to the others. What appeared to be simple is, in fact, not the case: "as indifferent to the dif- ferently determined intensities it has within itself the externality of the amount; and so intensive magnitude is equally essentially an extensive magnitude. " (WL. I 217)
After Hegel's death, Physics has made a big fuzz about the dis- tinction between heat and temperature. But even assuming that this distinction is real, what is truly necessary is to re-think if that coin- cides with the distinction between extensive and intensive. This is a typical case in which the scientists, without examining the meanings, use the first couple of existing words for two entities that seem dis- tinct to them. Furthermore, it is possible that we are not dealing in this case with realities which are empirically verifiable, but with one reality that has been postulated as subjacent in order to explain the existence of the other; and it is possible that both have been postulated in or- der to explain the empirical phenomenon of the varying height of the mercury column. Soon we will see the Hegelian critique against those supposedly explanatory entities.
As a last example of true working dialectic let us mention the effec- tive solution to one of the most seemingly irreducible and unsolvable antinomies, namely, the antinomy between necessity and freedom, with which even Kant did not know what to do. About it Hegel says:
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Or take an example from a higher sphere: We say that man has freedom; the opposite content is necessity. 'If the spirit is free, then it is not subjected to necessity': and then the oppositum: 'His will, thought etcetera is determined by necessity, hence he is not free'; and they say: 'one excludes the other'. In such opinions the contents are taken as mutually excluding, as if they did not constitute something concrete. But what is true is the union of the two opposites; we have to say that the spirit is free in its necessity and only therein has freedom [. . . ] What is easier than to fix the concrete is always to say that necessity excludes liberty and vice versa (EGP 116).
We indicated (III, 10) that nobody can give an empirical meaning to the word necessity. Hence, the origin of this concept can only be the reflection of the subject on itself. But the only necessity that we know by reflection and self-awareness is the imperative imposed to us whether we like it or not. That moral imperative, however, is the one that makes us free for the first time by providing us a responsibility that generates self-awareness; only in the moment of being addressed by obligation and in the response to that obligation man becomes truly free. Before that, he was only an animal. "In duty the individual frees itself for substantial freedom" (Rph 149). "Like ethicity, true freedom consists in that the will does not have subjective and egoistic ends but only those of universal content" (EPW 469 A).
Not only due to its terrifying practical consequences, but also from the rigorously analytic and theoretical point of view, it has been a giant mistake to conceive liberty as a negative issue, as the lack of something. One deducts from this that man is free by nature, that all the primi- tive human groups are free since the beginnings, for if freedom does not consist in something positive that has to be acquired, man posses it by the mere fact of existing, without the need of conferring himself anything. One sees in that conclusion how big such a mistake is, for man evidently is not born free; during his first years he lacks freedom in the exact way little animals do. In regard to this point of unequalled importance we could not present a testimony more unexpected than that of Rousseau:
What is meant by a virtuous man? He who can conquer his affections; for then he follows his reason, his conscience; he does his duty; he is his own master and nothing can turn him from the right way. So far you have had only the semblance of liberty, the precarious liberty of the slave who has not received his orders. Now is the time for real freedom; learn to be your own
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the italics are added).
That this is said by the greatest panegyrist of the natural man is something the reader should not disregard.
I repeat: if liberty consists in not having, if liberty is a form of nothing, anybody has it. It is easy for the natural man to come to the world equipped with something that consists of nothing. In fact, things are the other way around: "freedom has to be essentially affirmative" (WG 775).
To define liberty the way Hobbes does, as the absence of impedi- ments, is totally circular and lacks content. Hobbes pretends to give the word liberty a physical and empirical sense, and evidently confuses 'being free' with 'being loose', like if the wild pig in the jungle was free just because he can go anywhere. But the word impediment does not have the empirical meaning that Hobbes would like it to have. If it is a current physical motion, it is indeed an empirical data the fact that a jail impedes it; but then one should affirm that I am free in so far I physically and effectively move myself (and nobody sets impediments on me). If I deliberatively decide to meditate at ease about my issues, Hobbes has to affirm that I am not free because empirically, there is no motion without obstacles . Surely what Hobbes wanted to say is that I am free if I can move myself without obstacles, even if I do not actually move myself. What he would say is that freedom consists in the capacity of being able to move oneself. But we have made evident (III, 9) that 'can' and 'being able' are not empirical data; the only way to give meaning to those words is by means of self-consciousness, and the meaning that we perceive there is not a mere possibility or an in- compatibility of terms, but a positive capacity: the power of the spirit of giving itself different determinations. The only meaning possible for the word can is self-determination of the subject, the free will that Hobbes wanted to put sideways by means of his attempt of configur- ing a physical meaning.
In addition, it is obvious that even in political life the lack of physical impediments would be useless if the subjects were not psy- chologically free. Huxley and Orwell have showed this clearly. If the victim is drugged, the captors do not need chains or fences. And more efficient than drugs is the systematic disappearance of knowledge in education, culture and information, which means to say, the systematic
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disappearance of concepts. Man is free insofar he thinks, insofar he has distinct points of reference than those monoidetic stimuli that ir- remissibly motivate the animal. Only he who has awareness is free.
The absence of physical impediments only has sense in function of the psychical liberty and it depends on that, for only in function of the second is possible to give meaning to the first.
If freedom is not something negative, if it does not consist of a lack, Rousseau's quote acquires an extraordinary relevance: going against his dogmatic apriorism of a natural goodness --which made him famous--, Rousseau honestly recognizes that freedom consists in the genuinely moral act that overcomes the natural tendencies and acts even against them. The demagogy that makes fun of us in front of the great audience by ridiculing 'monastic' asceticism and praising a 'happi- ness' that as we will see (VI, 2), no one can define is out of the question. That sort of people can remain with their triumph. What we are deal- ing here with is truth. Kant demonstrated the trueness of Rousseau's intuition. And Hegel sums up concisely the Kantian analysis:
Formerly, the so-called theory of happiness prevailed in the practical; morality was grounded in impulses; the concept of man and the way in which he had to realize his own concept was conceived as happiness, as satisfaction of his impulses. Kant demonstrated correctly that such thing is heteronomy, not autonomy of reason; being determined by nature is not freedom (GP III 334).
In the cases in which the course of action is decided not by the self but by an extern impulse one cannot speak of autonomy or freedom: the action is heteronomous.
"Man is not autonomous because movement begins in him, but rather because he has the power of stopping the movement and thereby to break his own immediacy and naturalness" (VG 57).
The spirit is what he makes of himself, not what impulses make him be. This is why we said (III, 2) that "liberty is the only true thing in the spirit" (VG 55), and that: "the only determination of the spirit in which all the other ones are contained is his freedom" (NH 58). In the first chapter we pointed out: "The natural is rather what the spirit must suppress" (GP II 107).
The necessity that is produced by the moral imperative identifies it- self completely with freedom. And only in that moment is understood
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the meaning of necessity and liberty. The abstract intellect was the one that separated and isolated them, and in doing that it made them unintelligible; that abstraction was the cause of the antinomy; in con- crete, that is to say, in the spirit, these two concepts do not contradict each other; on the contrary, they have the same meaning.
2.
Logic
We had to multiply the examples of real dialectic in rigorous analy- sis of the terms, because both scientists and superficial commentators believe that in Hegel the transition from one concept to another is ca- pricious and of a literary kind. For Hegel, on the contrary, "all logic consists in this" (WL II 495).
The logic consists in the 'it follows'. Everything else is accessory. Logic consists in this question: With what right is one concept inferred from another? With what right can one deduce a proposition in which the subject has a predicate another than the one he originally had be- fore? How can one justify the transition from one predicate to another, which is evidently a transition from one concept to another?
In the light of the above, it is enormously disquieting that scientists and philosophers do not realize the total revolution that Hegel intro- duced in this science, upon which the scientificity of all sciences de- pend, in spite of the fact that he specifically warns that the Aristotelian logic is useless and that he, Hegel, is founding the real logic:
The syllogism in the fashion of the abstract intellect --which is the one ren- dered by the traditional logic form-- has the meaning of a content joined with a different content. In contrast, the syllogism of reason has the content that the subject, etcetera, is joined to himself; the syllogism of reason is that some content, God etcetera, is united to Himself by means of distinguishing itself. This identity constitutes the essential element of the speculative con- tent, of nature's syllogism of reason. Aristotle is, therefore, the founder of traditional logic; his forms correspond only to the relation between finite to finite; truth cannot be understood under such forms (GP II 241).
The real logic is based on what this chapter has underlined: one concept 'follows' from another because they are not understood separately. The logical necessity is the exigency that a concept has meaning and is understood.
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The implication between the concepts is what traditional logic as well as set logic ignore. But that implication is what allows a real in- ference of something new, of something that effectively increases our knowledge and is not tautologically reduced to what was said: what was said does not 'follow' because we had it already. For instance, the well-known syllogism: 'All men are mortal, Socrates is a man, therefore, Socrates is mortal', does not teach us anything in the conclusion, for what it said was already stated in the first premise. The first premise could have not been stated had we not known that the content of the conclusion was true. Such reasoning does not make us wiser.
In contrast, the logic of Hegel begins with the concept of being, and because of the exigency of providing this term with a meaning, it leads us (cfr III, 3) to a new content: the activity of giving determinations to oneself. Being and existing can only consist in that. That really does increase our knowledge. The inference can be denied only by he who is able to provide the word being with another meaning, but we saw already that such thing is impossible.
We saw (III, 4) what happens with the initial concept of substance: it is not understandable that something can exist in itself if it doesn't give to itself the determinations of its existence; and then pass from the substantial content to the subjectivity content.
Tautology is the way-out of the abstract intellect that does not un- derstand. When it comes to understand the concepts, our knowledge actually increases.
The only path that fixational logics can go through in order to avoid becoming sheer tautologies is the hypothetical syllogism. I call here hypothetic not only the syllogism that has that explicit form, but also every syllogism in which one of the premises is taken as truth and is not demonstrated. This occurs extremely often, for the common logician thinks that, if every premise must be demonstrated, the syllogism con- tained in the demonstration would also need premises that need to be demonstrated, and so on indefinitely. When that happens the common logician takes a secure path and assumes some of the premises.
The point has a pivotal importance for the very concept of scientificity. Science is concrete and demonstrated knowledge; otherwise, one can 'choose' to accept it, just like the worldviews which are continuously advanced by pasquinade writers. Although the individual scientists is allowed to suppose some things because the life of a person has some limitations of time and energy, science as such cannot suppose anything;
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its obligation is to demonstrate. But if common logic replies that the premises of its syllogisms should not be demonstrated, what they are in fact telling us is that science does not exist, or, if anything, a very funny and easy thing to do. One can embrace any thesis, as arbitrary as it may be, for one does not need to demonstrate the premises that ground such thesis.
The traditional syllogism is a deceit. It simulates to demonstrate the propositions, but in the end it leaves them as uncertain as before, because its truth depends on the truth of the premises, precisely that which is left aside.
One can make a big mess which is apparently true because it is ex- pressed in conditional terms that are formally valid. But knowledge does not advance a single step by this procedure, since we do not know if the conditions are met or not. It would be a mental game with no relationship to reality and truth.
How was it possible that essayists and the users of traditional logic did not realize that, if premises are uncertain, concepts themselves are also so.
Indeed, one can build up a perfectly correct syllogism in which all the concepts are uncertain. In that case, we may ask: Where are they taken from? How can we know their meaning? And more importantly: How can we know that they correspond to reality?
The desire of obtaining some judgments by empirical experiences is, of course, an illusion. The judgment is never 'given'. The allegedly empirical judgment does not identify itself with the empirical data. Despite that they call it observational, the allegedly empirical presup- position consists in words, while seeing or touching does not consist in words but in shudders of the diverse parts of the nervous system. The basic and observational propositions is only an interpretation of sen- sible data, highly questionable because it is constituted by concepts, and no concept as such has empirical meaning, as we have repeatedly demonstrated. In order that logic starts working "what is perceived must have at least the meaning of a universal" (PG 185); and in fact "for us the object can be nothing else but our notions of it. " (WL I 15); "the syllogisms with which one demonstrates are concepts formed by the subject" (GP III 280).
It is then when, with all its virulence, the problem of demonstrating premises indefinitely is posited, for it depends on the concepts. Some certainty has to be the condition of possibility of science; otherwise,
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 200 Hegel was right
one would have to define science as the 'uncertain', and there would be no distinction between it and ordinary knowledge, and hence science would not exist.
Let us repeat the question: how do we know if concepts capture reality or not? It is evident that the famous 'correspondence between mind and reality' has to consist in the 'identity between the mind and reality'. Hegel says: "Only in thought exists the true correspondence between the objective and the subjective: that is myself" (GP II 165).
There cannot be any separation between the spirit and the concept of spirit; there can be no distinction there, and in fact, there is not any. We saw before (III, 1) that the spirit consists in knowing itself. "The first thing one has to do when it comes to the concept is to quit believing that the concept is something that we have, something that we have in ourselves [. . . ] What we call soul is the concept; the concept as such becomes existing and is the spirit, the self-consciousness" (PR I 220).
In this is myself there is certainty as whether the concept adapts to reality or not, as whether the concept captures reality or not. What we have expressed in our previous chapters demonstrates that all concepts stem from the concept of the spirit. As Hegel says, "the knower [. . . ] has in its concept the whole essentiality of the objective world" (WL II 438). We have demonstrated that it is an illusion to define reality indepen- dently from the subject (II, 7), and that 'out of thought' is an expression lack of meaning.
The relations and interferences between concepts --in which logic consist-- are only then possible because all of them point towards the same reality: the spirit. Besides, that is what judgments affirm: that one is the other. Without Hegel's contribution, logic today faces a dead end: it deals with tautologies or with unjustifiable synthetic judgments.
By way of appendix, one should notice that set theory is a desperate attempt of evading the concept, by making everything visual, spatial and imaginary. It figures that, if an object is a part of a certain set of objects, and that set is the part of a larger set, it is a logically justified step to affirm that the object in the first set is also a part of the second one. It figures that in this 'it follows' one does not employ any concept whatsoever. But it is primal to state that --despite the opposite figu- rations--, when the set logician says 'the set of metallic objects' he is neither pointing out with his fingers to all the metallic objects, nor is he imagining them, nor he manages that we imagine them. Consequently, there is no such set. If we understand him it is because we both have
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the concept of a metallic object. The extentionalist does not have before him the set of metallic objects in imagination, in empirical perception or in the mind: the only thing that he has before him are concepts. And to affirm that a certain material object forms part of a concept is preposterous.
How can one know whether x belongs to set A, when we do not understand the word by which one is trying to encompass set A? It is not true that someone can designate by means of this word certain set of objects, for we do not know to which object --among the many ones there are in the world-- this word is referred. To designate is not a re- lation that exists between the word and the belonging objects without the intervention of the knowing subject.
Since the set logicist does not have before him either set A or B, if he is truly referring to them it is due to the fact that he has in mind the two belonging universal concepts, and the relationship between the both sets of which he speaks is a relation between concepts. Now, there can be no other thing between concepts as relations of content; any other relation between them would be a mere metaphor. But the relations of content are precisely those which are studied by the Hegelian logic.
3. force
In the fourth part of this present chapter we will show the most pervasive critique that has ever been done to the natural sciences, which is con- tained in the work titled The Science of Logic. Natural science disciplines had not attended to such devastating critique, not even after Einstein and Quantum theory, although in some way, both Relativity and Quan- tum physics confirm what Hegel said. Nevertheless, it happens that the intellection of the above mentioned work depends on understanding the message from, what Hegel calls, the second book, the essence book, in which the concept of force is so paradigmatic that deserves to be ex- amined by us in full detail. That second book is the one which contains the explicative concepts, in contrast to the merely descriptive ones; but among the explicative ones, force, according to Hegel, is 'the most no- table one' (GP III 84), while Hegel warns that it is not actually a concept but a certain 'mental way', certain 'way of thinking'.
It is true that General Relativity with its realm wants to delete from the world of Physics the gravitational force which is the key to
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 202 Hegel was right
the great Newtonian construction. During the eighties many physi- cists, following Einstein's example, pretended to delete every force by spaces formed up to eleven dimensions. But, in the first place, we will soon see that the Hegelian critique of force is perfectly valid against any other concept of explanatory intention. And in the second place, physicists continue e to speak carelessly about forces despite of Einstein and his imitators. Raymond A. Serway still enumerates as fundamental --besides gravity -- the electromagnetic force between charges, the strong nuclear force between subatomic particles and the weak nucle- ar force (1985, 72). In general, atomic physics draws explanation with forces as if nothing had ever happened: e. g. Rittenhouse (EB 14, 330,2), Ziman (EB 14,340,1), Cuninghame (EB 14,361,1). And one speaks even about the "London Forces" which are applied between the molecules (EB 23,690 ,2) and the Van der Waals force is appealed to explain the liquids and solids formation (EB 14,377,1). The four forces that Serway enumerates appear to continue unperturbed on their explicative task: cf. Rosenfeld (EB 28,252) and Brown (EB 25,819).
One does not have the slightest idea when people like Rosenblueth say nowadays that science does not pretend to explain the phenomena. The concept of strength can only have the aim of explaining and nothing more. At least the discipline to which Newton dedicated his life never pretended anything else. On the first page of his principal work Newton identifies physics with the force science: "the rational mechanics will be the science of movements that shall result out from any sort of strength, and from the strengths required to produce any sort of movement" (1977, 1).
Newton was not so much impressed by the attack that Leibnitz for- mulates against him on its fifth letter to Samuel Clarke, according to which those forces are not in any way different from the scholastic's 'hidden qualities', by means of which it is tremendously easy to explain any phenomena: e. g. if a liquid tastes acid, then that can be explained by the hidden quality called acidity. That is the way Newton's explanations are: if the apple falls down to the ground, that can be explained by a certain attraction force whose single definition is to be the movement's explanation that is intended to be explained. It is like ancient medicine: if an ill person suffers melancholy, then that can be explained by the melancholic fluids.
Hegel says that it was Newton who "contributed the most" (GP III 231) to the inclusion of those brilliant explanations to Physics. But
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