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I am taking a graduate-level course in a business-y/sociology-y field, and the logic presented in the literature is typically of the following format "X is a relatively simple and reasonable cause for Y, because reason_1,reason_2,reason_3. Also, we did a couple of case studies and this plays out."

It's not really inductive reasoning, because the case studies are wildly insufficient to alone support the hypotheses of the paper. It's not deductive reasoning because it is not proven that X causes Y.

Coming from a math/science background, I am good with mathematical proof, I am good with a rigorous statistical analysis, but the reasoning employed in this field is foreign and weird to me.

From some poking around, it looks like this type of logic is called "defeasible reasoning". Where can I read up on the epistemology behind defeasible reasoning from a source that would be accessible to a math/science guy?

EDIT heres an example of what I mean. A lot of claims are made, supported by invalid* arguments and a handful of case studies.

*invalid in the technical sense

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    Unclear. What are r1, r2, and r3? Also, what does it mean to "science the hypotheses of the paper"?
    – Bram28
    Apr 10, 2018 at 17:33
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    plato.stanford.edu/entries/reasoning-defeasible follow the bibliography. That being said, this is still definitely a case of inductive reasoning, contrary to your second sentence, it's just not as strong of an example of induction as is used in, for example, physics or chemistry.
    – Not_Here
    Apr 10, 2018 at 19:27
  • @Not_Here, I would disagree about the inductive reasoning bit. The reasoning does not follow "We witnessed X cause y in some circumstances, therefore X causes y generally", the meat of the reasoning is defeasible, and the case study is only used to do a sort of post hoc sanity check on the defeasible bits, imho.
    – Him
    Apr 10, 2018 at 19:39
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    This is called abductive reasoning now, a.k.a. inference to the best explanation, see Are “if smoke then fire” arguments deductive or inductive? that links to some references. The old terminology did not distinguish between this and the more conventional induction, and some are still using "induction" broadly, both are of course defeasible.
    – Conifold
    Apr 10, 2018 at 19:44

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There's quite a lot of useful philosophical work on this. I recommend Stephen Toulmin, philosopher and scientist, and Douglas Walton, esp. (1) and (4) :

(1) Stephen Toulmin, The Uses of Argument (2003) Published by CAMBRIDGE UNIVERSITY PRESS, United Kingdom ISBN 10: 0521534836 ISBN 13: 9780521534833

(2) Albert R. Jonsen, Stephen Toulmin, The Abuse of Casuistry: A History of Moral Reasoning (1990) Published by University of California Press (1990) ISBN 10: 0520069609 / ISBN 13: 9780520069602

(3) J.A. Blair, Conductive Argument. an Overlooked Type of Defeasible Reasoning (2016) ISBN 10: 1848900309 / ISBN 13: 9781848900301 Published by College Publications

(4) Douglas N. Walton, Informal Logic : A Pragmatic Approach 2nd Edition (2008) ISBN: 9780521713801 Published by CAMBRIDGE UNIVERSITY PRESS, United Kingdom.

(5) Douglas N. Walton, Ad Hominem Arguments (Studies Rhetoric & Communication) (1998) ISBN 10: 0817309225 / ISBN 13: 9780817309220 Published by University Alabama Press, 1998

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