My question of how well we can describe graph-based ... what? ... "statements"? "theorems"? Whatever. It's treated fairly well in List's paper:
Levels of Description and Levels of Reality: A General Framework by Christian List http://philsci-archive.pitt.edu/21103/ in section "6.3 Indexical versus non-indexical and first-personal versus third-personal descriptions". We tend to think of the 3rd person graph of possible worlds/states as if it's more universal ... a complete representation of the world. But there's something captured by the index/control-pointer *walking* some graph, with or without a scoping on how many hops away the index/subjective-locus can "see". I liken this to Dave's (and Frank's to some extent) consistent insistence that one's inner life is a valid thing in the world, Dave w.r.t. psychedelics and meditation and Frank's defense of things like psychodynamics. Wolpert seems to be suggesting a "deserialization" of the graph when he focuses on "finite sequences of elements from a finite set of symbols". I.e. walking the graph with the index at a given node. With the 3rd person ... whole graph of graphs, the serialization of that bushy thing can only produce an infinitely long sequence of elements from a (perhaps) infinte set. Is the bushiness *dense* (greater than countable, as Wolpert asks)? Or sparse? I'm sure I'm not wording all this well. But that's why I'm glad y'all are participating, to help clarify these things. On 9/12/22 06:13, glen∉ℂ wrote:
While math can represent circular definitions (what Robert Rosen complained about), there are deep problems in the foundations of math ... things like the iterative conception of sets ... that are attempts to do what Wolpert asks for in the later questions. And it's unclear to me that commutative categories reduce to "finite sequences of elements from a finite set", prolly 'cause I'm just ignorant. But diagrammatic loops in graphs don't look to me like finite sequences.
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