Logic

Can two people reason differently? Even when given the exact same premises? I mean ... can using reason EVER lead us to more than one conclusion?

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Well, yes of course, two incompetent reasoners could reach different conclusions by making different mistakes! So I take it the question is: could two people reason correctly to different conclusions from the same premisses?

But again the answer to that is, trivially, "yes". A given bunch of premisses will entail lots of conclusions (e.g. the axioms of Euclidean geometry entail both that the angles of a triangle add up to two right angles, and that the tangent at the point on a circle is at a right angle to the diameter through that point). One reasoner can correctly deduce one conclusion; another reasoner can correctly deduce a different conclusion.

Still, in that case, the different conclusions are all consistent with each other. So perhaps the question is supposed to be: can two two people reason correctly from the same premisses to conclusions that are "different" in the strong sense of being actually incompatible with each other?

Again, the answer to that is obviously "yes". For suppose the premisses are themselves inconsistent. Then we can hope to show this by a "reductio ad absurdum" argument -- which is in effect a pair of arguments, one of which correctly shows that the premisses entail some conclusion P, the other of which correctly shows that the same premisses entail the opposite conclusion not-P, from which we infer (since P and not-P can't be true together) that the premisses can't all be true together.

Another shot. Perhaps the question is supposed to be: given the same consistent set of premisses, can people correctly reason to a pair of conclusions which are inconsistent with each other? To which the answer is plainly "no" -- at least if it is deductive reasoning that is in question. For if they logically entail a pair of inconsistent conclusions then the premisses can't be consistent after all.

Perhaps though the question was not about strict deductive reasoning but about issues of inductive support: could people inductively reason from the same premisses to different conclusions? Well sure, the same consistent data-set can lend an equal degree of (non-conclusive) inductive support to two different hypotheses. But that still shouldn't lead to a case of "reasoning differently" in any very interesting sense -- for proponents of each hypothesis should both, if reasoning correctly from the same starting point, recognize that the hypotheses are so far equally well supported, so other things being equal it would be wrong at this point to endorse one conclusion as against the other.

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