If by "satisfying logically" you mean "meeting the conditions for logical validity," then my remarks in post #28 apply.

Otherwise, I don't understand what is being denoted by the notion of "logical satisfaction."

Also, the vagueness of the as-yet undefined term "worldview" needs to be resolved. I employed the term myself in post #26, but specified that I was addressing only the "foundational premises" (i.e., definitions and axioms) that might be involved, rather than the concept itself. So by "worldview," do you mean a collection of definitions and initial premises (axioms) which may serve as postulates in deductive proofs of theorems (and nothing other than this)? Or do you mean "worldview" in a more general sense, subsuming the one just described, but also including any of various inferential propositions and inductions that inevitably must be made and employed in the application of (previously and apodictically proved) deductive theorems?

No, it isn't. That a "triangle" does not have a number of sides other than three is adefinitionof "triangle." Of course, definitions may be superfluously wrapped up in theformof deductive arguments, but such "arguments" are actually just tautologous "applications" of those definitions - they partake of repitition rather than deduction. For example:

Given definition P1, conclusion C is just a restatment of P2 to which P1 has been applied. It does not deduce or "prove" that triangles don't have four sides; that triangles do not have four sides was already established in P1 by definitional fiat. Definitions are by nature "pre-logical" - it makes no more sense to speak of "proving" them (or of "disproving" their contraventions) via deductive argumentation than it does to speak of "proving" (or "disproving"), say, the Law of Noncontradiction.

But it does not make sense to speak of "argument[s] purporting to prove [or disprove] that triangles have"anynumber of sides (three or four or whatever). The number of sides possessed by a triangle can be neither "proved" nor "disproved" - it is simply established by definitional fiat (as exemplified by P1 in the above "argument"), andnotby deductive argumentation. If I wish, I have but to define triangles as having four sides (for whatever purpose), and it is so; there is no "argument" here whose details can be "bother[ed] with," one way or the other. IOW: There are no arguments to be had over definitions - they are given by fiat, and as such, they are not rationally disputable.

I understand what you are saying here, and I understand the purpose of your analogy - and I agree, as far as all that goes*. My point (as detailed above and in post #10) is that the a-triangle-has-three-sides "argument" is not a good analogy for this purpose - "proofs" that bachelors are not married are not exemplars of deductive reasoning ("pure" or otherwise).

*I say "as far as all that goes" because "any attempt to bridge the is-ought gap can ... be tossed aside" only within a strictly deductive context. Attempts to bridge that gap by deductive means (such as Argumentation Ethics or Natural Law or etc.) are indeed doomed to fail in some way or another. But man does not reason by deduction alone, and that which we can know with apodictic certainty does not encompass all that we may reasonably believe to be true (or close to the truth), even if we can never prove it so ...

Yes, but that does not belie the fact that reason cannot proceed without (at least some) definitions and initial premises.

It is indeed self-defeating if those definitions and axioms, when considered as a whole, embody any contradictions - but that is a separate issue.

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