> On Apr 25, 2016, at 12:15 PM, kirst...@saunalahti.fi wrote: > > The idea of meta-languages presents the way of thinking in levels > (characteristic to modern age). Thinking in terms of levels involves jumps. > Triadic thinking doen not. It incorpotes the idea of growth.
I’m not sure the two ways are necessarily opposed in the way you outline. It’s true that one can make such distinctions but I’m not sure one need do so. An interesting way of thinking about this problem of metalanguages can be found in some treatments of Gödel's Incompleteness Theorem. When we find something indeterminate in the system we add terms so that it isn’t indeterminate anymore. That’s an expansion of the system but can also be thought of as a metalanguage. Now Gödel was a realist who wanted (more or less) a kind of platonism where this expansion went on infinitely. (This might be a more controversial point - but he is read in this way relatively frequently) This can be seen in terms of Peirce’s continuity as well. (Admittedly Peirce’s notion comes from division rather than addition but I think it still works) My only real point in all this is that the divide between growth and jumps isn’t quite as clear as it may at first appear. As I understand it these issues of metamathematics are an ongoing fruitful area of mathematics. I’ll confess I don’t know as much about it as I perhaps should. I’m more familiar with certain “uses” of Gödel and meta-languages in philosophy. While none of these are in the Peircean arena, I think they fit in rather well. (Inquiry as a continual generation of higher metalanguage in terms of semiosis)
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