“Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.”

— Albert Einstein

1930s, Obituary for Emmy Noether (1935)

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German-born physicist and founder of the theory of relativi… 1879–1955

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“Pure mathematics is in its way the poetry of logical ideas.”

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

1930s, Obituary for Emmy Noether (1935)
Context: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

“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

“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

“Common Logic is the Grammar of the higher Speech, that is, of Thought; it examines merely the relations of ideas to one another, the Mechanics of Thought, the pure Physiology of ideas. Now logical ideas stand related to one another, like words without thoughts. Logic occupies itself with the mere dead Body of the Science of Thinking.”

Novalis (1772–1801) German poet and writer

Metaphysics, again, is the Dynamics of Thought; treats of the primary Powers of Thought; occupies itself with the mere Soul of the Science of Thinking. Metaphysical ideas stand related to one another, like thoughts without words. Men often wondered at the stubborn Incompletibility of these two Sciences; each followed its own business by itself; there was a want everywhere, nothing would suit rightly with either. From the very first, attempts were made to unite them, as everything about them indicated relationship; but every attempt failed; the one or the other Science still suffered in these attempts, and lost its essential character. We had to abide by metaphysical Logic, and logical Metaphysic, but neither of them was as it should be.
Pupils at Sais (1799)

“So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Source: 1910s, Introduction to Mathematical Philosophy (1919), Ch. 18: Mathematics and Logic

“It remains to mention some of the ways in which people have spoken misleadingly of logical form. One of the commonest of these is to talk of ' the logical form' of a statement; as if a statement could never have more than one kind of formal power; as if statements could, in respect of their formal powers, be grouped in mutually exclusive classes, like animals at a zoo in respect of their species. But to say that a statement is of some one logical form is simply to point to a certain general class of, e. g., valid inferences, in which the statement can play a certain role. It is not to exclude the possibility of there being other general classes of valid inferences in which the statement can play a certain role.”

P. F. Strawson (1919–2006) British philosopher

Source: Introduction to Logical Theory (1952), p. 53 as cited in: Ian Hacking (1975) Why Does Language Matter to Philosophy?, p. 83.

“The plain fact is that many of the reputations which today occupy the poetic limelight are such as would crumble immediately if poetry such as Empson's, with its passion, logic, and formal beauty, were to become widely known.”

William Empson (1906–1984) English literary critic and poet

John Wain "Ambiguous Gifts", in The Penguin New Writing no. 40 (1950); cited from John Lehmann and Roy Fuller (eds.) The Penguin New Writing 1940-1950: An Anthology (Harmondsworth: Penguin, 1985) p. 492.
Criticism

“Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.”

Albert Einstein book The Evolution of Physics

The Evolution of Physics (1938) (co-written with Leopold Infeld)
1930s

“There is a logic of language and a logic of mathematics.”

Thomas Merton (1915–1968) Priest and author

The Secular Journal of Thomas Merton (1959)
Context: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

“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)

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