Talk:Abductive reasoning

Induction vs. Abduction

I read and re-read this article and still do not get the distinction between "induction" and "abduction". Though the authors presented a very learned discussion with careful symbolic logic to support their definition of "abduction", they made nary a mention of "induction", which it seems to me they were defining. 3,568 is my answer to the angel question, by the way, but only on Sunday and other certain assumptions (assumptions of certainty) for uncertain things, i.e. definitions that constrain alternative interpretations. There may be a deep and meaningful distinction to be had between abduction and induction, but in my dense fog of ignorance, I can not see it. From that fog comes another popular saying "mountains out of molehills" to which I would add the corollary, molehills out of mountains (cp. Matthew 23:24, though I am not a Christian except by culture). The issue is how, from specific instances, we are able to draw and validate general statements, hypotheses, theories, or, as the authors cite other authors, "guesses". Patterns, of course, and observations of patterns, repeatable (helpful), recorded (helpful), and discussed with others (also helpful). The help, which we and I often first react to as an attack, attempts to uncover our inevitable social, political, religious, logical, and mathematical biases. (cp. Lao Tzu for a poetic advance of the "bias" hypothesis, to give ecumenicalism its due) "We", and I as but a lay person, have known this for a long time and heretofore called it, by convention, "induction". Science proceeds by making distinctions where none existed before, and I applaud the authors for their copious contribution, though I must learn more before understanding it. Ssinnock (talk) 21:41, 30 August 2013 (UTC)

Here's my amateur's crack at induction vs. abduction. Induction involves constructing a rule that a implies b from numerous examples. (Actually, there is a rigorous mathematical method of proof called induction.) Abduction is an inverse application of the rule a implies b: one infers that given b, a was the probable cause. Induction is as good as the data that supports the rule. Abduction is only as good as the uniqueness of the cause, a. For example, there could be two rules constructed from induction: a causes c, and b causes c. Both these inductive rules could be correct, and either could be applied inductively to show that if a or b occurs, then c occurs. Observing c, the abduction that a was the cause, is only probabalistic, since the cause might have been b. Wcmead3 (talk) 17:02, 17 June 2015 (UTC)

Deduction Example

"For example, given that all bachelors are unmarried males, and given that this person is a bachelor, it can be deduced that this person is an unmarried male."

This is a terrible example of deductive reasoning. Because the exact definition of bachelor is "an unmarried male", nothing at all is deduced, facts are only restated. The conclusion is just a restatement of the 2nd part of the premise, adding nothing new at all, so it's lacking the characteristic inference.

Something abstract might be better? Or a joke: If all politicians are liars, and Ted is a politician, then Ted is a liar. — Preceding unsigned comment added by Pmneeley (talk • contribs) 17:25, 23 April 2012 (UTC)

Probabilistic abduction

How is the term $p(y{\overline {\|}}x)=p(x)\left({\frac {a(y)p(x|y)}{a(y)p(x|y)+a({\overline {y}})p(x|{\overline {y}})}}\right)+p({\overline {x}})\left({\frac {a(y)p({\overline {x}}|y)}{a(y)p({\overline {x}}|y)+a({\overline {y}})p({\overline {x}}|{\overline {y}})}}\right)$ mathematically different from $p(y{\overline {\|}}x)=a(y)\left(p(x|y)+p({\overline {x}}|y)\right)$? Using current notation and argumentation they are equivalent, and the artificial expansion of the marginals does not convey clarity or usefulness of any kind. The difference (if any) between $p$ and $a$ could also be explained. — Preceding unsigned comment added by 66.235.53.84 (talk) 02:29, 7 January 2013 (UTC)

Also on Probabilistic abduction

Hello, in the sentence 'where "||" denotes conditional deduction', this is not understandable: in the right-hand side of the immediately preceding equation, substituting the conditional probabilities by their standard definitions, the multipliers $p(x)$ and $p({\overline {x}})$ cancel off, and by complementarity of $x$ and ${\overline {x}}$, the expression boils down to $p(y)$, leaving one with no clue of what $p(y\|x)$ actually is. Also, just next, the "base rate" is mentioned but not defined nor provided with a link to some other Wikipedia page explaining what it is (this is also, essentially, the same question as above asking the editor to clarify the difference between $p$ and $a$). Thanks for your attention. 83.63.244.118 (talk) 18:04, 7 September 2015 (UTC)