“In [Aristotle’s] formal logic, thought is organized in a manner very different from that of the Platonic dialogue. In this formal logic, thought is indifferent toward its objects. Whether they are mental or physical, whether they pertain to society or to nature, they become subject to the same general laws of organization, calculation, and conclusion — but they do so as fungible signs or symbols, in abstraction from their particular “substance.” This general quality (quantitative quality) is the precondition of law and order — in logic as well as in society — the price of universal control.”

— Herbert Marcuse , book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 136

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Herbert Marcuse 105

German philosopher, sociologist, and political theorist 1898–1979

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“By virtue of the universal concept, thought attains mastery over the particular cases. However, the most formalized universe of logic still refers to the most general structure of the given, experienced world; the pure form is still that of the content which it formalizes. The idea of formal logic itself is a historical event in the development of the mental and physical instruments for universal control and calculability. In this undertaking man had to create theoretical harmony out of actual discord, to purge thought from contradictions, to hypostatize identifiable and fungible units in the complex process of society and nature. Under the rule of formal logic, the notion of the conflict between essence and appearance is expendable if not meaningless; the material content is neutralized; the principle of identity is separated from the principle of contradiction (contradictions are the fault of incorrect thinking); final causes are removed from the logical order. Well defined in their scope and function, concepts become instruments of prediction and control. Formal logic is thus the first step on the long road to scientific thought”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 137

“The methods of logical procedure are very different in ancient and modem logic, but behind all difference is the construction of a universally valid order of thought, neutral with respect to material content. Long before technological man and technological nature emerged as the objects of rational control and calculation, the mind was made susceptible to abstract generalization. Terms which could be organized into a coherent logical system, free from contradiction or with manageable contradiction, were separated from those which could not. Distinction was made between the universal, calculable, “objective” and the particular, incalculable, subjective dimension of thought.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), pp. 137-138

“The subject of a science is never well circumscribed and there is little use sharpening its definition. However, nobody will deny that physics deals with nature and sociology with human society in some of their aspects. With logic, it is another matter. Logic is usually understood nowadays as a study of certain formal systems, though in former times there were philosophers who held that the subject matter of logic was the formal rules of human thought. In the latter sense it would be an empirical rather than a formal science, though its empirical subject matter would still be fundamentally different from that of psychology of thinking. One interpretation of logic does not exclude the other. Formal approaches are often easier than empirical ones, and for this reason one can understand why logic as a study of formal systems has till now made more progress than logic as a study of the formal rules of thought, even if restricted to scientific thought.”

Hans Freudenthal (1905–1990) Dutch mathematician

Source: Realistic models in probability (1968), p. 1

“Such signs are always abstract and general, because habits are general rules to which the organism has become subjected.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

On The Algebra of Logic (1885)
Context: Any character or proposition either concerns one subject, two subjects, or a plurality of subjects. For example, one particle has mass, two particles attract one another, a particle revolves about the line joining two others. A fact concerning two subjects is a dual character or relation; but a relation which is a mere combination of two independent facts concerning the two subjects may be called degenerate, just as two lines are called a degenerate conic. In like manner a plural character or conjoint relation is to be called degenerate if it is a mere compound of dual characters.
A sign is in a conjoint relation to the thing denoted and to the mind. If this triple relation is not of a degenerate species, the sign is related to its object only in consequence of a mental association, and depends upon a habit. Such signs are always abstract and general, because habits are general rules to which the organism has become subjected. They are, for the most part, conventional or arbitrary. They include all general words, the main body of speech, and any mode of conveying a judgment. For the sake of brevity I will call them tokens.