Clark,
I agree with your points. - But I did not use the word "necessarily".
As long as one stays within mathematics, what you write:
" 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)"
makes sense.
But as soon as chemistry, biology let alone social sciences come into
the picture, problems do arise. Also, they are left unrecocnized. In
order to understand the general nature of these problems, the Foucaldian
concept of the "episteme" is needed. (which is far too complex for me to
properly deal with here.
The most common form these problems appear, is in the form of just
jumping from "the level of individuals" (be they chemical reactions,
organisms or organelles, human or animal individuals) into the level of
science (theories, concepts. Then the priciple of continuity gets
violated.
Hope this clears my point a little.
Kirsti
Clark Goble kirjoitti 25.4.2016 21:37:
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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