I really like the construction. Thanks for engaging! The 2 remaining questions I have are:
1) do you imagine the underlying generator(s) evolving over time (i.e. open-ended spaces), and 2) do you commit (even if kindasorta) to the idea that the *structure* of the states of knowledge map well to the structure of the generator(s) (i.e. something like R. Rosen's "natural law")? It seems like we must say yes to (2), even if we hedge a bit. (1) is relevant to the *rates* of any convergence. If the answer is "yes, but the rate of convergence is faster than the evolution of the generator", then we can safely answer "no, for practical purposes". If the answer is "no", then it amounts to some metaphysical commitment to convexity. And (2) is relevant to my problem with using any singular logic to model reasoning (inferential vs. physical entailment). Together, an answer of "no" to (1) and "yes" to (2) seems to imply a commitment to a GUT. But that's really a tangent. On 12/30/20 11:24 AM, David Eric Smith wrote: > >> On Dec 30, 2020, at 1:18 PM, uǝlƃ ↙↙↙ <[email protected]> wrote: >> >> And given Peirce's work in alternative logics, it seems completely >> reasonable that he would allow for different types of consistency and, >> perhaps even, multiple sets of different networks, each of which may be >> self-consistent, but perhaps not connected to other networks. And if >> *that's* right, then there could be >2 final opinions converged upon by >2 >> collections of seekers, yet who disagree about what is real/true. > > Yes. I would hope that these mutually-incompatible positions are features of > a state of knowledge, and not the refutation that there is any possible > referent-notion for the term “truth”. > > Again, I have mental images that to me make this comfortable, but they aren’t > good models in any literal sense. I think of stochastic processes with > multiple basins of attraction, which on the short term can lead to > distributions of fluctuations entirely within one basin or another, with the > basin determined by initial conditions. On the longer term, however, the > process has an ergodic distribution, within which either of the former > distributions can be contextualized as a conditional distribution, relative > to the ergodic which is unconditioned. > > The generator for the underlying process would stand in analogy to what I am > looking for as the truth to be represented, and the various conditioned or > unconditioned distributions would be outputs from sample estimators in any > state of investigation or characterization. As we build up more and more > ways to situate the conditioned distributions within the unconditional, our > state of knowledge reflects more of the properties of the underlying > generator, and leaves fewer opportunities for incommensurate distributions or > unexplained differences in moments. But all these states of knowledge (the > various distributions) remain different kinds of things from the underlying > generator (the true generator of the process), and the states of knowledge > are of the same type as each other even as the knowledge is refined. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
