The extensive
magnitude
is mul- tiplicity, while the intensive magnitude, apparently, does not have multiplicity in itself but is rather a simple determination.
Hegel Was Right_nodrm
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Logic and Natural Sciences 187
says). Hegel said it one century before: "none of these determinations, taken separately has truth, but only the union of both" (WL I 191). The physics would have saved one century and many headaches if, as the real science requires, they had demanded rigorous definitions of every term they use.
"The continuity is this content of the identity-with itself of what is discrete; the follow up of the distinct ones in those that are distinct to them. Therefore, magnitude has in continuity the element of discretion immediately" (WL I 180).
The pseudodiscreet of the imagination consists in many which are not one: each one is entirely on their own. The pseudocontinuous of the imagination e. g. a line, the stretches are contiguous, but they lack continuity, because each of them can and exists on its own.
As we have seen, the reason why the physic and the natural scientist did not demand the definition of their terms is because they thought that meaning was some empirical data. We have proved that it is an illusion, and even in order to know if the empiric data corresponds to the belonging word it is still necessary to define it before, since the possession of any empiric data does not exempt them from the obliga- tion of defining. In this particular case, a little bit of reflection would have been enough to understand that sensation could only justify con- tiguity by itself, and besides, this is not the same as continuity. The continuity is something very metaphysical; there is nothing similar in the physical. In the best case scenario, what quantum physics was looking for was the juxtaposition of points, but juxtaposition is not continuity .
The sensibility ignores if the many elements that it thinks it veri- fies are one or many, i. e. does not know if they constitute or not only one individual, because, as we saw (IV, 6), individuality and sameness are not an empirical data. Hence sensibility cannot witness continuity. Further, its testimony of contiguity is completely unreliable for science, because it constitutes one single macroscopic impression due to the peculiarity of our sensorial organs. The atomic and corpuscular theory repudiated that testimony from the very beginning.
We said that Bohr's principle affirms complementarity between continuity and discretion. We need to support our affirmation because one commonly thinks it is a complementarity between wave and par- ticle. Margenau saw that this common interpretation is a mistake. "The point is that we have a reasonably satisfactory theory of the electron
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 188 Hegel was right
which assigns to it neither the cara? cter of a particle nor that of a wave. "
(1978, 89 n. 13) D'Abro has understood this with all clarity too:
According to our earlier views, the waves, being mere probability waves, must be regarded as symbolic, whereas the particles represent physical reality. But we must now suppose that particles also should be regarded as symbolic, for they come into existence only when a position observation is performed. (1952, 652).
Schro? dinger himself, whose equation is the operation center of quantum theory, emphatically told us that it was a mistake to con- serve the concepts of classical physics (Maxwell included) and not just denied them accurate definability. This is literally the way he puts it: "Concepts themselves must be abandoned, not only their clear de- finability" (1934, 519). That one still keeps talking about waves and particles shows that neither the public opinion nor physics themselves dare to accept the facts that quantum experimentation has discovered. The complementarity is not between wave and particle.
But if we take it part by part, the issue turns itself pretty obvious. One cannot talk about particle or corpuscle if the precise localization, the precise trajectory and the precise mass are denied. On the other hand, if Physics talks about the de Broglie's wave in association with the electron, it is evident that it does not consider the electron as a wave. In fact, the vector describes a global property of a physical system; it does not describe in fact a wave or a particle. Although it is common to call Schro? dinger's psi ondulatory, we are specifically warned that such a wave is a complex function and gives us plausible information about the whereabouts of the electron, but according to what we have just said, the electron is neither really a particle nor a corpuscle. Bohr himself emphasizes this when he speaks of "the renunciation of the absolute significance of conventional attributes of objects" (1958, 64).
The complementarity between continuity and discretion --affirmed by quantum physics-- is an overdue and not very lucid acknowledge- ment of the fact that none of these two concepts is true taken alone, but only the union of both. That was the Hegelian solution of the respec- tive antinomy, but in order to provide that solution the only thing that Hegel needed was the meaning of the concepts, or in other words, the fact that they can only have a meaning if they are united, and the real- ization of both can only happen in the spirit.
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"We call dialectics, the supreme movement of reason in which apparently and absolutely separated things go from one another by themselves, by what they themselves are, and the supposition that they are separated is thereby suppressed. " (WL I 92).
"The watch over the categories employed by the intellect that insults Philosophy is what the latter needs" (BS 370s).
In the case of all the examples we have just said, it would be redun- dant to say that the contradiction is effectively solved and does not remain as contradictory as before (this was the case in Kant). Likewise, it would also be redundant to repeat in the light of each example that the synthesis and the solution are not the beginning of a new antinomy, but rather their final solution, since one can only understand in it the meaning of the concepts involved.
The last quotation says very well that we have not put enough attention to the categories. If physicists and philosophers would have understood that continuity is one that is many, and that discretion is many that are one, they would have realized that they are the same, and that the fake security of the man who separates them and thinks he understands them is only imagination. The common sense has a lot of abstract intellect, which --as we have seen-- thinks like the imagi- nation. Hegel says: "common sense, just as the unilateral abstraction, tends to invoke itself" (NH 166).
The same happens with the contrast between the qualitative and the quantitative. Shamelessly, one supposes that they are diametrically opposed and that everybody knows what they mean but when the pos- itivist logicians try to clarify what a 'qualitative predicate' is, they sink into failure. They say that a predicate is qualitative if it is not applied to a finite number of objects. By excluding the finite number they think they are excluding the quantitative. But undoubtedly the number of green objects in the world is finite, and yet 'green' is one of the most frequent examples of qualitative predicated. In addition, finite and in- finite do not have any empirical meaning (cfr. IV, 1).
As for the scientists, it is obvious that the negligence with defini- tions can have its origin in the belief according to which it is enough to point with the finger at some empiric data to give meaning to the words qualitative and quantitative. But it is still more obvious that if we do not know beforehand what 'qualitative' means, we will never know on what aspect of the empirical fact we have to focus our attention. The color green gets in by the senses, but that the color green is a quality
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 190 Hegel was right
does not get in by the senses. That the green stops being green when it loses its essential property, is an entire metaphysical detour that the intellect promotes without the slightest intervention of the empirical data.
We have said (II, 6): even if the object is really contemporaneous, that is not enough for the contemporaneousness to be an empirical data, not even for seeing the object the idea of contemporaneous will take form in the mind, in the same way, even if the object or fact would be qualitative in reality, you can not conclude his qualitative character as an empirical data.
That the quantitative character is not an empiric data was demon- strated before (IV, 1 fine): the sensibility does not perceive the number. We beg you to confer.
This conclusion is imposed on us: these two concepts were originated not in the sensation but in the reflection of the subject on itself, and there cannot be contradiction because the meaning of both is the spirit; it hap- pens that the abstract intellect separates both notions in the imagination and stiffens them, making them unintelligible. Quality is a modified characteristic; when it is modified, the entity is not longer what it was, i. e. it loses its identity. Quantity is a modified characteristic in which the entity keeps being what it was, i. e. it conserves its identity. These couple of definitions --which are, by the way, the only ones available-- show that they are concepts which are openly anti-empirical, because the con- cept of identity is present in both (cfr. IV, 6).
From that definition, we conclude that the quality is a limit and implies denial; beyond that characteristic the entity is not anymore, quality is the "negative itself" (WL II 109).
On the contrary, the quantity is "the limit which is equally no lim- it" (WL I 332), "the indifferent determinateness, i. e. , posited as sublated" (WL I 331s), because the entity affected by a quantity is still what it was if this is modified; the entity is beyond this characteristic.
Now, for the realization of that notion of quality, one needs a sub- stance without substratum. It has to be something that, regardless of the qualitative affection, remains the same. In other words, the quality has to reside in a substance whose accidents are not accidental to it. The third chapter (III, 4) showed that this substance is the spirit. The deter- minations that the spirit acquires in its lifetime affect it completely, it identifies with each of them; there is no substratum that remains unal- tered; the spirit is its own acts.
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At the same time the fourth chapter (cfr. IV, 3), showed that the determinations that the spirit gives to itself are indifferent; those are limits that are there to be suppressed. With Hegel we said: "Infini- tude [. . . ] is to pose an immanent and proper determination, which is something indifferent to the one that poses it (NH 87s)". That is why we can say:
"The determination of pure quantity belongs also to the ego" for the self is "the continuity of universality or being-with-self un-interrupted by the infinitely manifold limits, by the content of sensations, intu- itions, and so forth. " (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:
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 194 Hegel was right
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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 195 master; control your heart, my Emile, and you will be virtuous (Emile, V:
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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 196 Hegel was right
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.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 198 Hegel was right
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.
says). Hegel said it one century before: "none of these determinations, taken separately has truth, but only the union of both" (WL I 191). The physics would have saved one century and many headaches if, as the real science requires, they had demanded rigorous definitions of every term they use.
"The continuity is this content of the identity-with itself of what is discrete; the follow up of the distinct ones in those that are distinct to them. Therefore, magnitude has in continuity the element of discretion immediately" (WL I 180).
The pseudodiscreet of the imagination consists in many which are not one: each one is entirely on their own. The pseudocontinuous of the imagination e. g. a line, the stretches are contiguous, but they lack continuity, because each of them can and exists on its own.
As we have seen, the reason why the physic and the natural scientist did not demand the definition of their terms is because they thought that meaning was some empirical data. We have proved that it is an illusion, and even in order to know if the empiric data corresponds to the belonging word it is still necessary to define it before, since the possession of any empiric data does not exempt them from the obliga- tion of defining. In this particular case, a little bit of reflection would have been enough to understand that sensation could only justify con- tiguity by itself, and besides, this is not the same as continuity. The continuity is something very metaphysical; there is nothing similar in the physical. In the best case scenario, what quantum physics was looking for was the juxtaposition of points, but juxtaposition is not continuity .
The sensibility ignores if the many elements that it thinks it veri- fies are one or many, i. e. does not know if they constitute or not only one individual, because, as we saw (IV, 6), individuality and sameness are not an empirical data. Hence sensibility cannot witness continuity. Further, its testimony of contiguity is completely unreliable for science, because it constitutes one single macroscopic impression due to the peculiarity of our sensorial organs. The atomic and corpuscular theory repudiated that testimony from the very beginning.
We said that Bohr's principle affirms complementarity between continuity and discretion. We need to support our affirmation because one commonly thinks it is a complementarity between wave and par- ticle. Margenau saw that this common interpretation is a mistake. "The point is that we have a reasonably satisfactory theory of the electron
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 188 Hegel was right
which assigns to it neither the cara? cter of a particle nor that of a wave. "
(1978, 89 n. 13) D'Abro has understood this with all clarity too:
According to our earlier views, the waves, being mere probability waves, must be regarded as symbolic, whereas the particles represent physical reality. But we must now suppose that particles also should be regarded as symbolic, for they come into existence only when a position observation is performed. (1952, 652).
Schro? dinger himself, whose equation is the operation center of quantum theory, emphatically told us that it was a mistake to con- serve the concepts of classical physics (Maxwell included) and not just denied them accurate definability. This is literally the way he puts it: "Concepts themselves must be abandoned, not only their clear de- finability" (1934, 519). That one still keeps talking about waves and particles shows that neither the public opinion nor physics themselves dare to accept the facts that quantum experimentation has discovered. The complementarity is not between wave and particle.
But if we take it part by part, the issue turns itself pretty obvious. One cannot talk about particle or corpuscle if the precise localization, the precise trajectory and the precise mass are denied. On the other hand, if Physics talks about the de Broglie's wave in association with the electron, it is evident that it does not consider the electron as a wave. In fact, the vector describes a global property of a physical system; it does not describe in fact a wave or a particle. Although it is common to call Schro? dinger's psi ondulatory, we are specifically warned that such a wave is a complex function and gives us plausible information about the whereabouts of the electron, but according to what we have just said, the electron is neither really a particle nor a corpuscle. Bohr himself emphasizes this when he speaks of "the renunciation of the absolute significance of conventional attributes of objects" (1958, 64).
The complementarity between continuity and discretion --affirmed by quantum physics-- is an overdue and not very lucid acknowledge- ment of the fact that none of these two concepts is true taken alone, but only the union of both. That was the Hegelian solution of the respec- tive antinomy, but in order to provide that solution the only thing that Hegel needed was the meaning of the concepts, or in other words, the fact that they can only have a meaning if they are united, and the real- ization of both can only happen in the spirit.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 189
"We call dialectics, the supreme movement of reason in which apparently and absolutely separated things go from one another by themselves, by what they themselves are, and the supposition that they are separated is thereby suppressed. " (WL I 92).
"The watch over the categories employed by the intellect that insults Philosophy is what the latter needs" (BS 370s).
In the case of all the examples we have just said, it would be redun- dant to say that the contradiction is effectively solved and does not remain as contradictory as before (this was the case in Kant). Likewise, it would also be redundant to repeat in the light of each example that the synthesis and the solution are not the beginning of a new antinomy, but rather their final solution, since one can only understand in it the meaning of the concepts involved.
The last quotation says very well that we have not put enough attention to the categories. If physicists and philosophers would have understood that continuity is one that is many, and that discretion is many that are one, they would have realized that they are the same, and that the fake security of the man who separates them and thinks he understands them is only imagination. The common sense has a lot of abstract intellect, which --as we have seen-- thinks like the imagi- nation. Hegel says: "common sense, just as the unilateral abstraction, tends to invoke itself" (NH 166).
The same happens with the contrast between the qualitative and the quantitative. Shamelessly, one supposes that they are diametrically opposed and that everybody knows what they mean but when the pos- itivist logicians try to clarify what a 'qualitative predicate' is, they sink into failure. They say that a predicate is qualitative if it is not applied to a finite number of objects. By excluding the finite number they think they are excluding the quantitative. But undoubtedly the number of green objects in the world is finite, and yet 'green' is one of the most frequent examples of qualitative predicated. In addition, finite and in- finite do not have any empirical meaning (cfr. IV, 1).
As for the scientists, it is obvious that the negligence with defini- tions can have its origin in the belief according to which it is enough to point with the finger at some empiric data to give meaning to the words qualitative and quantitative. But it is still more obvious that if we do not know beforehand what 'qualitative' means, we will never know on what aspect of the empirical fact we have to focus our attention. The color green gets in by the senses, but that the color green is a quality
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does not get in by the senses. That the green stops being green when it loses its essential property, is an entire metaphysical detour that the intellect promotes without the slightest intervention of the empirical data.
We have said (II, 6): even if the object is really contemporaneous, that is not enough for the contemporaneousness to be an empirical data, not even for seeing the object the idea of contemporaneous will take form in the mind, in the same way, even if the object or fact would be qualitative in reality, you can not conclude his qualitative character as an empirical data.
That the quantitative character is not an empiric data was demon- strated before (IV, 1 fine): the sensibility does not perceive the number. We beg you to confer.
This conclusion is imposed on us: these two concepts were originated not in the sensation but in the reflection of the subject on itself, and there cannot be contradiction because the meaning of both is the spirit; it hap- pens that the abstract intellect separates both notions in the imagination and stiffens them, making them unintelligible. Quality is a modified characteristic; when it is modified, the entity is not longer what it was, i. e. it loses its identity. Quantity is a modified characteristic in which the entity keeps being what it was, i. e. it conserves its identity. These couple of definitions --which are, by the way, the only ones available-- show that they are concepts which are openly anti-empirical, because the con- cept of identity is present in both (cfr. IV, 6).
From that definition, we conclude that the quality is a limit and implies denial; beyond that characteristic the entity is not anymore, quality is the "negative itself" (WL II 109).
On the contrary, the quantity is "the limit which is equally no lim- it" (WL I 332), "the indifferent determinateness, i. e. , posited as sublated" (WL I 331s), because the entity affected by a quantity is still what it was if this is modified; the entity is beyond this characteristic.
Now, for the realization of that notion of quality, one needs a sub- stance without substratum. It has to be something that, regardless of the qualitative affection, remains the same. In other words, the quality has to reside in a substance whose accidents are not accidental to it. The third chapter (III, 4) showed that this substance is the spirit. The deter- minations that the spirit acquires in its lifetime affect it completely, it identifies with each of them; there is no substratum that remains unal- tered; the spirit is its own acts.
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At the same time the fourth chapter (cfr. IV, 3), showed that the determinations that the spirit gives to itself are indifferent; those are limits that are there to be suppressed. With Hegel we said: "Infini- tude [. . . ] is to pose an immanent and proper determination, which is something indifferent to the one that poses it (NH 87s)". That is why we can say:
"The determination of pure quantity belongs also to the ego" for the self is "the continuity of universality or being-with-self un-interrupted by the infinitely manifold limits, by the content of sensations, intu- itions, and so forth. " (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,
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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.
