The specific question is whether induction can be a part of formal logic (it can be). The broader issue is what the nature (and purpose) of logic is.
I see. It should be crystal clear that formal logic allows for mathematical induction. The definitions in every formal system I’ve seen are specifically crafted to allow for the construction of inductive sets of well-formed formulas.
It is just as clear that scientific induction is not mathematical induction.
Is that stipulated or is that a point of contention?
It is just as clear that scientific induction is not mathematical induction.
I think what confuses Bob is that he does not understand that mathematical induction is not relevant to the discussion, and that we are talking about scientific induction; and that scientific induction is formalizable (though not in garden variety monotonic FOP logic).
if it includes just P( a ), P( b ) and P( c ) with no contradictor, then Ax(P(x)) must be inferred.
What if it included just P( a ), and you had no b or c that applied to P in your knowledge context? If I see one Goldfish cracker (sorry, I’m eating) that’s orange, can I say all crackers are orange if I’ve never seen another cracker?
What if it included just P( a ), and you had no b or c that applied to P in your knowledge context? If I see one Goldfish cracker (sorry, I’m eating) that’s orange, can I say all crackers are orange if I’ve never seen another cracker?
No, since a concept (as opposed to an individual) must be based on the integration of two or more units, so a single instance isn’t sufficient to form a concept. You must have two instances of cracker to have a cracker concept, which is necessary to arrive at a universal statement about crackers. In addition, you do in fact have numerous instances of non-orange crackers in your knowledge context, so that suffices to block inductive generalization. You would be better off with swan inductions I think, except that you’ve probably been ruined for that one as well, that is, I imagine you do know that not all swans are white. The point is that you can’t arbitrarily exclude propositions known to be true (or false).
In the instance of a “logical fallacy”, the “fallacy” lies in the “logistics” upon which an argument is presupposed…for someone to pursue a contention premised upon that which they either know to be fallacious at it’s inception, or which is uncovered during the discourse of the discussion, trapping the debaters in an endless, mindless, loop of baseless supposition and conjecture amounting to little more than “trolling”, albeit for for some misguided sense of accomplishment, is a waste of both intellect and time for all parties thereto, i.e., self-defeatist.