Fractals : Form, chance and dimension (1977)
Source: The mechanization of the world picture, 1961, p. 499
Source: Linear programming and extensions (1963), p. 2
Source: The Monkey Grammarian (1974), Ch. 4
Ch. 4 -->
Context: Fixity is always momentary. But how can it always be so? If it were, it would not be momentary — or would not be fixity. What did I mean by that phrase? I probably had in mind the opposition between motion and motionlessness, an opposition that the adverb always designates as continual and universal: it embraces all of time and applies to every circumstance. My phrase tends to dissolve this opposition and hence represents a sly violation of the principle of identity. I say “sly” because I chose the word momentary as an adjectival qualifier of fixity in order to tone down the violence of the contrast between movement and motionlessness. A little rhetorical trick intended to give an air of plausibility to my violation of the rules of logic. The relations between rhetoric and ethics are disturbing: the ease with which language can be twisted is worrisome, and the fact that our minds accept these perverse games so docilely is no less cause for concern. We ought to subject language to a diet of bread and water if we wish to keep it from being corrupted and from corrupting us. (The trouble is that a-diet-of-bread-and-water is a figurative expression, as is the-corruption-of-language-and-its-contagions.) It is necessary to unweave (another metaphor) even the simplest phrases in order to determine what it is that they contain (more figurative expressions) and what they are made of and how (what is language made of? and most important of all, is it already made, or is it something that is perpetually in the making?). Unweave the verbal fabric: reality will appear. (Two metaphors.) Can reality be the reverse of the fabric, the reverse of metaphor — that which is on the other side of language? (Language has no reverse, no opposite faces, no right or wrong side.) Perhaps reality too is a metaphor (of what and/or of whom?). Perhaps things are not things but words: metaphors, words for other things. With whom and of what do word-things speak? (This page is a sack of word-things.) It may be that, like things which speak to themselves in their language of things, language does not speak of things or of the world: it may speak only of itself and to itself.
Source: The Development of Mathematics (1940), p. 9
As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128
Acceptance speech, Alumni Achievement Award, Collinsville, Illinois. 2017.
Source: Math for the Layman (1999), Ch. 10, §D
“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.
