The definition of discontinuity or
discretion
is: many that simultaneously are one.
Hegel Was Right_nodrm
Infinite and Distinction 179
of thought; therefore, it places itself above the form of belief, but the content is exactly the same" (PR III 228s 2).
"Philosophy is not the only discipline that is essentially orthodox, but it is the most fundamental one; the statements have always been truth, the fundamental and essential truths of Christianity, are con- served and preserved by it [Philosophy]" (PR III 26s).
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? chapter v
Logic and Natural Sciences
? ? In the third and fourth chapters we exposed the core of Hegelian thought. Now, what has prevented people in our century from appreciating the Hegelian logic and the Hegelian critic of natural
sciences has been the incomprehension of that core. That is the reason why I think we are ready now to understand the real range of that logic, which is the only logic possible and whose importance for hu- man history increases every day.
1. diaLecticS
The key of dialects is this: We know that the contradiction or antithesis between two terms is solved, and we know that because the meaning of each of them is the spirit, and the spirit is not contradictory.
The opposition or contradiction is due to the fixational intellect. Moving away from the concrete, this intellect converts the terms into many abstractions that are unintelligible because no one can give them meaning if they remain away from the tangible.
The engine of the dialectics is the exigency of understanding the terms. Once we reach the realization of these terms --which is no
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 182 Hegel was right
other than the spirit-- they will become understood; and only then the oppositions and contradictions will be over. The pseudodialectics which posits that every synthesis becomes a thesis with a new an- tithesis and so on indefinitely, as we have seen (IV, I) does not share anything in common with Hegel and the dialectic; on the contrary, that is the indefinite progress that Hegel despises because it never achieves understanding. That dialectic cartoon lacks an engine, because it does not try to understand: it seeks not to understand. Therefore, every launch of a new thesis constitutes a display of arbitrariness.
The abstract is false [. . . ] The intellect resists the concrete; it insists on flattening it. By its reflections this intellect produces for the first time the abstract, the void, and clings to it in opposition to the truth [. . . ] Philosophy is diametrically opposed to the abstract; Philosophy is precisely the struggle against the abstract, the permanent war against the reflection of the intellect (EGP 113).
"The abstractions correspond to the reflection of the intellect, not to Philosophy" (EGP 97).
"The treatment of such intellect consists in maintaining each deter- mination or content of thought still" (GP III 262).
The pseudodialectic that tries to dissolve any particular notion and place it under skepticism is a cheap sophistic recourse, and this dialec- tic always stands in the middle of the road, since the end of the road is to understand.
"The dialectic that intends to dissolve the particular and to pro- duce thereby the general, is not yet a true dialectic, it does not go yet in the true direction; it is a dialectic that is common to both Plato and the sophists, who were experts in dissolving the particular".
The destiny of the supreme dialectics is to determine in itself the general, which has been the result of the mess of the particular, and in that universal to settle the contrasts, so that the dissolution of the contrast is the affir- mative. Thus the universal is determined as that which dissolves the con- tradictions and contrasts, and all of this has made it in itself; therefore, it is determined as the concrete, as that which is concrete in itself. Therefore, it becomes determined as the concrete, as that which is concrete in itself. From that superior point of view, this dialectics is the properly the Platonic one. This is the speculative dialectic, that which does not end in a negative result (GP II 65).
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 183
We have already seen (IV, 3) that the true universal is the spirit itself; it is "the universal, but that which determines itself, that is concrete in itself" (GP II 68).
The active universal, living, concrete, is which distinguishes itself in itself and remains in that free. This content consists in the identification of the one with itself in the other, in the many, in the distinct. Of all what is called Platonic philosophy this constitutes the true, the only thing true, the only interesting thing for knowledge; if one does not understand this, one does not understand what is fundamental (GP II 76).
The example of the real dialectic referred here by Hegel is the one we studied before (IV, 7): the abstract intellect separates identity and distinction and presents itself as incapable of defining and under- standing them. On the other hand, when reason comprehends that the very spirit --which is essentially intersubjetive-- is the only possible realization of both the concepts of identity and distinction, it realizes not only that they do not contradict each other, but that they have to be identical in order to exist and have meaning. Hence the opposition between these two concepts was due to the intellect kept them apart, and converted them thereby into abstractions, since they are not sepa- rated in the concrete; they are identical and only in this way can they be understood. Evidently, for the spirit, there cannot be something as concrete as itself.
"If the beginning was the universal, the result is the individual con- crete, subject" (WL II 499).
"Sense and meaning are something concrete" (GP II 591).
"This second negative thing to which we have arrived, the negative of the negative, is the suppression of contradiction; however, [. . . ] it is not the product of extrinsic reflection, but rather the most interior and objective element of life and spirit, that by means of which a subject is a person and is free" (WL II 496s), "the pure personality, the most subjec- tive thing there is" (WL II 502).
One cannot express with greater explicitness that the real dialectic is an exclusive patrimony of the spirit: the only solution of antinomies is the most intimate element of the life of the spirit. The pseudodialectic of materialism is an anti-scientific whim, because, being the realization called spirit the only one that makes that the concepts have meaning and become, for the first time understandable, such pseudodialectic is
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 184 Hegel was right
not directed to understand and hence it has no justification in its transi- tion from one concept to other.
"But as absolute negativity, the negative element of the absolute me- diation is the unity which consists in subjectivity and soul" (WL II 497). The commentators --specially the Marxist ones-- considered that dialectic was important by itself, but the really important thing for Hegel is to show that all the concepts mean spirit. Actually Hegel laughs at the "dull set square of triplicty" by which Kant "inserted the
thesis, the antithesis, and the synthesis carelessly" (GP III 385).
It is crucial to distinguish clearly between the Kantian and the Hegelian solution of the antinomies. Kant claimed that human mind is incapable of knowing the reality; hence, the mental categories do not say us anything about the real. It is then irrelevant that they contradict each other, e. g. that free will contradicts the necessary, finite contra- dicts the infinite, simple contradicts the compound, etcetera. It would be bad, Kant says, that the reality itself was contradictory; but it is not, because we do not know anything about reality. Our concepts don't reach it. It is the incognitum x. Our concepts contradict each other, but
reality remains immune from all of this.
The big question that Hegel raises up against such a solution is:
where do these concepts come from? How can one explain their exis- tence? And the great objection: the concepts are still as contradictory as before, the antinomy has not been solved; it has just been reinserted into the subject. Kant is very tender with the reality: he does not want it to be contradictory, so instead he makes the subject contradictory.
Hegel, however, confronts the problem directly: the contradiction has to be solved. That it is really solved is something that our above men- tioned example of identity and distinction proves.
Since each of the two opposed sides contains its other within itself and neither can be thought without the other, it follows that neither of these determinations, taken alone, has truth; this belongs only to their unity. This is the true dialectical consideration of them and also the true result. (WL I 191)
"The third is what is properly speculative, that means, to know the opposites in their truth are one. " (NH 415).
Now, the dialectic of identity and distinction underlies the dia- lectic of the simple and the compound, of the continuous and the
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 185
discrete, the qualitative and the quantitative, and the extensive and intensive.
For the simple and the compound we need to examine a larger quote:
The Eleats said that God was the one, which means to say, the simple. Now, the one, and the simple as such is completely void. What follows is that the simple can also be concrete and at the same time multiple in itself, so that that despite the distinction the unity remains. There is an example of this in our spirit. When one says, I am one, I am simple, I am a point, or I am one with myself, one has a representation of the self as something perfectly simple; there is nothing as simple as that self. However, we know that that self is a world in itself. Each man is in itself a world (the entire world); in this simplicity each man is an abyss that encloses an infinite content.
By thinking of oneself or remembering things, one brings into light the richness that one possesses as such. The self is, therefore, entirely simply, and at the same time it possesses a whole richness in itself. And when we say spirit instead of self, here we have from the very beginning not the rep- resentation of an abstract, but rather of a living organism. The spirit must be a totality, and yet this totality must be as simple as the self (EGP 277).
Let us comment the above quoted text. The concept of simplicity, evidently, does not have an empirical origin, because everything we can point with our finger, is always compound, in the sense that if we wish, we could divide it, at least imaginarily "one only points out matter which is compound" (GP I 359). Hence, only self-consciousness could make the idea that something simple exists. And actually, as we said before, the self is the simplest thing there can be; the very identity of the self depends on that. It is very important to realize that the idea of simplicity is something positive; it is an idea which has its proper content; it is impossible to define simplicity by denial of the compound, because then we would have to define the compound as that which is not simple, and by this circularity we would not obtain any content at all; we would not understand anything when we refer to the simple and the compound, but that is something that contradicts everyday experience.
We would have never called anything compound if it was not in comparison with something that is directly simple. In fact, the constitu- tive simplicity of what we call 'self' is so essential and prominent that in comparison to it any other thing hardly deserves to be called simple. Obviously the subtle thought that nothingness is simple could not be in
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 186 Hegel was right
the concept we are dealing with; it is something derived, because we do not understand nothingness by empiricity or by reflection; nothingness is a refined abstraction which is constructed through many negations of the positive; it cannot be the origin of any concept at all. Nothingness is not simple or compound: it simply does not exist.
Despite that the self is the simplicity par excellence, it is evident that the same self, which consists in self-consciousness, is constituted by a multitude of intellections, volitions, wishes, memories, decisions, et- cetera. Without that multiplicity we would not have the idea of calling the self simple, of saying that it is identical to itself and that is why, it is simple; the very idea that it identifies with itself implies some multiplicity of one and the same self. In order to be simple it needs to be compound. And vice versa too: those multiple life experiences, if they did not constitute the one and only identical self, they could not be called elements of a compound, but everyone would exist by itself and with no relation to the rest. The abstract intellect does not under- stand either simplicity or composition, because it incurs into the absurd "commits the same absurdity of making that which is pure relation into something devoid of all relation (WL I 211)".
The contradiction or antinomy is solved when we prove that the concrete to which the concept of simplicity refers is the same reality to which the concept of composition refers, and hence, the existence of antinomy has its origin in the stubbornness of the abstractions of the intellect and they want to remain separated and to still be abstractions. This situation makes it impossible to give them an intelligible meaning.
Now, the antinomy of the continuous and the discreet is hereby re- solved. The continuity of the self that we called simplicity does not only exclude the complicity of the diverse life experiences, but identi- fies with it in such level that the former cannot be defined without the latter. And vice versa too: no reality cannot be called discontinuous if its elements existed each by itself and without continuity between them; they would be separated entities with no relation whatsoever between them. They would not constitute the discontinuity of one only and the same entity.
Continuity is defined thus: one that simultaneously is many.
The definition of discontinuity or discretion is: many that simultaneously are one. Hence, they are the same. Scientists only discover a truism when they affirm that continuity and discretion are complementary concepts (as we will later see, this is what Bohr's complementarity principle
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 191
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,
? ? ? ? ? ? ? ? ? ? ? ?
of thought; therefore, it places itself above the form of belief, but the content is exactly the same" (PR III 228s 2).
"Philosophy is not the only discipline that is essentially orthodox, but it is the most fundamental one; the statements have always been truth, the fundamental and essential truths of Christianity, are con- served and preserved by it [Philosophy]" (PR III 26s).
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? chapter v
Logic and Natural Sciences
? ? In the third and fourth chapters we exposed the core of Hegelian thought. Now, what has prevented people in our century from appreciating the Hegelian logic and the Hegelian critic of natural
sciences has been the incomprehension of that core. That is the reason why I think we are ready now to understand the real range of that logic, which is the only logic possible and whose importance for hu- man history increases every day.
1. diaLecticS
The key of dialects is this: We know that the contradiction or antithesis between two terms is solved, and we know that because the meaning of each of them is the spirit, and the spirit is not contradictory.
The opposition or contradiction is due to the fixational intellect. Moving away from the concrete, this intellect converts the terms into many abstractions that are unintelligible because no one can give them meaning if they remain away from the tangible.
The engine of the dialectics is the exigency of understanding the terms. Once we reach the realization of these terms --which is no
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 182 Hegel was right
other than the spirit-- they will become understood; and only then the oppositions and contradictions will be over. The pseudodialectics which posits that every synthesis becomes a thesis with a new an- tithesis and so on indefinitely, as we have seen (IV, I) does not share anything in common with Hegel and the dialectic; on the contrary, that is the indefinite progress that Hegel despises because it never achieves understanding. That dialectic cartoon lacks an engine, because it does not try to understand: it seeks not to understand. Therefore, every launch of a new thesis constitutes a display of arbitrariness.
The abstract is false [. . . ] The intellect resists the concrete; it insists on flattening it. By its reflections this intellect produces for the first time the abstract, the void, and clings to it in opposition to the truth [. . . ] Philosophy is diametrically opposed to the abstract; Philosophy is precisely the struggle against the abstract, the permanent war against the reflection of the intellect (EGP 113).
"The abstractions correspond to the reflection of the intellect, not to Philosophy" (EGP 97).
"The treatment of such intellect consists in maintaining each deter- mination or content of thought still" (GP III 262).
The pseudodialectic that tries to dissolve any particular notion and place it under skepticism is a cheap sophistic recourse, and this dialec- tic always stands in the middle of the road, since the end of the road is to understand.
"The dialectic that intends to dissolve the particular and to pro- duce thereby the general, is not yet a true dialectic, it does not go yet in the true direction; it is a dialectic that is common to both Plato and the sophists, who were experts in dissolving the particular".
The destiny of the supreme dialectics is to determine in itself the general, which has been the result of the mess of the particular, and in that universal to settle the contrasts, so that the dissolution of the contrast is the affir- mative. Thus the universal is determined as that which dissolves the con- tradictions and contrasts, and all of this has made it in itself; therefore, it is determined as the concrete, as that which is concrete in itself. Therefore, it becomes determined as the concrete, as that which is concrete in itself. From that superior point of view, this dialectics is the properly the Platonic one. This is the speculative dialectic, that which does not end in a negative result (GP II 65).
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Logic and Natural Sciences 183
We have already seen (IV, 3) that the true universal is the spirit itself; it is "the universal, but that which determines itself, that is concrete in itself" (GP II 68).
The active universal, living, concrete, is which distinguishes itself in itself and remains in that free. This content consists in the identification of the one with itself in the other, in the many, in the distinct. Of all what is called Platonic philosophy this constitutes the true, the only thing true, the only interesting thing for knowledge; if one does not understand this, one does not understand what is fundamental (GP II 76).
The example of the real dialectic referred here by Hegel is the one we studied before (IV, 7): the abstract intellect separates identity and distinction and presents itself as incapable of defining and under- standing them. On the other hand, when reason comprehends that the very spirit --which is essentially intersubjetive-- is the only possible realization of both the concepts of identity and distinction, it realizes not only that they do not contradict each other, but that they have to be identical in order to exist and have meaning. Hence the opposition between these two concepts was due to the intellect kept them apart, and converted them thereby into abstractions, since they are not sepa- rated in the concrete; they are identical and only in this way can they be understood. Evidently, for the spirit, there cannot be something as concrete as itself.
"If the beginning was the universal, the result is the individual con- crete, subject" (WL II 499).
"Sense and meaning are something concrete" (GP II 591).
"This second negative thing to which we have arrived, the negative of the negative, is the suppression of contradiction; however, [. . . ] it is not the product of extrinsic reflection, but rather the most interior and objective element of life and spirit, that by means of which a subject is a person and is free" (WL II 496s), "the pure personality, the most subjec- tive thing there is" (WL II 502).
One cannot express with greater explicitness that the real dialectic is an exclusive patrimony of the spirit: the only solution of antinomies is the most intimate element of the life of the spirit. The pseudodialectic of materialism is an anti-scientific whim, because, being the realization called spirit the only one that makes that the concepts have meaning and become, for the first time understandable, such pseudodialectic is
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 184 Hegel was right
not directed to understand and hence it has no justification in its transi- tion from one concept to other.
"But as absolute negativity, the negative element of the absolute me- diation is the unity which consists in subjectivity and soul" (WL II 497). The commentators --specially the Marxist ones-- considered that dialectic was important by itself, but the really important thing for Hegel is to show that all the concepts mean spirit. Actually Hegel laughs at the "dull set square of triplicty" by which Kant "inserted the
thesis, the antithesis, and the synthesis carelessly" (GP III 385).
It is crucial to distinguish clearly between the Kantian and the Hegelian solution of the antinomies. Kant claimed that human mind is incapable of knowing the reality; hence, the mental categories do not say us anything about the real. It is then irrelevant that they contradict each other, e. g. that free will contradicts the necessary, finite contra- dicts the infinite, simple contradicts the compound, etcetera. It would be bad, Kant says, that the reality itself was contradictory; but it is not, because we do not know anything about reality. Our concepts don't reach it. It is the incognitum x. Our concepts contradict each other, but
reality remains immune from all of this.
The big question that Hegel raises up against such a solution is:
where do these concepts come from? How can one explain their exis- tence? And the great objection: the concepts are still as contradictory as before, the antinomy has not been solved; it has just been reinserted into the subject. Kant is very tender with the reality: he does not want it to be contradictory, so instead he makes the subject contradictory.
Hegel, however, confronts the problem directly: the contradiction has to be solved. That it is really solved is something that our above men- tioned example of identity and distinction proves.
Since each of the two opposed sides contains its other within itself and neither can be thought without the other, it follows that neither of these determinations, taken alone, has truth; this belongs only to their unity. This is the true dialectical consideration of them and also the true result. (WL I 191)
"The third is what is properly speculative, that means, to know the opposites in their truth are one. " (NH 415).
Now, the dialectic of identity and distinction underlies the dia- lectic of the simple and the compound, of the continuous and the
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discrete, the qualitative and the quantitative, and the extensive and intensive.
For the simple and the compound we need to examine a larger quote:
The Eleats said that God was the one, which means to say, the simple. Now, the one, and the simple as such is completely void. What follows is that the simple can also be concrete and at the same time multiple in itself, so that that despite the distinction the unity remains. There is an example of this in our spirit. When one says, I am one, I am simple, I am a point, or I am one with myself, one has a representation of the self as something perfectly simple; there is nothing as simple as that self. However, we know that that self is a world in itself. Each man is in itself a world (the entire world); in this simplicity each man is an abyss that encloses an infinite content.
By thinking of oneself or remembering things, one brings into light the richness that one possesses as such. The self is, therefore, entirely simply, and at the same time it possesses a whole richness in itself. And when we say spirit instead of self, here we have from the very beginning not the rep- resentation of an abstract, but rather of a living organism. The spirit must be a totality, and yet this totality must be as simple as the self (EGP 277).
Let us comment the above quoted text. The concept of simplicity, evidently, does not have an empirical origin, because everything we can point with our finger, is always compound, in the sense that if we wish, we could divide it, at least imaginarily "one only points out matter which is compound" (GP I 359). Hence, only self-consciousness could make the idea that something simple exists. And actually, as we said before, the self is the simplest thing there can be; the very identity of the self depends on that. It is very important to realize that the idea of simplicity is something positive; it is an idea which has its proper content; it is impossible to define simplicity by denial of the compound, because then we would have to define the compound as that which is not simple, and by this circularity we would not obtain any content at all; we would not understand anything when we refer to the simple and the compound, but that is something that contradicts everyday experience.
We would have never called anything compound if it was not in comparison with something that is directly simple. In fact, the constitu- tive simplicity of what we call 'self' is so essential and prominent that in comparison to it any other thing hardly deserves to be called simple. Obviously the subtle thought that nothingness is simple could not be in
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the concept we are dealing with; it is something derived, because we do not understand nothingness by empiricity or by reflection; nothingness is a refined abstraction which is constructed through many negations of the positive; it cannot be the origin of any concept at all. Nothingness is not simple or compound: it simply does not exist.
Despite that the self is the simplicity par excellence, it is evident that the same self, which consists in self-consciousness, is constituted by a multitude of intellections, volitions, wishes, memories, decisions, et- cetera. Without that multiplicity we would not have the idea of calling the self simple, of saying that it is identical to itself and that is why, it is simple; the very idea that it identifies with itself implies some multiplicity of one and the same self. In order to be simple it needs to be compound. And vice versa too: those multiple life experiences, if they did not constitute the one and only identical self, they could not be called elements of a compound, but everyone would exist by itself and with no relation to the rest. The abstract intellect does not under- stand either simplicity or composition, because it incurs into the absurd "commits the same absurdity of making that which is pure relation into something devoid of all relation (WL I 211)".
The contradiction or antinomy is solved when we prove that the concrete to which the concept of simplicity refers is the same reality to which the concept of composition refers, and hence, the existence of antinomy has its origin in the stubbornness of the abstractions of the intellect and they want to remain separated and to still be abstractions. This situation makes it impossible to give them an intelligible meaning.
Now, the antinomy of the continuous and the discreet is hereby re- solved. The continuity of the self that we called simplicity does not only exclude the complicity of the diverse life experiences, but identi- fies with it in such level that the former cannot be defined without the latter. And vice versa too: no reality cannot be called discontinuous if its elements existed each by itself and without continuity between them; they would be separated entities with no relation whatsoever between them. They would not constitute the discontinuity of one only and the same entity.
Continuity is defined thus: one that simultaneously is many.
The definition of discontinuity or discretion is: many that simultaneously are one. Hence, they are the same. Scientists only discover a truism when they affirm that continuity and discretion are complementary concepts (as we will later see, this is what Bohr's complementarity principle
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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
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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
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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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