"Mathematical induction […] is an entirely different procedure. Although it, too, leaps from the knowledge of particular cases to knowledge about an infinite sequence of cases, the leap is purely deductive. It is as certain as any proof in mathematics, and an indispensable tool in almost every branch of mathematics." (Martin Gardner, "Aha! Insight", 1978)
"The word ‘induction’ has two essentially different meanings. Scientific induction is a process by which scientists make observations of particular cases, such as noticing that some crows are black, then leap to the universal conclusion that all crows are black. The conclusion is never certain. There is always the possibility that at least one unobserved crow is not black." (Martin Gardner, "Aha! Insight", 1978)
"Science, since people must do it, is a socially embedded activity. It progresses by hunch, vision, and intuition. Much of its change through time does not record a closer approach to absolute truth, but the alteration of cultural contexts that influence it so strongly. Facts are not pure and unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural." (Stephen J Gould, "The Mismeasure of Man", 1980)
"All great theories are expansive, and all notions so rich in scope and implication are underpinned by visions about the nature of things. You may call these visions ‘philosophy’, or ‘metaphor’, or ‘organizing principle’, but one thing they are surely not - they are not simple inductions from observed facts of the natural world." (Stephen J Gould, "Time’s Arrow, Time’s Cycle", 1987)
"Nature is not ‘given’ to us - our minds are never virgin in front of reality. Whatever we say we see or observe is biased by what we already know, think, believe, or wish to see. Some of these thoughts, beliefs and knowledge can function as an obstacle to our understanding of the phenomena. […] mathematics is not a natural science. It is not about the phenomena of the real world, it is not about observation and induction. Mathematical induction is not a method for making generalizations." (Anna Sierpinska, "Understanding in Mathematics", 1994)
"Model building is the art of selecting those aspects of a process that are relevant to the question being asked. As with any art, this selection is guided by taste, elegance, and metaphor; it is a matter of induction, rather than deduction. High science depends on this art." (John H Holland," Hidden Order: How Adaptation Builds Complexity", 1995)
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