<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Glen, thank you, <br class=""><div><br class=""><blockquote type="cite" class=""><div class=""><div class="">1) do you imagine the underlying generator(s) evolving over time (i.e. open-ended spaces), and<br class=""></div></div></blockquote><div><br class=""></div><div>I wouldn’t want to rule out anything one could get to work. The obvious common application would be to evolutionary systems. I tend not to like overdoing the “evolution is special because its state at any time changes the rules for its dynamics”, as if somehow a science of evolution would float above those plebeian physical sciences and the people who practice them. Having different kinds of transitions available from different states is generic; to me the cases that are “evolutionary” in an interesting sense tend to be set apart by their dimensionality, complexity, and statefulness — what Yoshi Oono calls “fundamental conditions” as distinct from “boundary conditions”. </div><div><a href="https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5" class="">https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5</a></div><div>Where possible I find it preferable to look for a set of stable laws governing the space of all possible histories, and to locate state-dependence as a property of solutions within a history, much as one embeds an open dynamic thermal system as a transient within a larger in-principle closed system. But the evolutionists do have a good point: for systems where one can’t practically compute (and doesn’t care about) all possible trajectories, it would be nice to have a science that is more local to the trajectory, and to have ways to handle time-dependent “laws” or “aspects of truth”.</div><div><br class=""></div><div>The modern community that goes by the name of “rule-based modeling” does this in a way that I like, using category-theoretic constructs of pushouts and pullbacks to be explicit about how much context is needed. I have pointed on this list before to </div><div><a href="https://cheminf.imada.sdu.dk/mod/" class="">https://cheminf.imada.sdu.dk/mod/</a></div><div><a href="https://kappalanguage.org/" class="">https://kappalanguage.org/</a></div><div>and there is some really great work on more general rule-based systems by Nicolas Behr, finally installed in the CNRS:</div><div><a href="https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart" class="">https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart</a></div><div>They are interested in such questions as: what can you compute from the algebra of rule dependencies, without having to solve for a whole state? Or: when can you obtain information about correlation functions for limited sets of properties (effectively, governed by some marginal distribution) without having infinite regress of dependencies on the whole system? Walter Fontana et al. have a particular structure for such dependencies, which he calls “stories”, and has developed within the context of Kappa. </div><div><a href="https://academic.oup.com/bioinformatics/article/34/13/i583/5045802" class="">https://academic.oup.com/bioinformatics/article/34/13/i583/5045802</a></div><div>I don’t understand exactly what these are, and need to learn.</div><div><br class=""></div><blockquote type="cite" class=""><div class=""><div class="">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”)?<br class=""></div></div></blockquote><div><br class=""></div><div>Yes, I think this is necessary in order to be saying anything at all. The question of how two very different formal systems can have “the same structure” or “the same information” seems hard and interesting. With what further assumptions can I say that a small collection of unconditioned and conditional stationary distributions, and perhaps a few dynamical correlations functions, contain all the same information as is contained in an underlying generating process, and are effectively just one of the available representations of it. This would seem to be at the foundation of what reductionism in science can be. It is also about the theory of representations, of which I don’t know very much. I seem to remember JonZ's having some comments on this subject in the last go-round. Category theory appears to be the universal language these days for rule-based modeling.</div><div><br class=""></div><div>The ML implication here is of course obvious (I know, to all): can we learn useful things about the difference between an abstract structure and its representations by studying cases? Implicit representations, self-presentation by a learner, and things we have discussed here before.</div><div><br class=""></div><blockquote type="cite" class=""><div class=""><div class="">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”. </div></div></blockquote><div><br class=""></div><div>Totally agree.</div><br class=""><blockquote type="cite" class=""><div class=""><div class="">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.<br class=""></div></div></blockquote><div><br class=""></div><div>Also, yes. It’s interesting, GUTs have a bad name, I guess for a variety of reasons, whether boasting, false claims, cutting off useful questions just because they aren’t final, etc., all of which seem to me to be about human bad behavior and not about what is needed by an idea. It could be that associating “truth” with unification is appropriate, and need not be harmful to practice if one understands that states of knowledge don’t claim to be truth, but at best isomorphic to it in patches if we get lucky. </div><div><br class=""></div><div>Best,</div><div><br class=""></div><div>Eric</div><div><br class=""></div><br class=""><blockquote type="cite" class=""><div class=""><div class=""><br class=""><br class="">On 12/30/20 11:24 AM, David Eric Smith wrote:<br class=""><blockquote type="cite" class=""><br class=""><blockquote type="cite" class="">On Dec 30, 2020, at 1:18 PM, uǝlƃ ↙↙↙ <<a href="mailto:gepropella@gmail.com" class="">gepropella@gmail.com</a>> wrote:<br class=""><br class="">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.<br class=""></blockquote><br class="">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”.<br class=""><br class="">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.<br class=""><br class="">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.<br class=""></blockquote><br class="">-- <br class="">↙↙↙ uǝlƃ<br class=""><br class="">- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br class="">FRIAM Applied Complexity Group listserv<br class="">Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" class="">bit.ly/virtualfriam</a><br class="">un/subscribe <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,WXhD3v31uj4exDMUAs-DSkDIaYeH1MsOTJeXEZzhKOQLjJolT0eEAZsm3x5bx0KP9DaGWgrzUY7hWmmJjMU-spbwclFV8e6h0gz0dET1bHk4yoLqfbDnSsBmdg,,&typo=1" class="">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,WXhD3v31uj4exDMUAs-DSkDIaYeH1MsOTJeXEZzhKOQLjJolT0eEAZsm3x5bx0KP9DaGWgrzUY7hWmmJjMU-spbwclFV8e6h0gz0dET1bHk4yoLqfbDnSsBmdg,,&typo=1</a><br class="">archives: <a href="http://friam.471366.n2.nabble.com/" class="">http://friam.471366.n2.nabble.com/</a><br class="">FRIAM-COMIC <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,s7ZRLILfWlMKI-KD-YRtCnDfCFVAFpP1t4MLvVm5ZAGTNYv1m9rhRX2-HsPhp4DPEAtAgUtIc89R0I175IeXYdLvfJeOZI0uRuV4LTcYWswloaWEMGN7rA,,&typo=1" class="">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,s7ZRLILfWlMKI-KD-YRtCnDfCFVAFpP1t4MLvVm5ZAGTNYv1m9rhRX2-HsPhp4DPEAtAgUtIc89R0I175IeXYdLvfJeOZI0uRuV4LTcYWswloaWEMGN7rA,,&typo=1</a> <br class=""></div></div></blockquote></div><br class=""></body></html>