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]>> 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]>> 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>, 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>: λίθος, romanized
<https://en.wikipedia.org/wiki/Romanization_of_Greek>: /lithos/, lit. <https://en.wikipedia.org/wiki/Literal_translation>
'stone') is a chemical element <https://en.wikipedia.org/wiki/Chemical_element> with the symbol
<https://en.wikipedia.org/wiki/Symbol_(chemistry)> *Li* and 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>. Under standard conditions
<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)> 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)>, but moist air corrodes
<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>, such as pegmatitic
<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>. Lithium
metal is isolated electrolytically <https://en.wikipedia.org/wiki/Electrolysis> from a mixture of lithium chloride
<https://en.wikipedia.org/wiki/Lithium_chloride> and potassium chloride
<https://en.wikipedia.org/wiki/Potassium_chloride>.
On Sun, Jan 8, 2023 at 3:21 AM glen <[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)>)?
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/> 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]>>> 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. /*
>> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .
