Very nice. I had never seen the Oono article! I'm only barely familiar with Kappa, though more aware of the rule-based systems in general. It's great that you invoked them, here, because I haven't been thinking about them in the context of multi-paradigm modeling of human reasoning. When I asked the (1) question, I was thinking of progressive freezing as presented in your (and M's) book, contextual change over time more than gen-phen evolution. But you covered the larger ground with the self-modifying languages.
And I appreciate the comment on reduction(ism) to a best representation. In particular, the problem of uniqueness is a good foil for clear thinking. I agree completely re: GUTs. I always argue against them, but only because I *want* them, preferably many of them. >8^D I've got lots to work on, now. Thanks. On 12/31/20 7:33 AM, David Eric Smith wrote: > Glen, thank you, > >> 1) do you imagine the underlying generator(s) evolving over time (i.e. >> open-ended spaces), and > > 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”. > https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5 > <https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5> > 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”. > > 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 > https://cheminf.imada.sdu.dk/mod/ <https://cheminf.imada.sdu.dk/mod/> > https://kappalanguage.org/ <https://kappalanguage.org/> > and there is some really great work on more general rule-based systems by > Nicolas Behr, finally installed in the CNRS: > https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart > > <https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart> > 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. > https://academic.oup.com/bioinformatics/article/34/13/i583/5045802 > <https://academic.oup.com/bioinformatics/article/34/13/i583/5045802> > I don’t understand exactly what these are, and need to learn. > >> 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”)? > > 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. > > 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. > >> 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”. > > Totally agree. > >> 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. > > 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. -- ↙↙↙ 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/
