I do not know and have not read Feferman, so this may be totally off
base, but ...
glen stated:
/Worded one way: Schema are the stable patterns that emerge from the
particulars. And the variation of the particulars is circumscribed
(bounded, defined) by the schema.
/
This is a description of "culture." Restated—hopefully without
distorting the meaning:
*Culture is the stable patterns of behavior that emerge from
individual human actions which vary (are idiosyncratic) within bounds
defined by the culture.*
The second glen statement:
/Worded another way: Our perspective on the world emerges from the
world. And our perspective on the world shapes how and what we see of
the world./
alludes to the cognitive feedback loop (at least part of it) that I
developed in my doctoral dissertation on cognitive anthrpology.
davew
On Mon, Jan 16, 2023, at 3:32 AM, glen wrote:
> Well, not "languageless", but "language-independent". Now that you've
> forced me to think harder, that phrase "language-independent" isn't
> quite right. It's more like "meta-language" ... a family of languages
> such that the family might be "language-like" ... a language of
> languages ... a higher order language, maybe.
>
> Feferman introduced me to the concept of "schematic axiomatic
systems",
> which seems (correct me if I'm wrong) to talk about formal systems
> where one reasons over sentences with substitutable elements. I.e.
the
> *particulars* of any given situation may vary, but the "scheme" into
> which those particulars fit is stable/invariant. [⛧]
>
> EricS seemed to be proposing that not only do the particulars vary
> within the schema, but the schema also vary. The schema are ways to
> "parse" the world, the Play-Doh extruder(s) we use to form the
Play-Doh
> into something.
>
> Your "random yet not random" rendering of Peirce sounds to me similar
> to the duality between the particulars and the schema they populate.
>
> Worded one way: Schema are the stable patterns that emerge from the
> particulars. And the variation of the particulars is circumscribed
> (bounded, defined) by the schema.
>
> Worded another way: Our perspective on the world emerges from the
> world. And our perspective on the world shapes how and what we see of
> the world.
>
> And, finally, paraphrasing: The apparition of schema we experience is
> due to the fact that such schema are useful to organisms. Events
in the
> world that don't fit the schema are beyond experience.
>
>
> [⛧] I'm doing my best to avoid talking about jargonal things like
type
> theory, things that should have come very natural to Peirce, but
would
> be difficult to express in natural language.
>
> On 1/15/23 19:49, Nicholas Thompson wrote:
>> EricS and Glen,
>>
>> Sorry, again. Here is the short version. I apologize, again,
for appending that great wadge of gunk.
>>
>> I found the second Feferman even harder to understand than the
first. Glen, can you give me a little help on what you meant by a
languageless language.
>>
>> Thanks, all
>>
>>
>>
>> On Sun, Jan 15, 2023 at 4:09 PM Nicholas Thompson
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
>>
>> Aw crap! The shortish answer that I meant to send had all
sorts of junk appended! Sorry. Will resend soon. [blush]
>>
>> Sent from my Dumb Phone
>>
>> On Jan 12, 2023, at 8:54 PM, Nicholas Thompson
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
>>
>>
>> Dear EricS, Glen, and anybody else who is following.
>>
>> Thank you so much for pitching in. As I have often said, I
am incapable of thinking alone, so your comments are wonderfully
welcome. And thank you also for confirming that what I wrote was
readable. I am having to work in gmail at the moment, which is , to
me, an unfamiliar medium.
>>
>> First, Eric: I am trying to talk math-talk in this passage,
so poetry is not an excuse if I fail to be understood by you.
>>
>> /*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.*/
>> /*
>> */
>> I like very muchwhat you have written here and think it
states, perhaps more precisely than I managed, exactly what I was
trying to say. I do want to further stress the fact that if a
measurement system is tracking a variate that is going to stabilize
in the very long run, then it will on average approximate that value
with greater precision the more measures are taken. Thus, not only
does the vector of the convergence constitute evidence for the
location of the truth, the fact that there is convergence is evidence
that there is a truth to be located. Thus I agree with you that the
idea behind Peirce's notion of truth is the central limit theorem.
>>
>> Where we might disagree is whether there is any meaning to
truth beyond that central limit. This is where I found you use of
"ontology" so helpful. When talking about statistics, we are always
talking about mathematical structures in experience and nothing
beyond that. We are assuredly talking about only one kind of thing.
However, I see you wondering, are there things to talk about beyond
the statistical structures of experience? I hear you wanting to say
"yes" and I see me wanting to say "no".
>>
>> God knows ... and I use the term advisedly ... my hankering
would seem to be arrogant to the point of absurdity. Given all the
forms of discourse in which the words "truth" and "real" are used,
all the myriad language games in which these words appear as tokens,
how, on earth, could I (or Peirce) claim that there exists one and
only one standard by which the truth of any proposition or the
reality of any abject can be demonstrated? I think I have to claim
(and I think Peirce claims it) that whatever people may say about how
they evaluate truth or reality claims, their evaluation always boils
down to an appeal to the long run of experience.
>>
>> Our difference of opinion, if we have one, is perhaps
related to the difference of opinion between James and Peirce
concerning the relation between truth as a believed thing and truth
as a thing beyond the belief of any finite group of people. James
was a physician, and presumably knew a lot about the power of
placebos. He also was a ditherer, who famously took years to decide
whom to marry and agonized about it piteously to his siblings.
James was fascinated by the power of belief to make things true and
the power of doubt to make them impossible. Who could jump a chasm
who did not believe that he could jump a chasm! For Peirce, this
sort of thinking was just empty psychologizing. Truth was indeed a
kind of opinion, but it was the final opinion, that opinion upon
which the operation of scientific practices and logical inquiry would
inevitably converge.
>>
>> EricC, the Jamesian, will no doubt have a lot to say about
this, including that it is total garbage.
>>
>> As for Fefferman, my brief attempt to learn enough about
Fefferman to appear intelligent led me to the website,
http://www.vipfaq.com/Charles%20Fefferman.html
<http://www.vipfaq.com/Charles%20Fefferman.html>
<http://www.vipfaq.com/Charles%20Fefferman.html
<http://www.vipfaq.com/Charles%20Fefferman.html>>, which might be the
weirdest website I have ever gone to. I don't THINK that a
language-free language is my unicorn, but Glen NEVER says something
for nothing, so I am withholding judgement until he boxes my ears
again. I think my unicorn may be that all truth is statistical and,
therefore, provisional. Literally: a seeing into the future.
>>
>> Thanks again for helping out, you guys!
>>
>> Nick
>>
>>
>>
>> Consider, for a moment, the role of placebos in medicine.
>>
>> Consider the ritual of transubstantiation. At the moment
that you sip it, is the contents of the chalice Really "blood."
>>
>> /*Peirce writes, "Consider what effects, which may have
practical bearing, the object of your conception to have. Then our
**conception of those effects is our whole of our conception of the
object.*/
>>
>> "The Whole"?! Really? Now somebody of Peircean Pursuasion
would point out that, if a parishionner were to burst a blood vessel,
and a doctor with a transfusion kit were present, NObody would
conceive that the patient should b transfused with communion wine.
Since causing instant death upon tranfusion is not one of the
conceivable consequences of the chalice containing blood (leave aside
immunity issues ), and is a conceivable consequence of transfusing
communion wine, we are warranted to say that, despite what the
practice of communion implies, the stuff in the challice is wine not
blood.
>>
>> But it's entirely conceivable that some parissioners, at
theinstant of communion, do conceive of the wine as blood, and
experience changes of themselves and teh world around them as a
consequence of receiving communion.
>>
>> Fork 1 here "The Whole"?! Really? Consider the phenomenon of
a _________________ effects.
>> /*
>> */
>> The juice here is what we think we are estimating. Are we
estimating the true state of affairs in some world we cannot more
directly access or are we estimating the final resting place of the
statistic we are measuring. My point, here, is that the latter is
all we have. To the extent that anything in experience is non-random
(ie, some events are predictive of other events), any mechanism that
homes on these contingencies will be selected if the consequences are
of importance to reproduction of the organism. we live in a mostly
random world and to the extent that our methods of inquiry are
useful, further inquiry will probably narrow our estimate of some
property within finer and finer limits. This is a process I would
call inductive.
>>
>> Now I think, in your latter comments, you are getting at the
fact that this is only one kind of convergence,and is dependent on a
prior convergence concerning what identifies a substance as lithium.
Before we can determine the boiling point of lithium we have first to
agree upon which substances are lithium and which operations
constitute "boiling". These are decisions that are abductive in
nature, and, to that extent are less straight-forward. Lets say we
are interested in determining the boiling point of Li and we are sent
looking for some li to biol. We come accross a lump of grey metal
witha dark finish in our lab drawer and we want ot know if this is
lithium. The logic here (light grey substance with dark finish =?
lithiumisthe logic ofabduction. That this first test is positive
will lead you toperform yet another abductive lest: is it noticeably
light when youbalance it in yourhadn, can you cut it withthe
plasticknife you brought home with your take-out
>> lunch , etc. These tests are similarly abductive (Li is
light, theis substance is light, this sjumbstance isli;Li is soft,
this substance is soft, this substanve is Li. When enough of these
tests have come up positive you will declare the substance to be Li
an procede to measure its boiling point. (A similar series of
abductions willbe require to agree upon what constitutes "boiling".
>>
>> *Lithium* (from Greek
<https://en.wikipedia.org/wiki/Greek_language
<https://en.wikipedia.org/wiki/Greek_language>>: λίθος, romanized
<https://en.wikipedia.org/wiki/Romanization_of_Greek
<https://en.wikipedia.org/wiki/Romanization_of_Greek>>: /lithos/,
lit. <https://en.wikipedia.org/wiki/Literal_translation
<https://en.wikipedia.org/wiki/Literal_translation>> 'stone') is a
chemical element <https://en.wikipedia.org/wiki/Chemical_element
<https://en.wikipedia.org/wiki/Chemical_element>> with the symbol
<https://en.wikipedia.org/wiki/Symbol_(chemistry)
<https://en.wikipedia.org/wiki/Symbol_(chemistry)>> *Li* and atomic
number <https://en.wikipedia.org/wiki/Atomic_number
<https://en.wikipedia.org/wiki/Atomic_number>> 3. It is a soft,
silvery-white alkali metal
<https://en.wikipedia.org/wiki/Alkali_metal
<https://en.wikipedia.org/wiki/Alkali_metal>>. Under standard
conditions
<https://en.wikipedia.org/wiki/Standard_temperature_and_pressure
<https://en.wikipedia.org/wiki/Standard_temperature_and_pressure>>,
it is the least dense metal and the least dense solid element. Like
all alkali metals, lithium is highly reactive
<https://en.wikipedia.org/wiki/Reactivity_(chemistry)
<https://en.wikipedia.org/wiki/Reactivity_(chemistry)>> and
flammable, and must be stored in vacuum, inert atmosphere, or inert
liquid such as purified kerosene or mineral oil. When cut, it
exhibits a metallic luster
>> <https://en.wikipedia.org/wiki/Luster_(mineralogy)
<https://en.wikipedia.org/wiki/Luster_(mineralogy)>>, but moist air
corrodes <https://en.wikipedia.org/wiki/Corrosion
<https://en.wikipedia.org/wiki/Corrosion>> it quickly to a dull
silvery gray, then black tarnish. It never occurs freely in nature,
but only in (usually ionic) compounds
<https://en.wikipedia.org/wiki/Chemical_compound
<https://en.wikipedia.org/wiki/Chemical_compound>>, such as
pegmatitic <https://en.wikipedia.org/wiki/Pegmatite
<https://en.wikipedia.org/wiki/Pegmatite>> minerals, which were once
the main source of lithium. Due to its solubility as an ion, it is
present in ocean water and is commonly obtained from brines
<https://en.wikipedia.org/wiki/Brine
<https://en.wikipedia.org/wiki/Brine>>. Lithium metal is isolated
electrolytically <https://en.wikipedia.org/wiki/Electrolysis
<https://en.wikipedia.org/wiki/Electrolysis>> from a mixture of
lithium chloride <https://en.wikipedia.org/wiki/Lithium_chloride
<https://en.wikipedia.org/wiki/Lithium_chloride>> and potassium
chloride <https://en.wikipedia.org/wiki/Potassium_chloride
<https://en.wikipedia.org/wiki/Potassium_chloride>>.
>>
>> On Sun, Jan 8, 2023 at 3:21 AM glen <[email protected]
<mailto:[email protected]> <mailto:[email protected]
<mailto:[email protected]>>> wrote:
>>
>> 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)
<https://en.wikipedia.org/wiki/Moment_(mathematics)>
<https://en.wikipedia.org/wiki/Moment_(mathematics)
<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/
<https://logicprogramming.org/2023/01/in-memoriam-martin-davis/>
<https://logicprogramming.org/2023/01/in-memoriam-martin-davis/
<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]>
<mailto:[email protected] <mailto:[email protected]>>
<mailto:[email protected] <mailto:[email protected]>
<mailto:[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. /*
