"At root what is needed for scientific inquiry is just receptivity to data, skill in reasoning, and yearning for truth. Admittedly, ingenuity can help too." (Willard v O Quine, "The Web of Belief", 1970)
"All advances of scientific understanding, at every level, begin with a speculative adventure, an imaginative preconception of what might be true.[...] [This] conjecture is then exposed to criticism to find out whether or not that imagined world is anything like the real one. Scientific reasoning is, therefore, at all levels an interaction between two episodes of thought - a dialogue between two voices, the one imaginative and the other critical [...]" (Sir Peter B Medawar, "The Hope of Progress", 1972)
"Confidence in the omnicompetence of statistical reasoning grows by what it feeds on." (Harry Hopkins, "The Numbers Game: The Bland Totalitarianism", 1973)
"Heuristic reasoning is good in itself. What is bad is to mix up heuristic reasoning with rigorous proof. What is worse is to sell heuristic reasoning for rigorous proof." (George Pólya, "How to Solve It", 1973)
"When we can’t prove our point through the use of sound reasoning, we fall back upon statistical ‘mumbo jumbo’ to confuse and demoralize our opponents." (Audrey Haber & Richard P Runyon, "General Statistics", 1973)
"All perceiving is also thinking, all reasoning is also intuition, all observation is also invention." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974)
"Demonstrative reasoning differs from plausible reasoning just as the fact differs from the supposition, just as actual existence differs from the possibility of existence. Demonstrative reasoning is reliable, incontrovertible and final. Plausible reasoning is conditional, arguable and oft-times risky." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"Every science is permeated with proofs, and to the same extent as mathematics, for demonstrative reasoning is an integral part of mathematics." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"In mathematics the problem of the essence of proof has been thoroughly worked out and every mathematician must master the methods of demonstrative reasoning. Appropriate rules have been established for this purpose. These rules and the concepts of rigour and exactitude of reasoning vary from century to century, and at the present time every mathematician knows the level of rigour of modern mathematics." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"In plausible reasoning, one must distinguish a reasonable conjecture from a less reasonable conjecture and be able to substantiate the conjecture with the available facts, to find these facts, to search painstakingly for facts that contradict the conjecture, and to correlate the findings and again return to plausible arguments." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"In reasoning, as in every other activity, it is, of course, easy to fall into error. In order to reduce this risk, at least to some extent, it is useful to support intuition with suitable superstructures: in this case, the superstructure is logic" (or, to be precise, the logic of certainty)." (Bruno de Finetti, "Theory of Probability", 1974)
"Mathematical knowledge is fixed securely by means of demonstrative reasoning, but the approaches to such knowledge are strewn with plausible modes of reasoning." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"Mathematics is the sole avenue for learning how to reason via proof. On the other hand, one must also learn how to conjecture.[…] In a rigorous case of demonstrative reasoning, the main thing is to be able to distinguish proof from conjecture, justified proof from an unjustified attempt." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"Most people imagine mathematics to be a deductive science in which all theorems, results and facts are obtained via logical reasoning by proceeding from certain starting axioms, primal assertions, assumed to be self-evident or not requiring any proof." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"[Fuzzy logic is] a logic whose distinguishing features are (1) 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, etc.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact." (Lotfi A Zadeh, "Fuzzy logic and approximate reasoning", 1975)
"I find it more difficult, but also much more fun, to get the right answer by indirect reasoning and before all the evidence is in. It’s what a theoretician does in science. But the conclusions drawn in this way are obviously more risky than those drawn by direct measurement, and most scientists withhold judgment until there is more direct evidence available. The principal function of such detective work - apart from entertaining the theoretician - is probably to so annoy and enrage the observationalists that they are forced, in a fury of disbelief, to perform the critical measurements." (Carl Sagan, "The Cosmic Connection: An Extraterrestrial Perspective", 1975)
"What science and the quest for knowledge are after is irrefutable truth; that is, propositions that human beings are not free to reject — that are compelling. They are of two kinds, as we have known since Leibnitz: truths of reasoning and truths of fact." (Hannah Arendt, The New Yorker, 1977)
"[…] the use of analogies, particularly with metaphor, adds richness and dimension to arguments and descriptions not possible with ordinary discourse or with propositional reasoning." (Jeanette M Gallagher,"The Future of Formal Thought Research: The Study of Analogy and Metaphor", 1978)
"All mathematical problems are solved by reasoning within a deductive system in which basic laws of logic are embedded." (Martin Gardner, "Aha! Insight", 1978)
"Many people believe that reasoning, and therefore science, is a different activity from imagining. But this is a fallacy […] Reasoning is constructed with movable images just as certainly as poetry is." (Jacob Bronowski, "Visionary Eye", 1978)
"Mathematical Reasoning is not only exact; it has its own criteria of reality." (Paul K Feyerabend,"Science in a Free Society", 1978)
"Reasoning is constructed with movable images just as certainly as poetry is." (Jacob Bronowski, "Visionary Eye", 1978)
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