probabiLity
Probability deserves a whole different treatment.
Probability deserves a whole different treatment.
Hegel Was Right_nodrm
It is an entity that is posited in order to explain the empiri- cally perceivable data.
Since momentum is defined as the product of mass by acceleration, the moment implies all the force that is implicated in the mass. There- fore, it carries all the lack of content and all the tautological game of mirrors that the explanatory entity called force entails.
Since Einstein demonstrated that energy equals mass multiplied by the speed of light squared, we have to say the same in regard to energy itself. All the lack of content which characterizes force enters in the definition with mass.
But even leaving that aside, it is perfectly obvious that energy is iden- tified with force, for it is commonly defined as the energy of carrying
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out work. Work is the effect, the observable phenomenon, the transla- tion of a body from a position to another that is even higher. In addition, we saw that force is commonly conceived as the capacity of producing certain observable effects: the 'power' of causing certain manifestation. It follows that energy, in perfect identity with that Newtonian force that physics naively believe to have abandoned, is a non-perceptible entity whose existence is posed in order to explain the empirically observable phenomena. This is why Hegel warned us that the concept of force "is the most prominent one" (GP III 84), stressing the fact that it is not prop- erly a concept but rather certain 'way of thinking'. What physics has made after Hegel is to shuffle in very different ways this same concept or lack of concept, in the hope of inventing new and different ideas.
By the way, what the popular formula of Einstein affirms is that mass transforms energy and vice versa: as statement that seemed to be fabulous in its times and which is still regarded so, but if physics with true scientific rigor demanded themselves true definitions with contents, that would not need to surprise anybody, for both mass and energy are always force: a posited explanatory entity that lacks content.
The only difference that exists consists in the diverse kind of mea- surements that scientists whimsically decide to carry out. However, one should notice that they are not measuring mass or energy themselves, in spite of the fact that they believe to be measuring that. In the case of mass, what they measure is the acceleration that a body suffers when certain force is applied to it, that means to say, they measure the space covered by the body in a given time; in other words, they measure a length and they divide it in a certain number of seconds. Best case sce- nario, what would be empirically measurable is length and that thing which physics call time: mass in itself is not perceptible or measurable. In the case of energy what they are measuring is work, that means to say, the distance along which a mass has been moved and the dura- tion of that movement; the bigger the distance the bigger the work; the bigger the time the smaller the work; length and time, that is what they measure; energy itself is not perceptible or measurable. It all depends on the imaginative combinations that physics make with length and time; they call one certain combination mass and the other energy; but that one combination transforms into another should not surprise any- body, since they are all mere multiplications and divisions that one can make with a pencil and a sheet of paper. Since they are only force, mass and energy themselves lack content; and no one should be surprised
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by the fact that a thing that lacks content is transformed into a thing that also lacks content.
Since 1860, and specially since 1890, the law of conservation of energy has become the touchstone of physics and perhaps of all natu- ral sciences up to the extent that Max von Laue says that one intends to deduce from it the rest of all natural laws and constructed an entire worldview around its form (cfr. Schilpp II 1970, 515). As for physics in particular goes, whoever studies these treatises corroborates that they are constructed upon Hamiltonian equations, and all what these supposes is that the sum of kinetic energy and potential energy is un- alterably conserved.
One can appreciate in Taylor and Wheeler to what extent the enthu- siasm for the law of conservation of energy has escalated. Defined in Newton's terms as the product of mass by speed, the momentum is not unalterably conserved in the collision of particles that travel near the speed of light. "We must therefore choose: We must abandon either the Newtonian expression for momentum or the law of conservation of momentum. The law of conservation of momentum has become so im- portant to us that we shift to it as a new foundation. We start with the law of conservation of momentum and from it derive the expression for momentum defined as that vector quantity which is conserved in all frames of reference. " (1966, 102)
In other words, momentum is defined as what is 'conserved'.
At first sight, the person that comes to us, boasting about his large scientific experiments, seems to possess a very profound knowledge of the universe, especially when he says to us that the existing quantity of energy in the world does not decrease or increase: it is always con- served in his opinion. His words are sonorous and impressive; but if we ask him what energy is, what that august, impressive and unalter- able thing is, he answers to us: what is conserved.
The law of conservation of energy has this grandiose content: one conserves what one conserves.
To make such statement one does not need to carry out the most elementary experiment; one does not need either to have any knowledge of reality whatsoever or to open his eyes to look at the world. One only needs certain intellectual masochism to take pleasure in tautologies.
The sharply tautological character of the law of conservation of energy was obvious before Taylor and Wheeler made their mortifying choice. If the term energy does not have content and yet one affirms
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that 'it' is conserved, the only thing we are told is that the 'it' is being conserved. And the proposition is summarized thus: one conserves what one conserves.
Since the first time it was formulated, such thesis was an a priori proposition which was by definition unverifiable. And if it refers to the quantity of energy in the entire universe, one would have to measure the quantity of energy in the entire universe: a task that cannot be com- pleted even by all humans. Even worse: they would have to measure it one minute later to see if it has not increased or diminished, some- thing which would require another team of humans just as numerous because the first team would has not yet finished its task. The law is also unverifiable by definition in the case that it refers to an isolated system or a tiny region in the universe. Even if we were to suppose that we would carry out a measurement in this instant and another one after ten minutes, the thesis would not be probed thereby, because the quantity of energy could augment in the meantime and return to its previous quantity in ten minutes. The verification would suppose the paroxysm of a measurement indefinitely repeated, which is something impossible not only for technical reason but by principle: the proccessus in indefinitum cannot be completed. Let alone the problem of defining what physics call an isolated system, because everything seems to indi- cate that they define it as a 'portion of the universe in which the energy does not increase or decrease', which would render us this wonderful definition: in a portion of the universe in which the energy does not increase or decrease, the energy does not increase or decrease. Indeed, they only know that a system is isolated because of the fact that the energy does not increase or decrease in it. As for the imaginary or real isolating surfaces that limit the system goes, physics only know that they are isolating it because in its interior the energy does not increase or decrease. Therefore, the insolently and sensational tautological for- mulation we just mentioned is unavoidable.
In the entire business of the conservation of energy we find tautolo- gies everywhere. If the particles --which according to the law should be created at a given instant because the observable particles have lost their energy-- are not observable, the physics hold that the new ones commence to exist 'virtually', not effectively nor observably; and then, of course, the sum of all the energies in the system remains unaltered. In order to keep the equality unaltered we can always imagine that the electron is surrounded by a cloud of 'virtual' photons: that is what
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Rosenfeld calls the "dressed electron" (EB 28, 250, 1-2). If we do not need this virtual energy to equalize the sum, then we will simply con- sider that the electron is 'undressed'.
If the number of things that I can call energy is unlimited, I do not have any problems whatsoever to make my results match. But, naturally, if they do not have any common denominator (and they do not have it, because they have not defined energy), if the unlikeness and heterogeneity between them is unlimited, what is conserved is an abstraction; the energy is perhaps the most abstract abstraction ever invented. In fact what is conserved is the capacity of the intellect for making abstractions; what is conserved is the spirit.
We have gone through the principal explanatory concepts that have come into vogue after the death of Hegel. In all of them one confirms the Hegelian demonstration of the tautological failure of all scientific explanations. It is impressive to see how quantum physics have ar- rived to the conclusion that the physical explanations have failed. It is not a change of paradigm, as Kuhn would want; it is something much more earnest, so earnest that Einstein died without accepting it, despite all the efforts of Bohr to convince him.
Classical physics 'explained' fundamentally by saying that there is nothing to explain: it explained by continuity between a past state and a present state of a physical system; quantum physics breaks with this continuity and hence it tears away the possibility of explanation. Margenau says correctly: "If there were gaps in this understanding, missing links in the chain of continuous action, the term causal would not be applied to it. " (1978, 175) What quantum physics discover is that there are leaks; they find that some links are missing. With regard to the luminous phenomena and their dependency on experimental devices, Bohr himself states: "this real situation obligates us to renounce to a rigorous causal explanation" (1964, 8).
Commenting Bohr, Weizsa? cker says:
. . . we are forced, not to renounce classical models, but to renounce models. Nothing like a quantum-mechanical model which replaces classical models and which then would admit of description of nature in terms of an explanation by the quantum-mechanical model, exists. (Bastin 1971, 326)
Now, if the physical explanation of the world has failed --and Hegel demonstrated that it had to fail-- then the only explanation of the
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world is the spirit, or, as it is expressed in the Science of Logic, the true of the essence is the concept (= spirit). Zubiri did not understand this. The concept 'force' --which, as we saw, is the most eminent of the explanatory concepts-- is in short a projection of the concept, which is known directly in the self-consciousness of the cause that determines itself, namely, the self-determination of the spirit. "Will is power in itself, and it is the essence of all power, both in nature and in spirit" (VG 113). "The subject is what is meaningful to itself and what is explained by itself" (A? sth I 435). Reason identified with method is the "supreme force or, more precisely, the only and absolute force [. . . ]
(WL II 486).
Whoever thinks he/she can explain differently the production of
something entirely new in the world is employing a concept of cause (III, 8) which cannot be given any meaning. How childish is the process by which some think a phenomenon is determined by another phe- nomenon --in a magical transmigration of properties-- indefinitely, without ever reaching a being that determines itself, and for that rea- son the entire set lacks determination and remains unexplained. The only source is the spirit: the being that determines itself.
The difficulty that some people bear to accept the Hegelian thesis is a problem of imagination only. We would like to say stress the merely imaginative character of this difficulty which is in itself a triviality but which is very widespread. They suppose that the world is "outside" from the spirit, and they do not realize that this expression lacks mean- ing completely, for the spirit is not a spatial thing of which one can speak of an inside and an outside. The objectors of Hegel are imaginatively creating distances and distinctions that do not even exist.
It is inspiring to see that a physic like Henry Margenau has under- stood that difficulties of such kind lack all kind of meaning:
"As the majority of scientists, Einstein did not solve the basic meta- physical problem that underlies all science, namely, the meaning of exteriority" (1978, 249).
If, in contrast to idealism, realism consists in saying that physical world is 'outside' from the spirit, then it is a thesis which does not have any meaning whatsoever.
Public opinion was shocked when the quantum physics experiments revealed that the electron becomes a bodkin only because the subject chooses to observe its position and that even, as Heisenberg said, "its size depends on the experiment that we carry out" (1930, 34). And
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this does not go only for quantum physics. As Eddington pointed out ". . . the relativity view is that a field of force can, like length and dura- tion, be nothing but a link between nature and the observer. " (1978, 43; orig. 1920) Max Born also said that "A gravitational field [. . . ] has no meaning at all independent of the choice of coordinates" (1962, 345). But the universal astonishment --even among the physics themselves-- evidently had as its cause the so-called belief according to which the world is 'outside' from the spirit, which is pure and sheer non-sense. And if Einstein himself was scared because he thought this was 'te- lepathy', then we can only conjecture that he was imagining that the physical remained far away from the spirit.
It has been a tremendous mistake to believe that Hegel denies the reality of the physical world. What he denies is that 'being real' means 'being outside'. It is the spirit what makes real the material, which means that the material is real. "Natural things are false existences; that does not mean they do not exist, but rather that they do not have their truth in themselves" (EGP 116).
5.
probabiLity
Probability deserves a whole different treatment. According to some, it is a theory that is explanatory. Besides, it is a theory on which biology has a keen interest, especially in regard to evolution, which is our next subject.
A probabilistic law is imaginary projected as a real factor which is not empirical in itself but which 'explains the empirical' data. In a like manner as with determinism, one supposes that probability is a real en- tity that works among and in the things themselves, and that it causes some effects which are the phenomenon, which in this case is a certain frequency of events. Of course, the mirror game and the 'double see- ing' is just as true as the other allegedly explanatory entities which we have considered, because the probabilistic law has the same phenom- enon it aims to describe. In this point, there is no difference between a probabilistic and a necessary law, because one supposes that the ob- served frequencies necessarily follow from the 'objective probability': that is the myth of what is 'unpredictable but unavoidable' of Manfred Eigen. In the same line, Mario Bunge says the following: "In short, our version of QM is as deterministic as classical mechanics [. . . ] as soon as
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the probabilities are both objective and lawful, indeterminism evapo- rates and stochastic determinism remains. " (1973, 100) Such an illusion should not cause any wonder, since the dilettante-philosopher speaks of the 'law of the big numbers'.
Before analyzing the concept of probability, one should notice that the explanation by a probable law demands from the mind a bigger desire of self-deceit as the explanation by a necessary law. If an 'it always happens like that' does not explain nothing, an "it frequently happens like that" explains even less. We said that if we ask why it thunders when it rains and one answers to us: 'because every time there are black clouds it thunders' we have not received any explanation; but if one answers to us 'because sixty percent of the times there are black clouds it thun- ders', the explanatory nullity would be even more accentuated. In that case, we could even speak of an anti-explanation, because what one should really be explaining is why sometimes it thunders and why sometimes it doesn't.
Statistics is a technique, not knowledge. It is an effective way or pro- ceeding in the practice, but it is not an explanation of reality. By means of a statistical law, we could foresee how much percentage of the popu- lation studied will adopt certain conduct, but by any means we could ex- plain why it adopts it. As we have said, the probabilistic thinkers figure that there is a being or a real factor (the 'objective probability') among things whose influx explains why seventy percent of the times something happens and why thirty percent of the times it doesn't. Even though we supposed such entity exists, it is by no means sufficient to explain the observed frequencies. If the entire population is under its influx, but some individual behave in the observed way and some of them don't, then it is not its influx what makes that, since in theory both of them are under its influx. As Hegel says "amounts to no more that the great influence of environment; and this does not tell us what does and what does not strictly belong to this influence. " (PG 194). Such entity is not even explanatory for the case of a majority: the only cause that would be explanatory is that which tells why A proceeds in the observed way, and B do not behave in the observed way even though A and B are un- der its same influx. The influx of such entity does not suffice to explain the behavior of A, because B was also under such influx and did not behave like that.
Let us go to the concept of the probable. Hegel did not treat it, but he mocked the concept of the 'possible', making clear thereby that it is
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a replica and a poor copy of the existing; it is merely an speculation of the real, which is projected by philosophers as if it was an entity in the world of the 'possible'. The possible has the same content than the real, but it is projected to an inexistent world. Now, the multitude of the 'possible' is divided into two groups: the probable and the improbable. For something to be probable it needs to be possible. If the possible only has meaning as a product or as a reflection of the intelligence, the probabil- ity deserves the same luck.
Possible is that which 'can' be. But we have stated that a 'can' does not have an empirical meaning, and also that in order to infer an 'is' from a 'can be' we need to take the content of can from someplace else, for the content and the meaning are not in the empirical data (cfr. III, 9). Now, if the concept of 'can' is not of empirical precedence, its origin is the reflection of the subject upon himself, and its meaning is that which we know by self-consciousness: the very real power that has the spirit of producing determinations and experiences that were not there before, that is to say, the causality of the spirit. That something is pos- sible means that the spirit can do it. The word 'possible' lacks meaning completely if we do without the spirit.
That something passes from being inexistent to be real is a fact that evidently requires a cause, for that which does not exist cannot do any- thing. Now, to say that something is possible is tantamount to say it can go from being inexistent to being real. The real possibility is not reduced by any means to non-contradiction. It is obvious that the ca- pacity of existing --which is characteristic of the possible-- does not lie in it because it does not exist, but rather in the cause that can make it being.
Therefore, to speak of probabilities and possibilities before the spirit existed is tantamount to utter non-sense. If there is something that can- not be the product of evolution that thing is the spirit.
Fortunately, Niels Bohr the most intelligent physic of our century, and his Danish school understood with perfect clearness right from the start of quantum physics that "probabilities concern only mental states; a probability value can only measure the strength of our belief and the accuracy of our information" (Bunge, 1973, 66). We said that the word 'possible' lacks meaning if one does away with the spirit; the same thing goes for the probable, for that is only a species of the 'possible'. By defini- tion, what is probable does not exist yet. Consequently, one cannot say it exists independently from the intelligence that considers it probable.
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In order to determine the degree of probability of something, all the relevant information has to be taken into account. To judge whether a piece of information is relevant or not is a prudential consideration that inanimate things cannot obviously make. The intervention of intelligence is necessary.
But there is more to it. I can judge whether a piece of information that I possess is relevant or not, for I do not have it before my mind; there- fore it is impossible to gain absolute and mechanical certainty as whether or not we have obtained all the relevant information. For pragmatic needs, because I cannot remain indecisive all my life, a moment comes in which I decide prudentially that the information that I have ob- tained is sufficient to me. In function of this, I calculate the probability in question and proceed. Despite what the 'objectivists' may say, the only probabilities that exist are the ones which are built up the way we just indicated. Many operations of the intellect intervene in their constitution.
To think that there is an entity called percentual probability with- in things is to fall into the illusion denounced by Hegel; one projects imaginatively an entity which is not seen but which is 'under' the phe- nomena that we can see, and whose only definition is being cause or explanation of these same phenomena.
In order to make probability something 'objective', the following thinkers want it to be a propensity or a tendency: Smoluchowski, Poin- care? , Popper, Margenau and Bunge. But none of these authors has paid attention to the fact that a propensity or a tendency is not empirical data; not even the tendency to eat called hunger is an empirical data. The meaning of these words is something known by reflection of the subject towards himself. Here we are before the inwardness and the subjec- tivity that objectivism pretended to dismiss. Naturally, it would be very equivocal to attribute propensities to what is probable in itself, for that which does not exist yet cannot have any propensity. One should attri- bute them to the causes, but if these are material and physical objects, such attribution would be animism, and H. R. Post has mocked "". . . the pagan device of investing the world of phenomena with pervasive wood spirits called propensities. " (Bastin, 1971, 279). The causes would have to be true spirits, and there we find again the subject which was trying to be avoided by the objectivists.
The above mentioned authors do not realize that the propensity which they affirm is a propensity towards existence, and hence it would
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be a propensity of a fact that does not yet exist; it follows from this that neither the fact nor its property can be the real referent of the word probability; the only real referent that exists in this moment is knowl- edge; therefore, probability can only mean 'the strength of our belief and the accuracy of our information', that is what the Danish sustain.
On the other hand, the Spielraumtheorie, the range theory, was held with variants by Bernoulli, von Kries, Bolzano, Waismann, Wittgenstein, Keynes and Carnap. Although its ambition went far beyond, this theory only tells what the expression 'percentage' means, which is the expres- sion of the degree of probability. This theory tells us that the percentage is the quotient or fraction whose numerator is the number of the favor- able events, and whose denominator is the added number of favorable and unfavorable events. In order to talk about probability, this theory insists in that the number of unfavorable events must have a priori the same probability of occurring than the favorable events. It is the famous indifference or equipossibility they are always speaking about.
This has been acutely observed, but as von Wright notices "The question may be raised whether randomness and equipossibility can be satisfactorily accounted for without reference to states of knowledge or ignorance. " (EB 23, 631, 1s. ) It is evident to me that the amount of events covered by the so-called denominator cannot be determined without a prudential judgment similar to the one we employ when we determine if the data we have are sufficient. There is no mechanical or absolute procedure in order to know whether I am taking into account all the relevant facts. In other words: in order to determine the amount of events or facts in a percentage is something which is determined by a prudential judgment, and as Von Wright says, this does not happen without reference to one's own state of knowledge or ignorance.
Lastly, von Mises and Reichenbach believe that probability means certain frequency which is empirically observable. But this theory suffers from a misunderstanding of concepts. Probability is perhaps (and not always) measured by a certain frequency, probability may be the cause of a certain frequency of events, probability may be inferred from a certain frequency observed, but no probability has frequency as its meaning. First, we pointed out that physics often measure intensities of spectral lines to calculate the probability: if the line is brilliant, the transition of state is highly probable; if the line is cloudy, the transi- tion is slightly possible; if there is no spectral line, the transition is not probable. Now, these intensities are not frequencies by any means. In
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addition, there are other ways in physics to measure probability, which are not frequencies. Therefore, it is absolutely false that probability means frequency.
But the most important thing to point out is that probability is prob- ability of a possible event, that is to say, an event that does not yet exists, while the frequency --in order to be an empirical data, as von Mises and Reichenbach would want-- is the computation of the event that have occurred, events that exist or that have existed. Perhaps the observed frequency authorizes us to infer a certain probability for the future, but this demonstrates that probability is not frequency, for the former would still have to be inferred while we already have the latter. One doesn't infer A from A; if we have A, we do not need to infer it.
By the way, the inference in question requires as a premise a prin- ciple which is itself unverifiable and which is must certain false 'there is regularity in nature' and 'the future resembles the past'. It requires it because the rationalizing assumption of the inference is that the fre- quency of the past will also be the frequency of the future.
The individual facts of which we speak when talking about fre- quency or probability are distinct: in the first case we say that from one hundred observed events, x were positive. In the second case we speak of a new event which hast no yet occurred and which is not one of the one hundred cases that have been observed. How justified is it to speak about the probability of such future event after proving some- thing in regard to one hundred different events is a question we do not need to go into now. In any case, it supposes a highly doubtable premise, which is the so-called principle we previously alluded to. But even if we graciously supposed that this logical step is valid, it re- mains clear that frequency and probability are different concepts. First: because they cannot be predicated simultaneously in regard to a same event. Second: because in order to go logically from one to the other one needs the intervention of a highly metaphysical principle: a clear sign which tells us that the content of one of the concepts is not the same as the content of the other.
6. Life
If what has been said in this book proves to be right in its thesis that physics is not an empirical science, with much more reason can we say
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the same in regard to biology and behavioral disciplines, since their own cultivators only refer to the empiricity of the physical sciences as the ideal their methodologies strive for. Nevertheless, we need to explain the non-empirical character of the biological and behavioral sciences, for the belief in their empirical character is widespread and has particular consequences.
Since momentum is defined as the product of mass by acceleration, the moment implies all the force that is implicated in the mass. There- fore, it carries all the lack of content and all the tautological game of mirrors that the explanatory entity called force entails.
Since Einstein demonstrated that energy equals mass multiplied by the speed of light squared, we have to say the same in regard to energy itself. All the lack of content which characterizes force enters in the definition with mass.
But even leaving that aside, it is perfectly obvious that energy is iden- tified with force, for it is commonly defined as the energy of carrying
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out work. Work is the effect, the observable phenomenon, the transla- tion of a body from a position to another that is even higher. In addition, we saw that force is commonly conceived as the capacity of producing certain observable effects: the 'power' of causing certain manifestation. It follows that energy, in perfect identity with that Newtonian force that physics naively believe to have abandoned, is a non-perceptible entity whose existence is posed in order to explain the empirically observable phenomena. This is why Hegel warned us that the concept of force "is the most prominent one" (GP III 84), stressing the fact that it is not prop- erly a concept but rather certain 'way of thinking'. What physics has made after Hegel is to shuffle in very different ways this same concept or lack of concept, in the hope of inventing new and different ideas.
By the way, what the popular formula of Einstein affirms is that mass transforms energy and vice versa: as statement that seemed to be fabulous in its times and which is still regarded so, but if physics with true scientific rigor demanded themselves true definitions with contents, that would not need to surprise anybody, for both mass and energy are always force: a posited explanatory entity that lacks content.
The only difference that exists consists in the diverse kind of mea- surements that scientists whimsically decide to carry out. However, one should notice that they are not measuring mass or energy themselves, in spite of the fact that they believe to be measuring that. In the case of mass, what they measure is the acceleration that a body suffers when certain force is applied to it, that means to say, they measure the space covered by the body in a given time; in other words, they measure a length and they divide it in a certain number of seconds. Best case sce- nario, what would be empirically measurable is length and that thing which physics call time: mass in itself is not perceptible or measurable. In the case of energy what they are measuring is work, that means to say, the distance along which a mass has been moved and the dura- tion of that movement; the bigger the distance the bigger the work; the bigger the time the smaller the work; length and time, that is what they measure; energy itself is not perceptible or measurable. It all depends on the imaginative combinations that physics make with length and time; they call one certain combination mass and the other energy; but that one combination transforms into another should not surprise any- body, since they are all mere multiplications and divisions that one can make with a pencil and a sheet of paper. Since they are only force, mass and energy themselves lack content; and no one should be surprised
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 218 Hegel was right
by the fact that a thing that lacks content is transformed into a thing that also lacks content.
Since 1860, and specially since 1890, the law of conservation of energy has become the touchstone of physics and perhaps of all natu- ral sciences up to the extent that Max von Laue says that one intends to deduce from it the rest of all natural laws and constructed an entire worldview around its form (cfr. Schilpp II 1970, 515). As for physics in particular goes, whoever studies these treatises corroborates that they are constructed upon Hamiltonian equations, and all what these supposes is that the sum of kinetic energy and potential energy is un- alterably conserved.
One can appreciate in Taylor and Wheeler to what extent the enthu- siasm for the law of conservation of energy has escalated. Defined in Newton's terms as the product of mass by speed, the momentum is not unalterably conserved in the collision of particles that travel near the speed of light. "We must therefore choose: We must abandon either the Newtonian expression for momentum or the law of conservation of momentum. The law of conservation of momentum has become so im- portant to us that we shift to it as a new foundation. We start with the law of conservation of momentum and from it derive the expression for momentum defined as that vector quantity which is conserved in all frames of reference. " (1966, 102)
In other words, momentum is defined as what is 'conserved'.
At first sight, the person that comes to us, boasting about his large scientific experiments, seems to possess a very profound knowledge of the universe, especially when he says to us that the existing quantity of energy in the world does not decrease or increase: it is always con- served in his opinion. His words are sonorous and impressive; but if we ask him what energy is, what that august, impressive and unalter- able thing is, he answers to us: what is conserved.
The law of conservation of energy has this grandiose content: one conserves what one conserves.
To make such statement one does not need to carry out the most elementary experiment; one does not need either to have any knowledge of reality whatsoever or to open his eyes to look at the world. One only needs certain intellectual masochism to take pleasure in tautologies.
The sharply tautological character of the law of conservation of energy was obvious before Taylor and Wheeler made their mortifying choice. If the term energy does not have content and yet one affirms
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that 'it' is conserved, the only thing we are told is that the 'it' is being conserved. And the proposition is summarized thus: one conserves what one conserves.
Since the first time it was formulated, such thesis was an a priori proposition which was by definition unverifiable. And if it refers to the quantity of energy in the entire universe, one would have to measure the quantity of energy in the entire universe: a task that cannot be com- pleted even by all humans. Even worse: they would have to measure it one minute later to see if it has not increased or diminished, some- thing which would require another team of humans just as numerous because the first team would has not yet finished its task. The law is also unverifiable by definition in the case that it refers to an isolated system or a tiny region in the universe. Even if we were to suppose that we would carry out a measurement in this instant and another one after ten minutes, the thesis would not be probed thereby, because the quantity of energy could augment in the meantime and return to its previous quantity in ten minutes. The verification would suppose the paroxysm of a measurement indefinitely repeated, which is something impossible not only for technical reason but by principle: the proccessus in indefinitum cannot be completed. Let alone the problem of defining what physics call an isolated system, because everything seems to indi- cate that they define it as a 'portion of the universe in which the energy does not increase or decrease', which would render us this wonderful definition: in a portion of the universe in which the energy does not increase or decrease, the energy does not increase or decrease. Indeed, they only know that a system is isolated because of the fact that the energy does not increase or decrease in it. As for the imaginary or real isolating surfaces that limit the system goes, physics only know that they are isolating it because in its interior the energy does not increase or decrease. Therefore, the insolently and sensational tautological for- mulation we just mentioned is unavoidable.
In the entire business of the conservation of energy we find tautolo- gies everywhere. If the particles --which according to the law should be created at a given instant because the observable particles have lost their energy-- are not observable, the physics hold that the new ones commence to exist 'virtually', not effectively nor observably; and then, of course, the sum of all the energies in the system remains unaltered. In order to keep the equality unaltered we can always imagine that the electron is surrounded by a cloud of 'virtual' photons: that is what
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Rosenfeld calls the "dressed electron" (EB 28, 250, 1-2). If we do not need this virtual energy to equalize the sum, then we will simply con- sider that the electron is 'undressed'.
If the number of things that I can call energy is unlimited, I do not have any problems whatsoever to make my results match. But, naturally, if they do not have any common denominator (and they do not have it, because they have not defined energy), if the unlikeness and heterogeneity between them is unlimited, what is conserved is an abstraction; the energy is perhaps the most abstract abstraction ever invented. In fact what is conserved is the capacity of the intellect for making abstractions; what is conserved is the spirit.
We have gone through the principal explanatory concepts that have come into vogue after the death of Hegel. In all of them one confirms the Hegelian demonstration of the tautological failure of all scientific explanations. It is impressive to see how quantum physics have ar- rived to the conclusion that the physical explanations have failed. It is not a change of paradigm, as Kuhn would want; it is something much more earnest, so earnest that Einstein died without accepting it, despite all the efforts of Bohr to convince him.
Classical physics 'explained' fundamentally by saying that there is nothing to explain: it explained by continuity between a past state and a present state of a physical system; quantum physics breaks with this continuity and hence it tears away the possibility of explanation. Margenau says correctly: "If there were gaps in this understanding, missing links in the chain of continuous action, the term causal would not be applied to it. " (1978, 175) What quantum physics discover is that there are leaks; they find that some links are missing. With regard to the luminous phenomena and their dependency on experimental devices, Bohr himself states: "this real situation obligates us to renounce to a rigorous causal explanation" (1964, 8).
Commenting Bohr, Weizsa? cker says:
. . . we are forced, not to renounce classical models, but to renounce models. Nothing like a quantum-mechanical model which replaces classical models and which then would admit of description of nature in terms of an explanation by the quantum-mechanical model, exists. (Bastin 1971, 326)
Now, if the physical explanation of the world has failed --and Hegel demonstrated that it had to fail-- then the only explanation of the
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world is the spirit, or, as it is expressed in the Science of Logic, the true of the essence is the concept (= spirit). Zubiri did not understand this. The concept 'force' --which, as we saw, is the most eminent of the explanatory concepts-- is in short a projection of the concept, which is known directly in the self-consciousness of the cause that determines itself, namely, the self-determination of the spirit. "Will is power in itself, and it is the essence of all power, both in nature and in spirit" (VG 113). "The subject is what is meaningful to itself and what is explained by itself" (A? sth I 435). Reason identified with method is the "supreme force or, more precisely, the only and absolute force [. . . ]
(WL II 486).
Whoever thinks he/she can explain differently the production of
something entirely new in the world is employing a concept of cause (III, 8) which cannot be given any meaning. How childish is the process by which some think a phenomenon is determined by another phe- nomenon --in a magical transmigration of properties-- indefinitely, without ever reaching a being that determines itself, and for that rea- son the entire set lacks determination and remains unexplained. The only source is the spirit: the being that determines itself.
The difficulty that some people bear to accept the Hegelian thesis is a problem of imagination only. We would like to say stress the merely imaginative character of this difficulty which is in itself a triviality but which is very widespread. They suppose that the world is "outside" from the spirit, and they do not realize that this expression lacks mean- ing completely, for the spirit is not a spatial thing of which one can speak of an inside and an outside. The objectors of Hegel are imaginatively creating distances and distinctions that do not even exist.
It is inspiring to see that a physic like Henry Margenau has under- stood that difficulties of such kind lack all kind of meaning:
"As the majority of scientists, Einstein did not solve the basic meta- physical problem that underlies all science, namely, the meaning of exteriority" (1978, 249).
If, in contrast to idealism, realism consists in saying that physical world is 'outside' from the spirit, then it is a thesis which does not have any meaning whatsoever.
Public opinion was shocked when the quantum physics experiments revealed that the electron becomes a bodkin only because the subject chooses to observe its position and that even, as Heisenberg said, "its size depends on the experiment that we carry out" (1930, 34). And
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this does not go only for quantum physics. As Eddington pointed out ". . . the relativity view is that a field of force can, like length and dura- tion, be nothing but a link between nature and the observer. " (1978, 43; orig. 1920) Max Born also said that "A gravitational field [. . . ] has no meaning at all independent of the choice of coordinates" (1962, 345). But the universal astonishment --even among the physics themselves-- evidently had as its cause the so-called belief according to which the world is 'outside' from the spirit, which is pure and sheer non-sense. And if Einstein himself was scared because he thought this was 'te- lepathy', then we can only conjecture that he was imagining that the physical remained far away from the spirit.
It has been a tremendous mistake to believe that Hegel denies the reality of the physical world. What he denies is that 'being real' means 'being outside'. It is the spirit what makes real the material, which means that the material is real. "Natural things are false existences; that does not mean they do not exist, but rather that they do not have their truth in themselves" (EGP 116).
5.
probabiLity
Probability deserves a whole different treatment. According to some, it is a theory that is explanatory. Besides, it is a theory on which biology has a keen interest, especially in regard to evolution, which is our next subject.
A probabilistic law is imaginary projected as a real factor which is not empirical in itself but which 'explains the empirical' data. In a like manner as with determinism, one supposes that probability is a real en- tity that works among and in the things themselves, and that it causes some effects which are the phenomenon, which in this case is a certain frequency of events. Of course, the mirror game and the 'double see- ing' is just as true as the other allegedly explanatory entities which we have considered, because the probabilistic law has the same phenom- enon it aims to describe. In this point, there is no difference between a probabilistic and a necessary law, because one supposes that the ob- served frequencies necessarily follow from the 'objective probability': that is the myth of what is 'unpredictable but unavoidable' of Manfred Eigen. In the same line, Mario Bunge says the following: "In short, our version of QM is as deterministic as classical mechanics [. . . ] as soon as
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the probabilities are both objective and lawful, indeterminism evapo- rates and stochastic determinism remains. " (1973, 100) Such an illusion should not cause any wonder, since the dilettante-philosopher speaks of the 'law of the big numbers'.
Before analyzing the concept of probability, one should notice that the explanation by a probable law demands from the mind a bigger desire of self-deceit as the explanation by a necessary law. If an 'it always happens like that' does not explain nothing, an "it frequently happens like that" explains even less. We said that if we ask why it thunders when it rains and one answers to us: 'because every time there are black clouds it thunders' we have not received any explanation; but if one answers to us 'because sixty percent of the times there are black clouds it thun- ders', the explanatory nullity would be even more accentuated. In that case, we could even speak of an anti-explanation, because what one should really be explaining is why sometimes it thunders and why sometimes it doesn't.
Statistics is a technique, not knowledge. It is an effective way or pro- ceeding in the practice, but it is not an explanation of reality. By means of a statistical law, we could foresee how much percentage of the popu- lation studied will adopt certain conduct, but by any means we could ex- plain why it adopts it. As we have said, the probabilistic thinkers figure that there is a being or a real factor (the 'objective probability') among things whose influx explains why seventy percent of the times something happens and why thirty percent of the times it doesn't. Even though we supposed such entity exists, it is by no means sufficient to explain the observed frequencies. If the entire population is under its influx, but some individual behave in the observed way and some of them don't, then it is not its influx what makes that, since in theory both of them are under its influx. As Hegel says "amounts to no more that the great influence of environment; and this does not tell us what does and what does not strictly belong to this influence. " (PG 194). Such entity is not even explanatory for the case of a majority: the only cause that would be explanatory is that which tells why A proceeds in the observed way, and B do not behave in the observed way even though A and B are un- der its same influx. The influx of such entity does not suffice to explain the behavior of A, because B was also under such influx and did not behave like that.
Let us go to the concept of the probable. Hegel did not treat it, but he mocked the concept of the 'possible', making clear thereby that it is
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a replica and a poor copy of the existing; it is merely an speculation of the real, which is projected by philosophers as if it was an entity in the world of the 'possible'. The possible has the same content than the real, but it is projected to an inexistent world. Now, the multitude of the 'possible' is divided into two groups: the probable and the improbable. For something to be probable it needs to be possible. If the possible only has meaning as a product or as a reflection of the intelligence, the probabil- ity deserves the same luck.
Possible is that which 'can' be. But we have stated that a 'can' does not have an empirical meaning, and also that in order to infer an 'is' from a 'can be' we need to take the content of can from someplace else, for the content and the meaning are not in the empirical data (cfr. III, 9). Now, if the concept of 'can' is not of empirical precedence, its origin is the reflection of the subject upon himself, and its meaning is that which we know by self-consciousness: the very real power that has the spirit of producing determinations and experiences that were not there before, that is to say, the causality of the spirit. That something is pos- sible means that the spirit can do it. The word 'possible' lacks meaning completely if we do without the spirit.
That something passes from being inexistent to be real is a fact that evidently requires a cause, for that which does not exist cannot do any- thing. Now, to say that something is possible is tantamount to say it can go from being inexistent to being real. The real possibility is not reduced by any means to non-contradiction. It is obvious that the ca- pacity of existing --which is characteristic of the possible-- does not lie in it because it does not exist, but rather in the cause that can make it being.
Therefore, to speak of probabilities and possibilities before the spirit existed is tantamount to utter non-sense. If there is something that can- not be the product of evolution that thing is the spirit.
Fortunately, Niels Bohr the most intelligent physic of our century, and his Danish school understood with perfect clearness right from the start of quantum physics that "probabilities concern only mental states; a probability value can only measure the strength of our belief and the accuracy of our information" (Bunge, 1973, 66). We said that the word 'possible' lacks meaning if one does away with the spirit; the same thing goes for the probable, for that is only a species of the 'possible'. By defini- tion, what is probable does not exist yet. Consequently, one cannot say it exists independently from the intelligence that considers it probable.
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In order to determine the degree of probability of something, all the relevant information has to be taken into account. To judge whether a piece of information is relevant or not is a prudential consideration that inanimate things cannot obviously make. The intervention of intelligence is necessary.
But there is more to it. I can judge whether a piece of information that I possess is relevant or not, for I do not have it before my mind; there- fore it is impossible to gain absolute and mechanical certainty as whether or not we have obtained all the relevant information. For pragmatic needs, because I cannot remain indecisive all my life, a moment comes in which I decide prudentially that the information that I have ob- tained is sufficient to me. In function of this, I calculate the probability in question and proceed. Despite what the 'objectivists' may say, the only probabilities that exist are the ones which are built up the way we just indicated. Many operations of the intellect intervene in their constitution.
To think that there is an entity called percentual probability with- in things is to fall into the illusion denounced by Hegel; one projects imaginatively an entity which is not seen but which is 'under' the phe- nomena that we can see, and whose only definition is being cause or explanation of these same phenomena.
In order to make probability something 'objective', the following thinkers want it to be a propensity or a tendency: Smoluchowski, Poin- care? , Popper, Margenau and Bunge. But none of these authors has paid attention to the fact that a propensity or a tendency is not empirical data; not even the tendency to eat called hunger is an empirical data. The meaning of these words is something known by reflection of the subject towards himself. Here we are before the inwardness and the subjec- tivity that objectivism pretended to dismiss. Naturally, it would be very equivocal to attribute propensities to what is probable in itself, for that which does not exist yet cannot have any propensity. One should attri- bute them to the causes, but if these are material and physical objects, such attribution would be animism, and H. R. Post has mocked "". . . the pagan device of investing the world of phenomena with pervasive wood spirits called propensities. " (Bastin, 1971, 279). The causes would have to be true spirits, and there we find again the subject which was trying to be avoided by the objectivists.
The above mentioned authors do not realize that the propensity which they affirm is a propensity towards existence, and hence it would
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be a propensity of a fact that does not yet exist; it follows from this that neither the fact nor its property can be the real referent of the word probability; the only real referent that exists in this moment is knowl- edge; therefore, probability can only mean 'the strength of our belief and the accuracy of our information', that is what the Danish sustain.
On the other hand, the Spielraumtheorie, the range theory, was held with variants by Bernoulli, von Kries, Bolzano, Waismann, Wittgenstein, Keynes and Carnap. Although its ambition went far beyond, this theory only tells what the expression 'percentage' means, which is the expres- sion of the degree of probability. This theory tells us that the percentage is the quotient or fraction whose numerator is the number of the favor- able events, and whose denominator is the added number of favorable and unfavorable events. In order to talk about probability, this theory insists in that the number of unfavorable events must have a priori the same probability of occurring than the favorable events. It is the famous indifference or equipossibility they are always speaking about.
This has been acutely observed, but as von Wright notices "The question may be raised whether randomness and equipossibility can be satisfactorily accounted for without reference to states of knowledge or ignorance. " (EB 23, 631, 1s. ) It is evident to me that the amount of events covered by the so-called denominator cannot be determined without a prudential judgment similar to the one we employ when we determine if the data we have are sufficient. There is no mechanical or absolute procedure in order to know whether I am taking into account all the relevant facts. In other words: in order to determine the amount of events or facts in a percentage is something which is determined by a prudential judgment, and as Von Wright says, this does not happen without reference to one's own state of knowledge or ignorance.
Lastly, von Mises and Reichenbach believe that probability means certain frequency which is empirically observable. But this theory suffers from a misunderstanding of concepts. Probability is perhaps (and not always) measured by a certain frequency, probability may be the cause of a certain frequency of events, probability may be inferred from a certain frequency observed, but no probability has frequency as its meaning. First, we pointed out that physics often measure intensities of spectral lines to calculate the probability: if the line is brilliant, the transition of state is highly probable; if the line is cloudy, the transi- tion is slightly possible; if there is no spectral line, the transition is not probable. Now, these intensities are not frequencies by any means. In
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addition, there are other ways in physics to measure probability, which are not frequencies. Therefore, it is absolutely false that probability means frequency.
But the most important thing to point out is that probability is prob- ability of a possible event, that is to say, an event that does not yet exists, while the frequency --in order to be an empirical data, as von Mises and Reichenbach would want-- is the computation of the event that have occurred, events that exist or that have existed. Perhaps the observed frequency authorizes us to infer a certain probability for the future, but this demonstrates that probability is not frequency, for the former would still have to be inferred while we already have the latter. One doesn't infer A from A; if we have A, we do not need to infer it.
By the way, the inference in question requires as a premise a prin- ciple which is itself unverifiable and which is must certain false 'there is regularity in nature' and 'the future resembles the past'. It requires it because the rationalizing assumption of the inference is that the fre- quency of the past will also be the frequency of the future.
The individual facts of which we speak when talking about fre- quency or probability are distinct: in the first case we say that from one hundred observed events, x were positive. In the second case we speak of a new event which hast no yet occurred and which is not one of the one hundred cases that have been observed. How justified is it to speak about the probability of such future event after proving some- thing in regard to one hundred different events is a question we do not need to go into now. In any case, it supposes a highly doubtable premise, which is the so-called principle we previously alluded to. But even if we graciously supposed that this logical step is valid, it re- mains clear that frequency and probability are different concepts. First: because they cannot be predicated simultaneously in regard to a same event. Second: because in order to go logically from one to the other one needs the intervention of a highly metaphysical principle: a clear sign which tells us that the content of one of the concepts is not the same as the content of the other.
6. Life
If what has been said in this book proves to be right in its thesis that physics is not an empirical science, with much more reason can we say
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the same in regard to biology and behavioral disciplines, since their own cultivators only refer to the empiricity of the physical sciences as the ideal their methodologies strive for. Nevertheless, we need to explain the non-empirical character of the biological and behavioral sciences, for the belief in their empirical character is widespread and has particular consequences.
