Philosophy and Ideology. Z. A. Jordan 1963
One of the fundamental and perhaps one of the most important principles of Marxist-Leninist philosophy is the assumption that internal contradictions are inherent in all things and in all phenomena of Nature. ‘In its proper meaning’, wrote Lenin, ‘dialectics is the study of the contradictions within the very essence of things’ . The formulation and the context make it clear beyond any possible doubt that for Lenin there was nothing phenomenal (in the Kantian sense) about the contradictions; they are inherent in the Ding an sich.
From the historical viewpoint it would be untrue to say that any science, including mathematics and formal logic, is invariably free from contradiction. Consistency is not an inalienable privilege providentially granted to science; paradoxes, antinomies, and contradictions do appear in the advancement of knowledge. The history of the infinitesimal calculus, the theory of sets and of classes, or the development of semantical concepts testify to the fact that contradictions did occur in the past and continue to appear in the present. It is accepted, however, that the appearance of contradictions is a symptom of the imperfection of our knowledge and that they must be resolved if the distinction between truth and falsehood is to retain its meaning. It is also a matter of historical record that the resolution of contradictions results from or is followed by the expansion of scientific knowledge. For both these reasons, consistency is one of the supreme goals pursued by every science.
If we are to believe Lenin, this goal can never be achieved, nor is it worth striving for. Knowledge and contradiction are not mutually exclusive, but mutually inclusive. This truth is revealed by dialectics which ‘is the theory of how opposites can be and commonly are identical, how they become and under what conditions they remain identical, when transforming from one to the other’s.
A dialectical contradiction is defined either in terms of the so-called unity and struggle of the opposites or in terms of logic. We are told that as long as we consider things as static and lifeless, we do not run up against any contradictions in them. The ‘position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradiction’ . A body in motion does and does not occupy a given position, a changing object is and is not such and such at the same time. Change and motion are a contradiction, the principle
(x, φ) ∼ (φx . ∼ φx)
does not apply to them Consequently, it is not true to say that contradictory statements are never true together. If X is the class of changing or moving bodies, then
(x, φ)(∃ψ): φx . ∼ . ψx. ∼ ψx.
Since it is ‘possible to assert and deny the same’, we obtain the dialectical metalogical principle of contradiction
T ‘φx’' . T ‘∼ φx’ .
For the same reason
(x, φ) (∃ψ): φx . ⊃ . ∼ (ψx∼∼ ψx),
from which follows the dialectical metalogical principle of the non-excluded middle
∼ (T ‘φx’ ∼ T ‘∼φx’).
Finally, the principle of identity is no longer valid. With respect to moving and changing bodies ‘abstract identity is totally inadequate’ and must be replaced by the dialectical ‘inclusion of difference within identity’, the ‘inseparability of identity and difference’, the unity or identity of the opposites.
Thus, Marxist-Leninist philosophy appears to deny or to restrict the validity of formal logic, or at least the validity of some of its laws, as well as of their corresponding semantical formulations. It accepts Hegel’s doctrine who rose above ‘a fundamental prejudice of hitherto existing logic’ and recognised in contradiction the truly essential and profound determination of being.
In this manner Marxist-Leninist philosophy has exposed itself to an easy criticism and to the objection of absurdity. A logically trained philosopher has no use for a system that denies the principle of non-contradiction. Let us assume that two sentences like ?p? and ?∼p? are true together. Then by means of a well known formula of propositional calculus
p. ⊃ . ∼ p ⊃ q
we can by applying the detachment rule twice derive from these contradictory premisses an arbitrary sentence ‘q’, i.e. any sentence whatsoever. The rejection of the principle of non-contradiction results in complete arbitrariness of thought – true and false statements turn out to be equally valid. Moreover, if contradictory statements were true together, and a statement is true if it corresponds to what it asserts and false otherwise, no statement would be true or false and the difference between truth and falsehood would disappear. This, however, would be the end of philosophy, of science, of any rational thinking.
The disclosure that Marxism-Leninism has a logic of its own, in which the principle of non-contradiction is no longer valid, raises the question whether the admissibility of contradictions does not destroy the rational basis of any discussion. With the rejection of the principle of non-contradiction and of the excluded middle no reasoning, no argument, no confrontation of views is in fact possible. We can neither establish our own point, nor disprove that of our opponent, because in this procedure we have to make use of the rejected principles by pointing out the contradictions within the stated opinions or with the accepted premisses or with statements of fact. Contra principia negantem, the schoolmen of the Middle Ages used to say non est disputandum. Notwithstanding their declarations, Engels and Lenin also provided testimony in their writings that they were unable to dispense with the laws of logic.
With the rejection of the principle of non-contradiction Marxist-Leninist philosophy itself would face destruction. A Marxist-Leninist may reject the thesis that consciousness determines being, but he is logically bound to accept it, and for that matter any other statement with which he disagrees or which he specifically denies. He can escape this conclusion only by rejecting logic altogether. If he succeeds in actually achieving it, that is, if he actually disregards every rule of logic in his thinking and not merely says that he does, a Marxist-Leninist would reach mentally the point of no return. Not a philosopher but only a psychiatrist could be of help to him then.
The contention that Marxism-Leninism has a logic of its own, different from that commonly used, cannot be accepted in earnest. A Marxist-Leninist is not indifferent to the contradictions in his own system. He does not consider a contradiction as a valuable addition to his doctrine, but, on the contrary, declares it superior to any other by virtue of its being free from contradictions. The principle of non-contradiction must, after all, possess some merits.
Marxism-Leninism claims that it is a theory as well as a guide to action. In considering Marxist-Leninist solutions of abstract problems the question of what they imply in practice cannot, therefore, be overlooked. Change and motion, Marxism-Leninism contends, involve contradictions. A horse-race, a flood, a war, are certainly instances of change and motion. When a Marxist-Leninist goes to a horse-race does he bet on a horse because he assumes that it will both win and lose the race? Does not a Marxist-Leninist engineer act on the assumption that the flood might carry the bridge away or does he rather believe that the flood will and will not destroy it at the same time? Would not a Marxist-Leninist general be shot if in war he failed to apply the law of non-contradiction to his enemy’s anticipated movements? Can a single example of sound reasoning that rejects this principle be given at all?.
To accept contradictions as a significant and permissible means of describing facts is to frustrate one of the main purposes of speech, expressing thoughts and conveying knowledge. A man who contradicts himself or utters contradictory statements may make audible sounds, but from the point of view of communicating facts it is as if he never opened his mouth. ‘He utters words but does not say anything’ . If, as Marxist-Leninists contend, there is any ‘profundity’ in a conjunction of contradictory statements, in saying something and unsaying it, in combining expressions which cancel each other, this ‘profundity’ must remain forever inexpressible. If it is inexpressible, we can call it ‘profundity’ or by any other term. Without being aware of it, a Marxist-Leninist seems to inhabit a world more strange, more personal and more barred from communication with any other human being than Wittgenstein’s world of the Tractatus LogicoPhilosophicus. The approach to Wittgenstein’s world leads through questions that can be put and answers that can be given. A Marxist-Leninist offers no Wittgensteinean ladder, the inexpressible faces us from the start. In spite of this fact a Marxist-Leninist follows just the opposite course to what No. 7 of the Tractatus enjoins us to.
It is the law of Duns Scotus which is responsible for making a system of state ments, that includes a pair like '?p? and ?∼p? , ‘over-complete’, i.e., co-extensive with the set of all meaningful sentences of this system. There arises, therefore, the question whether a propositional calculus could be constructed which is rich enough to make reasoning possible and which does not permit the inference of an arbitrary statement from two contradictory premisses. This question has been successfully solved by Jaskowski.
Jaskowski’s D2 system, the so-called ‘logic of discussion’, contains many theorem of ordinary logic, is not consistent in the ordinary sense, that is to say, accepts statements of the '?p? and ?∼p? form, and is not ‘absolutely inconsistent’, i.e., cannot be shown to be equivalent to the set of all the meaningful statements. Since the law of Duns Scotus is not a valid theorem of the ‘logic of discussion’, the inference of an arbitrary statement from two contradictory premisses is unjustifiable.
The usefulness of the ‘logic of discussion’ for Marxist-Leninist philosophy is, however, doubtful. An assertion of the ‘logic of discussion’ is a statement which contains terms with an ambiguous meaning and which can thus be asserted in a different sense by various participants in the discussion. Strictly speaking, ?p? and ?∼ p? are not contradictory statements. They do not assert and deny the same or in the same respect. The law of non-contradiction is a theorem of the ‘logic of discussion’. Also the formula
p . ∼ p ⊃ q
holds in it.
It follows, therefore, that if one of the disputants asserts two statements, contradictory in the ordinary sense, to be true together, he is bound to accept any other arbitrary statement and his system becomes again ‘over-complete’. The ‘logic of discussion’ does not allow any disputant to contradict himself, and thus it cannot grant what the dialectical law of contradiction seems to demand.
A Marxist-Leninist would not gain anything from the acceptance of the ‘logic of discussion’, unless he changed the meaning of what he calls ‘contradiction’.
The philosophical purpose behind the ‘logic of discussion’ differs from that by which Marxism-Leninism is inspired. The recent developments in logic, such as Gödel’s incompleteness theorem, the discovery of antinomial risks inherent in any semantically closed language, various antinomies and elaborate techniques intended to deal with them, impose considerable restrictions on the language and theoretical constructions. These restrictions are associated with formally complicated procedures and the abandonment of more ambitious schemes. They result in a more careful treatment of concepts, a more precise use of language, the ruling out of some word combinations from the domain of meaningful sentences. The advantages gained by these developments are as conspicuous as their disadvantages. Among the latter one of the most far-reaching is the tendency, as Professor Ryle put it, to become ‘excessively microscopic’, to ‘stick too closely to the grindstone and go too little out into the wood’ . The possibility of formulating a comprehensive view of the world, construction of which requires a rich language and a high degree of freedom in using different logical procedures, moves further and further away. Jaskowski wished to remedy this position and his ‘weaker’ logical system goes a little way in this direction. While contradictions sensu stricto are as much inadmissible in Jas + 0304kowski’s ‘weaker’ logic as in any other logical system, it does not exclude every kind of ‘contradictory statements’ and provides a guarantee against inferences that would involve us in asserting falsehood.
Unlike the ‘logic of discussion’ which was meant to be a particular subsidiary instrument of dealing with paradoxes and antinomies, Marxism-Leninism does not shun them. It accepts them as its starting point and considers them as an important part of knowledge of the external world to be incorporated in a comprehensive view of the world. If contradictions are inherent in the essence of things and phenomena of Nature, the inconsistencies in our knowledge need not necessarily be regarded as a falsehood.
The burden of this truth-destroying view, stubbornly defended for a few years, turned out to be too heavy for Marxist-Leninists in Poland. Faced by logicians and philosophers for whom no inconsistent theory could be significant, valid and true, Marxist-Leninists were at once driven to the defensive. They could spread and popularise their views among the philosophically uneducated and naive, but those with scientific training could not be really persuaded to accept Marxist-Leninist philosophy as a sound and justifiable system of beliefs. A Marxist-Leninist was tainted with absurdity through the mere enunciation of his fundamental principles.
Consequently, the relation of dialectics to formal logic became the main question at issue between Marxist-Leninist and non-Marxist philosophy. Very early in the day it was recognised by both sides that a satisfactory solution of this problem was a prerequisite of finding a common language in all other matters. Its orthodox solution, the rejection of the principles of non-contradiction and the condemnation of the whole of logic to oblivion, would create an abyss which nothing could bridge.
In this respect Polish Marxist-Leninists remained entirely isolated, unaided by anybody outside their own small circle of believers. Also those logicians who were not unsympathetic to some Marxist-Leninist opinions concerning the theory of logic, were clearly not on the side of Marxist-Leninism in so far as its views on the principle of non-contradiction and, in general, its attitude to formal logic were concerned. All ‘over-complete’ systems, wrote Greniewski, in agreement with every self-respecting logician, are equally useless and valueless.