This will be a series of posts on various subjects, but united, first, by the composition itself in a series; second, by dedicating themselves to the thematicization and formalization of issues that are uncommon in this blog.
For this first entry, I would like to make just a brief but provocative comment: induction and deduction form something like a continuum.
Let me explain: any powerful enough induction will be equivalent to a deduction in that same particular case.
Interpretative caveats belong to our approach to the particular case and do not strictly belong to the inductive reasoning in question.
These interpretative caveats are currently part of our approach to induction, but should they be so? Or should they belong to the epistemology of inductive reasoning? Induction, then, seems to be born tainted by the brand of the particular case: it must always be restricted to a specific situation, and cannot aim above time and space as deduction.
But given enough time, a sufficiently strong induction will work as a deduction.
What does this allow us to understand? Not much, because we are talking about induction and this limits us to the present as a time boundary.
For this entry, that's it. More time is needed to address the consequences. But it is impossible to move on without noticing it.
P.S.: the relationship between induction and the sources of information that feed the reasoning in question seems to be another sensitive point of the issue.
I remember the amused shock I felt the first time that heartless fellow, David Hume, dared to claim the sun won't necessary rise tomorrow :D
ResponderExcluirBut, in a more serious note, I think you're most definitely right on the money when you treat them as a continuum. I mean, if induction is supposed to present a theory, deduction should attempt to falsify it (or test it, if we want to be kind). Of course there's also the generalization/specification perspective, too, in the sense the two, induction and deduction, move in rather opposite direction — which of course precisely reaffirms your idea of the continuum.
I also wonder how we define "specific situation" in the context of "it must always be restricted to a specific situation". This is a bit Hegelian, perhaps, but generic/specific is often a matter of relational patterns.
Anyway, fascinating stuff; looking forward to more!
Oh, I'm thankful I was not the only one shook!
ExcluirAs for the relational pattern: yes, and this is a restriction I've seen with induction, but not deduction, which, as I understand now, derives from Hume's positing of the problem of induction. As I understand it, the problem is that deductions preserve their truth along the whole inferential chain, while induction always presents some issue in this front. But I still think it is more of a continuous than a discrete problem, as any sufficiently strong induction will, for all practical purposes, be indistinguishable from a deduction (except, of course, if we are aware of this meta-theoretical level, but let's shun this aside for a moment).