“Dialectical logic undoes the abstractions of formal logic and of transcendental philosophy, but it also denies the concreteness of immediate experience. To the extent to which this experience comes to rest with the things as they appear and happen to be, it is a limited and even false experience. It attains its truth if it has freed itself from the deceptive objectivity which conceals the factors behind the facts — that is, if it understands its world as a historical universe, in which the established facts are the work of the historical practice of man.”

— Herbert Marcuse , book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 141

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Herbert Marcuse 105

German philosopher, sociologist, and political theorist 1898–1979

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“The contemporary mathematical and symbolic logic is certainly very different from its classical predecessor, but they share the radical opposition to dialectical logic. In terms of this opposition, the old and the new formal logic express the same mode of thought. it is purged from that “negative” which loomed so large at the origins of logic and of philosophic thought — the experience of the denying, deceptive, falsifying power of the established reality. And with the elimination of this experience, the conceptual effort to sustain the tension between “is” and “ought”, and to subvert the established universe of discourse in the name of its own truth is likewise eliminated from all thought which is to be objective, exact, and scientific. For the scientific subversion of the immediate experience which establishes the truth of science as against that of immediate experience does not develop the concepts which carry in themselves the protest and the refusal. The new scientific truth which they oppose to the accepted one does not contain in itself the judgment that condemns the established reality. … In contrast, dialectical thought is and remains unscientific to the extent to which it is such judgment.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), pp. 139-140

“Dialectical thought understands the critical tension between “is” and “ought” first as an ontological condition, pertaining to the structure of Being itself. However, the recognition of this state of Being — its theory — intends from the beginning a concrete practice. Seen in the light of a truth which appears in them falsified or denied, the given facts themselves appear false and negative.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 133

“Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development…. Philosophy of mathematics… has its paradoxes and antimonies, and also diverse schools of thought…”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Variant, from Preface to Max Planck's Where is Science Going? (1933): The supreme task of the physicist is the discovery of the most general elementary laws from which the world-picture can be deduced logically. But there is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance, and this Einfühlung [literally, empathy or 'feeling one's way in']' is developed by experience.
1910s, Principles of Research (1918)
Context: The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest.