“I have tried to make clear in this brief sketch of the nature of deductively formulated theories, at least as they occur in economics, that, although their origin lies in common observation and introspection, nevertheless they are capable of a purely mathematical development through the exact statement of a of a set of postulates which, however, since they must inevitably contain assumptions about human behaviour, require to be tested by reference to actual events.”

Source: The Role of Measurement in Economics. 1951, p. 14-15

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Richard Stone11

British economist, Nobel Memorial Prize winner 1913–1991

Richard Stone (1913–1991) British economist, Nobel Memorial Prize winner

Source: The Role of Measurement in Economics. 1951, p. 12

“All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. vii.

“The theory of games was first formalised by Von Neumann & Morgenstern (1953) in reference to human economic behaviour. Since that time, the theory has undergone extensive development… Sensibly enough, a central assumption of classical game theory is that the players will behave rationally, and according to some criterion of self-interest. Such an assumption would clearly be out of place in an evolutionary context. Instead, the criterion of rationality is replaced by that of population dynamics and stability, and the criterion of self-interest by Darwinian fitness.”

John Maynard Smith book Evolution and the Theory of Games

Source: Evolution and the Theory of Games (1973), p. 1-2.

“It is clear that the building of models is not a purely mechanical process but requires skill of a high order – not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1950s, The Skills of the Economist, 1958, p. 16-17 as cited in Andrew Mearman (2011).

“Most psychologists agree at least some of our analytical ability is innate; however, most also agree common sense is not innate but derived from learned experiences; since common sense which I refer to as reasoned judgment requires analysis, then reasoned judgment must be partly innate.”

Gandolfo – (RJ Intindola)

2002

“When the theory performs well you also think, “Are there parallel results in naturally occurring field data?” You look for coherence across different data sets because theories are not specific to particular data sources. Such extensions are important because theories often make specific assumptions about information and institutions which can be controlled in the laboratory, but which may not accurately represent field data generating situations. Testing theories on the domain of their assumptions is sterile unless it is part of a research program concerned with extending the domain of applications of theory to field environments”

Vernon L. Smith (1927) American economist

Source: "Theory, experiment and economics," 1989, p. 151.

“It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

“What makes a piece of mathematical economics not only mathematics but also economics is, I believe, this: When we set up a system of theoretical relationships and use economic names for the otherwise purely theoretical variables involved, we have in mind some actual experiment, or some design of an experiment, which we could at least imagine arranging, in order to measure those quantities in real economic life that we think might obey the laws imposed on their theoretical namesakes.”

Trygve Haavelmo (1911–1999) Norwegian economist and econometrician

Trygve Haavelmo, "The probability approach in econometrics" in: Supplement to Econometrica. 12 91944), p. 5; Cited in Pearl (2012, 1-2)

“Every process which arises from our physical being and is related to it, is an event which lies outside of our volition. Every social process, however, arises from human intentions and human goal setting and occurs within the limits of our volition.”

Rudolf Rocker book Nationalism and Culture

Source: Nationalism and Culture (1937), Ch. 1 "The Insufficiency of Economic Materialism"
Context: Every process which arises from our physical being and is related to it, is an event which lies outside of our volition. Every social process, however, arises from human intentions and human goal setting and occurs within the limits of our volition. Consequently, it is not subject to the concept of natural necessity. … We are here stating no prejudiced opinion, but merely an established fact. Every result of human purposiveness is of indisputable importance for man's social existence, but we should stop regarding social processes as deterministic manifestations of a necessary course of events. Such a view can only lead to the most erroneous conclusions and contribute to a fatal confusion in our understanding of historical events.
It is doubtless the task of the historian to trace the inner connection of historical events and to make clear their causes and effects, but he must not forget that these connections are of a sort quite different from those of natural physical events and must therefore have quite a different valuation.

“Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.”

Joshua Girling Fitch (1824–1903) British educationalist

The Fourth Dimension simply Explained. (New York, 1910), p. 58. Reported in Moritz (1914); Also cited in: Howard Eves (2012), Foundations and Fundamental Concepts of Mathematics, p. 167

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