This smacks of Feferman's claim that "implicit in the acceptance of given schemata
is the acceptance of any meaningful substitution instances that one may come to meet, but
which those instances are is not determined by restriction to a specific language fixed
in advance." ... or in the language of my youth, you reap what you sow.
To Nick's credit (without any presumption that I know anything about Peirce),
he seems to be hunting the same unicorn Feferman's hunting, something like a
language-independent language. Or maybe something analogous to a moment (cf
https://en.wikipedia.org/wiki/Moment_(mathematics))?
While we're on the subject, Martin Davis died recently:
https://logicprogramming.org/2023/01/in-memoriam-martin-davis/ As terse as he was with me
when I complained about him leaving Tarski out of "Engines of Logic", his loss
will be felt, especially to us randos on the internet.
On 1/7/23 15:20, David Eric Smith wrote:
Nick, the text renders.
You use words in ways that I cannot parse. Some of them seem very poetic,
suggesting that your intended meaning is different in its whole cast from one I
could try for.
FWIW: as I have heard these discussions over the years, to the extent that
there is a productive analogy, I would say (unapologetically using my words,
and not trying to quote his) that Peirce’s claimed relation between states of
knowledge and truth (meaning, some fully-faithful representation of “what is
the case”) is analogous to the relation of sample estimators in statistics to
the quantity they are constructed to estimate.
We don’t have any ontological problems understanding sample estimators and the
quantities estimated, as both have status in the ordinary world of empirical
things. In our ontology, they are peers in some sense, but they clearly play
different roles and stand for different concepts.
When we come, however, to “states of knowledge” and “truth” as “what will bear out in the long run”, in addition to the fact that we must study the roles of these tokens in our thought and discourse, if we want to get at the concepts expressive of their nature, we also have a hideously more complicated structure to categorize, than mere sample estimators and the corresponding “actual” values they are constructed to estimate. For sample estimation, in some sense, we know that the representation for the estimator and the estimated is the same, and that they are both numbers in some number system. If we wish to discuss states of knowledge and truth, everything is up for grabs: every convention for a word’s denotation and all the rules for its use in a language that confer parts of its meaning. All the conventions for procedures of observation and guided experience. All the formal or informal modes of discourse in which we organize our intersubjective experience pools and
build something from them. All of that is allowed to “fluctuate”, as we would say in statistics of sample estimators. The representation scheme itself, and our capacities to perceive through it, are all things we seek to bring into some convergence toward a “faithful representation” of “what is the case”.
Speaking or thinking in an orderly way about that seems to have many technical
as well as modal aspects.
Best,
Eric
On Jan 7, 2023, at 5:05 PM, Nicholas Thompson <[email protected]
<mailto:[email protected]>> wrote:
*/The relation between the believed in and the True is the relation between a
limited function and its limit. {a vector, and the thing toward which the
vector points?] Ultimately the observations that the function models
determine/**/the limit, but the limit is not determined by any particular
observation or group of observations. Peirce believes that The World -- if, in
fact, it makes any sense to speak of a World independent of the human
experience -- is essentially random and, therefore, that contingencies among
experiences that lead to valid expectations are rare. The apparition of order
that we experience is due to the fact that such predictive contingencies--rare
as they may be-- are extraordinarily useful to organisms and so organisms are
conditioned to attend to them. Random events are beyond experience. Order is
what can be experienced. /*
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