“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

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

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Hans Freudenthal 27

Dutch mathematician 1905–1990

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“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

“Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.”

Rudolf Carnap (1891–1970) German philosopher

Rudolf Carnap (1937) cited in: Irving J. Lee (1967) The Language of Wisdom and Folly: Background Readings in Semantics. International Society for General Semantics, p. 44

“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

“Not only the tools of manual labour, but also the tools of human thought — words — are subject to the laws of historical development. The history of the meanings of words is outside the area of interest of formal logic, and could not be fruitfully studied by the methods of that discipline.
The history of language in what is its most essential content is the history of language as a social instrument of thought; it is historical epistemology which cannot be studied within the scope of any other discipline.
The linguist is of necessity only marginally interested in all conventional terminology, whereas certain votaries of formal logic are inclined to investigate domains which are alien to linguistics and even to some extent in contradiction to its basic assumptions!”

Witold Doroszewski (1899–1976) Lexicographer and linguist

As cited in Schaff (1962;7).
"Comments on Semantics", 1952

“Formal logic and the logical syllogism encapsulate connectedness in reasoning.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

1980s, Laws of Media: The New Science (with Eric McLuhan) (1988)

“Logic aims to instruct the human mind as to its own nature and processes; it will lay bare the interior working of our mind for our guidance. The object of the study of logic is thought, its nature, and its proper classification.”

Joseph Dietzgen (1828–1888) german philosopher

Letter 2
Letters on Logic: Especially Democratic-Proletarian Logic (1906)

“Even though principles of rationality seem as often violated as followed, we still cling to the notion that human thought should be rational, logical, and orderly. Much of law is based upon the concept of rational thought and behavior. Much of economic theory is based upon the model of the rational human who attempts to optimize personal benefit, utility, or comfort. Many scientists who study artificial intelligence use the mathematics of formal logic—the predicate calculus—as their major tool to simulate thought. […] Human thought is not like logic; it is fundamentally different in kind and spirit. The difference is neither worse nor better. But it is the difference that leads to creative discovery and to great robustness of behavior.”

Donald A. Norman book The Design of Everyday Things

Source: The Design of Everyday Things (1988, 2002), Ch. 5, pp. 114–115.

“People can be fooled into thinking of mathematics as logical, formal, symbolic reasoning. But this is far from reality...computers are far better at formal computation and formal reasoning, but humans are far better mathematicians.”

William Thurston (1946–2012) mathematician

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“I am inclined to doubt that anything very resembling formal logic could be a good model for human reasoning.”

Marvin Minsky (1927–2016) American cognitive scientist

Jokes and their Relation to the Cognitive Unconscious (1980)
Context: I am inclined to doubt that anything very resembling formal logic could be a good model for human reasoning. In particular, I doubt that any logic that prohibits self-reference can be adequate for psychology: no mind can have enough power — without the power to think about Thinking itself. Without Self-Reference it would seem immeasurably harder to achieve Self-Consciousness — which, so far as I can see, requires at least some capacity to reflect on what it does. If Russell shattered our hopes for making a completely reliable version of commonsense reasoning, still we can try to find the islands of "local consistency," in which naive reasoning remains correct.

“Whenever logical processes of thought are employed — that is, whenever thought for a time runs along an accepted groove — there is an opportunity for the machine. Formal logic used to be a keen instrument in the hands of the teacher in his trying of students' souls. It is readily possible to construct a machine which will manipulate premises in accordance with formal logic, simply by the clever use of relay circuits. Put a set of premises into such a device and turn the crank, and it will readily pass out conclusion after conclusion, all in accordance with logical law, and with no more slips than would be expected of a keyboard adding machine.”

Vannevar Bush book As We May Think

As We May Think (1945)

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Hans Freudenthal 27

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