
Source: The mechanization of the world picture, 1961, p. 499
Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 11
Source: The mechanization of the world picture, 1961, p. 499
As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128
“Mathematics is not just a language. Mathematics is a language plus reasoning.”
Source: The Character of Physical Law (1965), chapter 2, “The Relation of Mathematics to Physics”
Context: Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.
At a Yale faculty meeting, during a discussion of language requirements in the undergraduate curriculum. Quoted in Muriel Rukeyser, Willard Gibbs (Garden City, NY: Doubleday, Doran & Co., 1942), p. 280.
Attributed
Mathematics is a way of preparing for decisions through thinking. Sets and classes provide one way to subdivide a problem for decision preparation; a set derives its meaning from decision making, and not vice versa.
C. West Churchman, Leonard Auerbach, Simcha Sadan, Thinking for Decisions: Deductive Quantitative Methods (1975) Preface.
1960s - 1970s
Source: Our Modern Idol: Mathematical Science (1984), p. 95.
Acceptance speech, Alumni Achievement Award, Collinsville, Illinois. 2017.
“There is a logic of language and a logic of mathematics.”
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.