Leon Chwistek - Sound Reason vs. Anti-Rationalism and Thoughts on Logics and Mathematics. And Marxism-Leninism -

Sound Reason vs. Anti-Rationalism

"The history of the spiritual culture of mankind may be reduced to the struggle between faith in the creative power of exact thinking on the one hand, and doubt and powerless self-humiliation in the face of the irresponsible aberrations of fanatics who never attempt to solve any concrete problem and relinquish the pleasure of overcoming real difficulties on the other hands. This struggle has been carried on for centuries with varying fortune. But at present we have entered into a period of incredible abasament of science, a period of the noisy superiority of groups of puffed-up eulogist of irrational nonsense, who are leading mankind toward open crime and violence - as a rule unknowingly but often quite consciously".

(The Limits of Science. Outline of Logic and of the Methodology of the Exacts Sciences (translated by H. C. Brodie and A. P. Coleman) [1935], Routledge and Kegan Paul, London 1949 [2ª ed.], p. 1).

"Hegel was undoubtedly the creator of contemporary anti-rationalism. His doctrine resulted from misunderstandings which were caused by a superficial knowledge of Kant's philosophy and a completely erroneous conception of mathematical analysis [...] I think that the fundamental duty of the representative of true science is to combat this doctrine".

(Ib., pp. 12-3).

"The fact that recently a nation with a great cultural tradition [the nazi Germany] has been mastered by brutal, ignorant individual shows only that this nation was permeated by an irrational metaphysics. History teaches that ultimately victory has always been the destiny of societies who employ the principle of exact reasoning. Exact analysis depraves only weak and inept individuals who find it too difficult for them. It should not be feared by young and healthy societies. They will always find sufficient strenght to act upon thoughts which were obtained over a period of years by means of exact analysis and to work out a well rounded fruitful life on the basis of these thoughts"

(Ib., p. 23).

"The conclusions obtained by means of sound reason must be distinguished from the popular view of the world. The popular view of the world is called 'common sense'; [...] [it] is a definite metaphysical system whose principle cannot be precisely formulated but which work quite successfully through the operations of habits."

(Id., p. 24)

"Positivism is the apotheosis of sound reason. It involves the complete rejection of metaphysics and of irrational dialectic. Its proponents were the first to attempt to formulate the aims of science and of social life in conformity with the principles of sound reason"

(Id., p. 45).

"The criteria of sound reason must be employed to unmask invalid arguments arising from a desire for absolute truth. It should be added that this desire frequently springs from the inadequacy of the little knowledge the individual does have. In brief he knows nothing, since it is impossible to know absolute truth and its not worth while to know relative truth. The system of metascience is necessary to strengthen sound reason precisely at those points where its criteria cease to operate directly. Sound reason is not sufficiently courageous and does not differ from common sense sufficiently to pursue its own course against authority, idealistic logic, and public opinion. In this struggle sound reason requires the aid of an external logical apparatus which althought it is its own product, functions independently of its whims."

(Ib., p. 288)

"The construction of new systems of thought, new criteria of beauty, and new forms of life is the essence of progress in science, art, and life. Creative power is not the result of slow evolution. There has been non continuous transition from the wings of Daedalus to areoplans. The discovery of radium and Roentgen rays and the invention of radio were as sudden and unexpected events as revolutions. Beginning with Byzantine and Gothic art and ending in the impressionistic art of the present day, the development of art has been characterized by a series of revolutions. Life on earth has developed in a similar fashion. It is a well known fact that the path of progress is marked by pools of blood and unconditional revolutions. Everything which has been brought about through evolution might have been accomplished elsewhere and much earlier through revolution, but in any case it would inevitably have been accomplished. This important truth was discovered by Karl Marx, the creator of the theory of historical materialism. Comte's successors disregarded this discovery. Althought the adherents of positivism were very great thinkers, they have had no significant influence upon the history of culture in recent times".

(Id., p. 45).

"The reduction of arithmetic and geometry to the principles of formal logic, which was attained by Wittgenstein and Russell at the beginnings of the century, was the crucial moment in the attempt to fix the boundary of the exact sciences. If the attempt to construct a great system of logic from which all the apriori sciences could be derived were successuful, completely new perspectives would be opened up to science and an adeguate base for a critical and a rationalistic method would be attained. A system of logic which permits mathematical theorems to be proved without the aid of the intuition of the creative individual by mechanical operations, which can be performed by one who can understand ordinary arythmetic was sought. The attainment of this ideal would have been so a great triumph for science that in comparison with it the attempt of the irrationalists would seem like child's play. It was to be expected that the representative of radical criticism would have accepted the work of Whitehead and Russell with enthusiasm. However, the exact opposite actually occurred.

"Cantor's theory is an apparent triumph of idealism [...]. [...] a consideration of Cantor's genius shows that it was inseparably connected with a firm belief in the world of ideal objects and almost a mystical religiosity. [...] However, it must be understood that the value of all thoughts which have ever been produced depends upon some mysterious profundity, and their metaphysical character, if any, does not affect their scientific value. What Cantor directly associated with the actual infinite was his personal survival, which has nothing in common with the fruitfulness of his ideas. The greatness of his doctrine has nothing in common with the mysterious allure of the infinite. It lies in the fact that certain operations can be performed with the help of signs which have been defined. However, it must be kept in mind that if Cantor had confined himself to performing these operations and if the fires of a mystical yearning for infinity had not burned in his soul, he would never have discovered the simple laws which he left mankind as a permanent acquisition (aere perennius). However, it must be confessed that Cantor's metaphysics became the source of tragic errors which decided its fate".

"[...] The discovery of the paradoxes which follow from Cantor's theory of aggregates [...] [was] involved in the foundations of the new logic. Russell succeeded in removing these paradoxes by means of his famous theory of logical types but he was able to do so only by introducing certain metaphysical suppositions which a critical mind could not accept. In the first place it was necessary to presuppose the existence of individuals which could not be further characterized. The existence of these individuals was an integral part of system but no example of them could be given. In other words the domain of logic became an abstract world similar to the platonic world. The primitive concepts of logic became platonic ideas because they had to be explicitly distinguished from the signs by which they were introduced. Finally it was necessary to accept an additional hypothesis which assured the existence of infinitely many individuals. Otherwise finitism could not be avoided. On the other hand, if this hypothesis were accepted the existence of objects not definable in terms of the concepts of the system would have to be accepted. In short it must admitted that the system of Whitehead and Russell is such that either it does not contain the class of natural numbers or it contains a class of real numbers which contains as a sub-class numbers not definable in terms of the concept of the system. The latter consequence, which at the same time leads to the affirmation of the existence of the actual infinte, evoked a particularly veement reaction on the part of Poincaré. Poincaré was a decided nominalist and could not become reconcilied to the existence of indefinable objects, much less to the existence of infinite classe of such objects"

"Further investigations showed that the metaphysical suppositions of the system of Whitehead and Russell can be eliminated by basing the construction of a consistent system of logic upon a pure theory of types and upon the science of expressions, formulated symbolically, which I have called semantics. In other words the additional suppositions made by Whitehead and Russell are unnecessary. Thus a new system of logic which satisfies the nominalistic postulate of Poincaré and which is compatible with the spirit of critical rationalism was developed. In spite of the extensive restrictions of this system it is no poorer than the system of mathematics which is based upon the axioms of Zermelo. Consequently it is adequate to develop all the material which is desired by most mathematician. When this new system is completely worked out, we will be able to say, that we have at our disposal an infallible apparatus which sets off exact thought from other forms of thought. The old dream of the logicians concerning a consistent logical apparatus will no longer be a mirage."

(Ib., p. 22)

Marxism-Leninism

"Hegel's dialectic was not necessary to see the inconsistency of a social structure which was characterized by the oppression of the poor classes by the ruling class. The Aristotelian principle of consistency and cultivation of the emotions, based upon the doctrine of Christ, was quite sufficient for this purpose. That Karl Marx, the great defender of the wronged, was a disciple of Hegel and appealed to Hegel's dialectic was the result of a fortuitous concurrence of circumstances. Hegel's dialectic was a minor influence in the works of Marx and did more harm than good because it produced the illusion that Marx was concerned with the self-contradictory idea. Actually Marx was concerned only with the distress of the working class and with the creation of a view of the world which would remove this distress. The dialectic of Marx does not differ essentially from the constructive methods of the exact sciences. Marx did not write on the 'love thy neightbour' principle only because even at that time this principle was an outworn requisite, which could not restrain bestialized business men".
(The Limits of Science. Outline of Logic and of the Methodology of the Exacts Sciences (translated by H. C. Brodie and A. P. Coleman) [1935], Routledge and Kegan Paul, London 1949 [2ª ed.], pp. 11).

"Because of the historical connection between dialectical materialism and Hegel's anti-rationalistic dialectic and because the very name dialectical materialism has many anti-rational associations, this doctrine is generally regarded with a certain prejudice. Actually, as has already been emphasized, it is not only the negation of anti-rationalism but it is a doctrine which is based upon the principles of sound reason entirely. Its strength is its complete opposition to idealistic metaphysics and its introduction of the constructive method into sociology".
(Ib., pp. 47-8).

"The fundamental thesis of Marxism is mutability. According to Engels it depends upon the conception of the world as a process, i. e. as something which continually develops. This thesis must be accepted to-day by all philosophers because it is based upon unquestionable natural and historical facts. If it were desired that this thesis be rejected, troblesome contradictions would result or at best artificial subterfuges would have to be empoloyed. Such would likewise be the case if the second fundamental thesis of marxism, namely the close dependence of intellectual life upon physiological processe, were rejected. [...]. Thus the estabishment of these theses is based only upon the results of investigations in the exact sciences and there is no need to employ special methods of reasoning to establish them. It suffice to keep in mind that the realm of applicability of concepts is always restricted".
(Ib., p. 49).