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. /*
