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Science proceeds by inference, rather than by the deduction of mathematical proof. A series of observations is accumulated, forcing the deeper question: What must be true if we are to explain what is observed? What "big picture" of reality offers the best fit to what is actually observed in our experience? American scientist and philosopher Charles S. Peirce used the term "abduction" to refer to the way in which scientists generate theories that might offer the best explanation of things. The method is now more often referred to as "inference to the best explanation." It is now widely agreed to be the philosophy of investigation of the world characteristic of the natural sciences.

Alister E. McGrath
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Science proceeds by inference, rather than by the deduction of mathematical proof. A series of observations is accumulated, forcing the deeper question: What must be true if we are to explain what is observed? What "big picture" of reality offers the best fit to what is actually observed in our experience? American scientist and philosopher Charles S. Peirce used the term "abduction" to refer to the way in which scientists generate theories that might offer the best explanation of things. The method is now more often referred to as "inference to the best explanation." It is now widely agreed to be the philosophy of investigation of the world characteristic of the natural sciences.

Alister E. McGrath
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The word 'proof' should strictly only be used when we are dealing with deductive inferences.... Popper claimed that scientists only need to use deductive inferences.... So if a scientist is only interested in demonstrating that a given theory is false, she may be able to accomplish her goal without the use of inductive inferences.... When a scientist collects experimental data, her aim might be to show that a particular theory...is false. She will have to resort to inductive reasoning.... So Popper's attempt to show that science can get by without induction does not succeed.

Samir Okasha, Philosophy of Science: A Very Short Introduction
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We cannot infer from prosperity that God is pleased with us, nor can we infer from adversity that he is displeased with us.

Wilson Benton
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The dull mind, once arriving at an inference that flatters the desire, is rarely able to retain the impression that the notion from which the inference started was purely problematic.

George Eliot, Silas Marner
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I remember what Old Joe Hun said when arguing with Adrian: that mental states can be inferred from actions. That’s in history—Henry VIII and all that. Whereas in the private life, I think the converse is true: that you can infer past actions from current mental states.

Julian Barnes, The Sense of an Ending
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Remarkably, studies of visual perception have found that two-dimensional images projected onto the retina only achieve full dimensionality as a result of our perception: we infer the third dimension of depth. Sadly, though, as the urgency to expedite all communicative transactions usurps out customary patterns of exchange, perception is accelerated as well. There does not seem to be a great deal of time left over to infer--or interpret, or imagine--much of anything at all. In the end, of course, there is nothing real about this at all, except for our propensity to let it happen.

Jessica Helfand, Screen: Essays on Graphic Design, New Media, and Visual Culture
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The aim of scientific thought, then, is to apply past experience to new circumstances; the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience.

William Kingdon Clifford, Lectures and Essays by the Late William Kingdon Clifford, F.R.S.
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People have a hard time accepting free-market economics for the same reason they have a hard time accepting evolution: it is counterintuitive. Life looks intelligently designed, so our natural inclination is to infer that there must be an intelligent designer--a God. Similarly, the economy looks designed, so our natural inclination is to infer that we need a designer--a government. In fact, emergence and complexity theory explains how the principles of self-organization and emergence cause complex systems to arise from simple systems without a top-down designer.

Michael Shermer
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It remains to mention some of the ways in which people have spoken misleadingly of logical form. One of the commonest of these is to talk of 'the logical form' of a statement; as if a statement could never have more than one kind of formal power; as if statements could, in respect of their formal powers, be grouped in mutually exclusive classes, like animals at a zoo in respect of their species. But to say that a statement is of some one logical form is simply to point to a certain general class of, e.g., valid inferences, in which the statement can play a certain role. It is not to exclude the possibility of there being other general classes of valid inferences in which the statement can play a certain role

Peter Frederick Strawson, Introduction to Logical Theory
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Tragedy's language stresses that whatever is within us is obscure, many faceted, impossible to see. Performance gave this question of what is within a physical force. The spectators were far away from the performers, on that hill above the theatre. At the centre of their vision was a small hut, into which they could not see. The physical action presented to their attention was violent but mostly unseen. They inferred it, as they inferred inner movement, from words spoken by figures whose entrances and exits into and out of the visible space patterned the play. They saw its results when that facade opened to reveal a dead body. This genre, with its dialectics of seen and unseen, inside and outside, exit and entrance, was a simultaneously internal and external, intellectual and somatic expression of contemporary questions about the inward sources of harm, knowledge, power, and darkness.

Ruth Padel, In and Out of the Mind: Greek Images of the Tragic Self
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