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In my opinion the example in the section "Deductive Reasoning" is not an example of a valid argument. The conclusion does not necessarily follow from the premises. The premise that rectangles have four sides does not warrant the conclusion that everything with four sides is a rectangle. 188.8.131.52 (talk) 16:27, 25 March 2015 (UTC)
- Good catch! I've changed it. In future, when you see mistakes I encourage you to make changes yourself. Thanks, Sunrise (talk) 16:41, 25 March 2015 (UTC)
"Deduction is generally an inference by reasoning from the general to the specific." <-- from the section on deductive, inductive, and abductive reasoning.
Quite simply, no, it isn't. Deductive reasoning has no essential relationship with generality OR particularity, and for that matter neither do the other two species. It's about *entailment* vs. *probability*, and that's *all* it's about.
I actually teach logic at College. If any myth about deductive vs. non-deductive logic needs to DIE, it's this one about "generality" and "particularity." — Preceding unsigned comment added by 184.108.40.206 (talk) 19:59, 15 April 2015
- Welcome to Wikipedia! Please feel free to make changes yourself. I've removed the statement for now, since it wasn't cited. If anyone objects, they should post here. If they do, a link to a textbook or other academic work you're aware of that discusses the issue might be useful. Sunrise (talk) 19:31, 18 April 2015 (UTC)
The idea of deduction going from the general to the specific and induction from the specific to the general goes back to Aristotle. It is preserved in the difference between mathematics and science. The pattern in mathematics, set in place by Euclid, is Axiom, Definition, Theorem, Proof. You cannot deduce the truth of a theorem without axioms and definitions (and, in modern mathematical logic, a proof schema, e.g. If A is true, and A implies B, then B is true.) Since Axioms and definitions are general statements, deduction necessarily goes from the general. Since theorems are less general, requiring hypotheses as well as conclusions, they are more specific, though the applications of theorems to particular cases are more specific still. Maybe the sentence objected to should read "Deduction is reasoning from general axioms and definitions to less general theorems which only hold under certain hypotheses." Another property of deduction is that it is (or, at least, nobody has ever been able to show that it isn't) absolute ("entailment"?) while induction is falsifiable ("probability"?). Rick Norwood (talk) 11:57, 19 April 2015 (UTC)
- In any case, and maybe this is what you are saying, the sentence seemed to contain something worth getting right. I think we should try to replace with something which allows for the tradition plus modern definitions. I do hope our new contributor can be dragged into the crazy world of Wikipedia!--Andrew Lancaster (talk) 16:16, 19 April 2015 (UTC)