Logic, in the traditional sense, has always been thought of in the form of identity and I don't think i have to explain what that entails, suffice with, the above descriptions. However, identity, implies identity with some "thing" and element that is shared by at least 2 "things". This shared thing became the model, the paradigm which served the sameness into which these things fitted, as in a mold. Later, much later, this paradigm became deconstructed. And a different kind of logic came to be the predominant form of apprehending reasoning, vis, difference. The differential calculus was the analytical foreshadowing of of limits, approximations, and literally, the functional use of logic. The point is, discerning the steps (logical) became more and more an exercise in delineating the in between the either/or in any logical problem. In Meno's paradox, the half steps become increasingly small,and the logical limits become approximations. This correlates with the arc of the circle, where increasingly many sided figures of equal sides can be constructed within the circle, where the limit appears to be the figure with infinite sides. However the such a figure, would have sides with no length, only an infinite number of points. The concept of infinity is not accessible to Meno because, it was obvious the turtle would eventually reach the end. This concept was prevalent all through the Middle Ages, when it was thought that the earth's horizon consisted of a drop off point. The language of logic was based here on the paradigm of the perfect circular objects the ideal figure, with which other objects shared identity.
When it was found that the horizon was ever moving away from the point of view of the observer,
the ideal object of circularity changed, from a static point of view of the observer, to that of the moving toward a never ending horizon of circularity. The concept of perfect circularity was destroyed, as in the concept of identity, A=A, and there became no two perfectly identical circles or spheres. Logical difference became the form of reasoning, and the principle of exclusion, made the logical deduction shift toward inductive reasoning, by processes of elimination. If A=B and if B=C, then A could =X,Y,Z, if all other elements are equal. But from premise to conclusion, there may be any number of elements, and any one being indeterminable or variable, could upset the syllogism. This meant, that hypotheses had to be made, on basis of probability, as to what premis(s) could satisfy that hypothesis. Functional analysis does not start at the starting gate of meno’s paradox, but guessing at the most probable result and working it back, to a probable starting point by excluding all elements most unlikely to effect change. The fact that those elements were effected by other most probable events, makes this logic verifiable not by simple reductionism but by processes best described by game theory of sets, i believe.
Would like to add, my take is philosophical and am looking at paradox, as a foreshadowing of this coming problem of analytic/synthetic propositions, in classical times.
It is paradoxical that there is no agreement in the OP’s assertion, but science has developed by leaps and bounds by virtue of seemingly paradoxical understanding of phenomenon, so there is no clear cut model to understanding, except looking at the OP/ hypothetically, and working it out through game theory.
Obviously we would not want a world to be ruled by machines, and how does this probable future relate to the present? How can certain events be excluded, so as to make that scenario less likely? Or put in another way, what elements can be safely excluded, or safely left undiscovered, so as not to pose as a logical flaw to this objective?(to avoid a machine run scenario).
I was hoping for a neat logical way to point to an answer, but found it impossible without laying some kind of credible foundation. I can’t help but to think, though, that this reversal, was meant to imply some kind of test, rather then a serious doubt about what usual syllogisms entail. Since reversibility in logic is not entirely ex-post facto, i have confidence in james’ holdout for formal elements. I share those views to an extent, in the effect of “tacit knowledge”(M.Polanyi), has on game theory.