“The function of logic in mathematics is critical rather than constructive.”

— George Frederick James Temple

100 Years of Mathematics: a Personal Viewpoint (1981)

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George Frederick James Temple 21

British mathematician 1901–1992

George Kelly (psychologist) (1905–1967) American psychologist and therapist

Attributed to George A. Kelly in Hinkle (1970, p. 91), as cited in: Fay Fransella and Robert A. Neimeyer. "George Alexander Kelly: The man and his theory." International handbook of personal construct psychology (2003): 21-31.

“The true function of logic … as applied to matters of experience … is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates imagination as to what the world may be, it refuses to legislate as to what the world is.”

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

Source: 1910s, Our Knowledge of the External World (1914), p. 8

“The new art must be based upon science — in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.”

Albrecht Dürer (1471–1528) German painter, printmaker, mathematician, and theorist

As quoted in Dictionary of Scientific Biography (1970 - 1990) edited by M Steck.

“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.