Paul Cohen quote: “The object of mathematics is to discover "true" theorems. We shall use the term "valid" to describe statements formed a…”

“Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

“Because we cannot discover God's throne in the sky with a radiotelescope or establish (for certain) that a beloved father or mother is still about in a more or less corporeal form, people assume that such ideas are "not true."”

C.G. Jung book Man and His Symbols

I would rather say that they are not "true" enough, for these are conceptions of a kind that have accompanied human life from prehistoric times, and that still break through into consciousness at any provocation.
Man and His Symbols (1964)

“We are told … statements that are not mathematical or logical formulae may look as if they were necessarily or certainly true, but they only look like that. They cannot really be either necessary or certain.”

Robert Maynard Hutchins (1899–1977) philosopher and university president

Great Books: The Foundation of a Liberal Education (1954)

“I shall often discuss mathematical discoveries… I shall try to make up a likely story how the discovery could have happened. I shall try to emphasize the motives underlying the discovery, the plausible inferences that led to it… everything that deserves imitation.”

George Pólya (1887–1985) Hungarian mathematician

Induction and Analogy in Mathematics (1954)

“Unlike pure theorists, we shall not assume at the outset that rational behavior exists or that rational behavior constitutes the topic of economic analysis. We shall study economic behavior as we find it. In describing and classifying different reactions, as well as the circumstances that elicit them, we shall raise the question whether and in what sense certain reactions may be called “rational.” After having answered that question and thus defined our terms, we shall study the fundamental problem: Under what conditions do more and under what conditions do less rational forms of behavior occur?”

George Katona (1901–1981) American psychologist

George Katona (1951). Psychological Analysis of Economic Behavior. McGraw-Hill, New York. p. 16; as cited in: Erik Angner and George Loewenstein. "Behavior economics," in: Philosophy of Economics, (2012), p. 657

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

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

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

“[ Fuzzy logic is ] a logic whose distinguishing features are (i) fuzzy truth-values expressed in linguistic terms, e. g., true, very true, more or less true, or somewhat true, false, nor very true and not very false, etc2.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Zadeh (1975) "Fuzzy logic and approximate reasoning". Synthese 30: p. 407
1970s

“The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very fake, etc…. As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very quite.”

George Klir (1932–2016) American computer scientist

Lotfi Asker Zadeh, George Klir, Bo Yuan (1996) Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers. p. 238.

“The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very fake, etc…. As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very quite.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Lotfi Asker Zadeh, George Jiri Klir, Bo Yuan (1996) Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers. p. 238
1990s

“In discussing tradition, we are not discussing arbitrary rules and conventions. We are discussing answers that have been discovered to enduring questions.”

Roger Scruton book How to Be a Conservative

Source: How to Be a Conservative (2014), p. 21

“The object of mathematics is to discover "true" theorems. We shall use the term "valid" to describe statements formed according to certain rules and then shall discuss how this notion compares with the intuitive idea of "true."”

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