I would like to return to a point where the paths of discussion began to diverge and then bifurcated so chaotically that I could not track them further, namely, here:
I imagine different readers derive different morals from the passage Gary Fuhrman quoted. It resonates for me with a host of themes going back to my Vita Nuova in many dimensions of life during my first years of college. But memories from fifty years ago are hard to put in order and so what comes more freshly to mind are later harvests of those seeds.
One of those outgrowths was the work I did applying Peirce’s paradigm to fundamental problems in AI, or Intelligent Systems Engineering as my advisor in Systems Engineering preferred to call it. I posted a link to a section from one of my project reports:
Many distractions kept me from following up at the time, so I’ll copy here the introduction of that section with the aim of moving forward from there:
Functional Logic : Inquiry and Analogy
Functional Conception of Quantification Theory
Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements. Merely to write down quantified formulas like and involves a subscription to such notions, as shown by the membership relations invoked in their indices. Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage. Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.