Chuck G.:
-clip- Just to bring up some of my old time favorites, let's see, the mythological mind (Piaget, Levi-Strauss), attempted to map out the abstract schema of how we use representation to think and then tried to turn that into a syntactical-like system called Structuralism. But it was far too formal, ridged, and absuredly abstract. They also implied that these formalisms were part of the hardwired structure of the individual developing mind. Although Chomsky and the structuralists were adversaries, I am not sure why exactly. Perhaps it was the French position that all of these sorts of structures were not entirely genetic, but more of an invention or craft, core cultural development using the available biologically (genetic, material, deterministic, evolutionary) formed systems. You gotta put Gould in there somewhere.
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CB: Note that both Levi-Strauss and Chomsky's grammars/structures are unconscious. There is this big system of symbols in everybody's head that the average, native speaker cannot articulate abstractly, but which they know and follow in speech and behavior. Of course, in that period Freudian unconscious was still en vogue. Today there is almost no mention of the claim of unconscious systems of thinking and acting. I think that there is an unconscious aspect to these has some importance, and maybe even for politics.
The grammar of a specific language is not innate.
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Oh, but I can't leave it go. One of the most profound hints that Cassirer left was the idea that mathematics deals with the abstract syntax of representation through the theory of groups. But he died in 1946, before he could pursue this thought. It takes a lot of very unmathematical (as well as very abstract mathematical) thinking to see that the various algebraic heirarchies (metamathematics of algebras) sets, semi-groups, groups, rings, fields are systems in a tiered hierarchy in which the elements and their operators become increasingly complex. From a simple Cartesian pairing of elements in sets (coordinates of a two dimensional plane), which follows simple operations like union, to the more complicated system of association, if A -> B, B -> C, then A -> C, or the associative rule (associative groups), each additional operation (or rule of combination) adds a degree of complexity, in which the available syntax is enriched and made more articulate (speaking in metaphorical terms). One finally arrives at a general theory of morphisms, or homeomorphic groups(?), or in even more abstract language homeomorphic topological groups.
^^^^ CB: I guess we Chucks think alike. I sent my mention of group theory before I read your post.
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In some crude sense, all this verbage is just a way of saying that many of the shapes and their motions in space that compose the way we think about the world, have a logical order and structure about them that inform and expand (define?) both our perception and understanding of the physical world.
^^^^^ CB: So, if the basic elements used to model molecules in a thermodynamical system and wealth in an economic/class system with rich and poor have significant analogies, we might expect them to be alike in the way the study claims ?
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I would actually reverse the causal order and say that the physical world (temporal apriori) has informed us of its homeomorphic topology through its contact and intimate relationsip with our co-evolving kinesthetic complex---called the brain or mind.
^^^^^ CB: Yes, that's Marxism, materialism. The material world has made and shaped the human mind out of human practice. However, it would get vulgar to claim a true "one-to-one correspondence", to use a group theory metaphor, between physical molecules' concentrations and where dollars concentrate or the something like that. No cause directly from that basic physics level and the human social rich/poor level .
So getting back to metaphor, the important point is not the poetics of the metaphor, but its operational characteristics (structuralism) that links up our perception with the way we think.
So, now we get back to the problem in linguistics that the languages of the world all have slightly to greatly divergent systems for forming these metaphors and analogies that are somehow deeply linked to the underlying linguistic formal structures of the language. We do not understood exactly how, but while the physical world remains a constant, the way we dissect it is not constant and not determinant. We improvise through our linguistic structures how to understand the world---and there in lays a kind of mysterious relevativism. Yes, I do believe we think differently, depending on our cultural-linguistic complex within which we were raised.
Oh, well, so much for a trip down memory lane. Gee wasn't it great for just a moment? Some fleeting respite from the mire?
CG