On the differences between deduction and induction

I’m finally taking the time to comment on a December post from the Maverick Philosopher, this one concerning the nature of deduction and induction. Dr. Vallicella makes some good points, but seems to overlook a key distinction.

Dr. Vallicella begins in a dialectic form, explaining why the usual notions of deductive reasoning moving from the universal to the singular and inductive moving from the singular to the universal are inadequate. I generally agree with his comments on this. However, I would hope in a discussion designed to illustrate reasoning, a better choice would be used for the example of a deductive argument that goes from the singular to the general than the use of a contradiction of singulars to derive a universal general, a usage even Dr. Vallicella acknowledges is artificial. A better choice would have been an argument that is at least hypothetically sound, rather than valid yet vapid. For example, from the singular propositions John is the only chess player born on Feb. 29, 1992 and John is fat, you could come to universal conclusion that every chess player born on Feb. 29, 1992 is fat without having to rely on a contradiction.

However, it is with the last paragraph that I find the thinking clumsy. In saying "To be a bit more precise, a deductive argument is one that embodies the following claim: Necessarily, if all the premises are true, then the conclusion is true", Dr. Vallicella basically removes the meat from the sandwich. A deductive argument is a demonstration of that relationship between the premises and the conclusion by the use the accepted rules of argumentation. That is the separation from the inductive argument, which makes no offer of demonstration except example. In the example of "All As are Bs; All Bs are Cs; ergo, All As are Cs", this is a straight-forward syllogism, and we use the rules of inference to determine it. My example is a little more complex syllogistically, but is straightforward in symbolic logic.

Also, while "the universal to the singular" and "the singular to the universal" are not strictly true, they are simplifications of a more accurate understanding of the scopes of the conclusions. For example, if you interpret propositions as statements about sets, deductive arguments are basically arguments that the set of the conclusion is a subset of the intersection of the sets containing the premises. That is, A∧B ⇒ C is another way of saying C ⊆ A∧B. So, deductive arguments go can decrease their inclusivity from premises to conclusion, but never increase it. Meanwhile, inductive arguments increase inclusivity, by extending membership in a set to something when it was not previously considered a member of that set. So, this is another good way of looking at the difference between deductive and inductive arguments, even if the word choice Dr. Vallicella rejected is inferior.
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