<!DOCTYPE html><html><head><title></title><style type="text/css">p.MsoNormal,p.MsoNoSpacing{margin:0}</style></head><body><div style="font-family:Arial;">I do not know and have not read Feferman, so this may be totally off base, but ...<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">glen stated:<br></div><div style="font-family:Arial;"><i>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.<br></i><br></div><div style="font-family:Arial;">This is a description of "culture." Restated—hopefully without distorting the meaning:<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;"><b>Culture is the stable patterns of behavior that emerge from individual human actions which vary (are idiosyncratic) within bounds defined by the culture.</b><br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">The second glen statement:<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;"><i>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.</i><br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">alludes to the cognitive feedback loop (at least part of it) that I developed in my doctoral dissertation on cognitive anthrpology.<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">davew<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">On Mon, Jan 16, 2023, at 3:32 AM, glen wrote:<br></div><div style="font-family:Arial;">> Well, not "languageless", but "language-independent". Now that you've <br></div><div style="font-family:Arial;">> forced me to think harder, that phrase "language-independent" isn't <br></div><div style="font-family:Arial;">> quite right. It's more like "meta-language" ... a family of languages <br></div><div style="font-family:Arial;">> such that the family might be "language-like" ... a language of <br></div><div style="font-family:Arial;">> languages ... a higher order language, maybe.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> Feferman introduced me to the concept of "schematic axiomatic systems", <br></div><div style="font-family:Arial;">> which seems (correct me if I'm wrong) to talk about formal systems <br></div><div style="font-family:Arial;">> where one reasons over sentences with substitutable elements. I.e. the <br></div><div style="font-family:Arial;">> *particulars* of any given situation may vary, but the "scheme" into <br></div><div style="font-family:Arial;">> which those particulars fit is stable/invariant. [⛧]<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> EricS seemed to be proposing that not only do the particulars vary <br></div><div style="font-family:Arial;">> within the schema, but the schema also vary. The schema are ways to <br></div><div style="font-family:Arial;">> "parse" the world, the Play-Doh extruder(s) we use to form the Play-Doh <br></div><div style="font-family:Arial;">> into something.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> Your "random yet not random" rendering of Peirce sounds to me similar <br></div><div style="font-family:Arial;">> to the duality between the particulars and the schema they populate.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> Worded one way: Schema are the stable patterns that emerge from the <br></div><div style="font-family:Arial;">> particulars. And the variation of the particulars is circumscribed <br></div><div style="font-family:Arial;">> (bounded, defined) by the schema.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> Worded another way: Our perspective on the world emerges from the <br></div><div style="font-family:Arial;">> world. And our perspective on the world shapes how and what we see of <br></div><div style="font-family:Arial;">> the world.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> And, finally, paraphrasing: The apparition of schema we experience is <br></div><div style="font-family:Arial;">> due to the fact that such schema are useful to organisms. Events in the <br></div><div style="font-family:Arial;">> world that don't fit the schema are beyond experience.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> [⛧] I'm doing my best to avoid talking about jargonal things like type <br></div><div style="font-family:Arial;">> theory, things that should have come very natural to Peirce, but would <br></div><div style="font-family:Arial;">> be difficult to express in natural language.<br></div><div style="font-family:Arial;">><br></div><div style="font-family:Arial;">> On 1/15/23 19:49, Nicholas Thompson wrote:<br></div><div style="font-family:Arial;">>> EricS and Glen,<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Sorry, again. Here is the short version. I apologize, again, for appending that great wadge of gunk.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Thanks, all<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> On Sun, Jan 15, 2023 at 4:09 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a> <mailto:<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>>> wrote:<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Aw crap! The shortish answer that I meant to send had all sorts of junk appended! Sorry. Will resend soon. [blush]<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Sent from my Dumb Phone<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> On Jan 12, 2023, at 8:54 PM, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a> <mailto:<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>>> wrote:<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Dear EricS, Glen, and anybody else who is following.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> /*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.*/<br></div><div style="font-family:Arial;">>> /*<br></div><div style="font-family:Arial;">>> */<br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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".<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> EricC, the Jamesian, will no doubt have a lot to say about this, including that it is total garbage.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> As for Fefferman, my brief attempt to learn enough about Fefferman to appear intelligent led me to the website, <a href="http://www.vipfaq.com/Charles%20Fefferman.html">http://www.vipfaq.com/Charles%20Fefferman.html</a> <<a href="http://www.vipfaq.com/Charles%20Fefferman.html">http://www.vipfaq.com/Charles%20Fefferman.html</a>>, 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Thanks again for helping out, you guys!<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Nick<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Consider, for a moment, the role of placebos in medicine.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Consider the ritual of transubstantiation. At the moment that you sip it, is the contents of the chalice Really "blood."<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> /*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.*/<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> "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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> Fork 1 here "The Whole"?! Really? Consider the phenomenon of a _________________ effects.<br></div><div style="font-family:Arial;">>> /*<br></div><div style="font-family:Arial;">>> */<br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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<br></div><div style="font-family:Arial;">>> 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".<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> *Lithium* (from Greek <<a href="https://en.wikipedia.org/wiki/Greek_language">https://en.wikipedia.org/wiki/Greek_language</a>>: λίθος, romanized <<a href="https://en.wikipedia.org/wiki/Romanization_of_Greek">https://en.wikipedia.org/wiki/Romanization_of_Greek</a>>: /lithos/, lit. <<a href="https://en.wikipedia.org/wiki/Literal_translation">https://en.wikipedia.org/wiki/Literal_translation</a>> 'stone') is a chemical element <<a href="https://en.wikipedia.org/wiki/Chemical_element">https://en.wikipedia.org/wiki/Chemical_element</a>> with the symbol <<a href="https://en.wikipedia.org/wiki/Symbol_(chemistry)">https://en.wikipedia.org/wiki/Symbol_(chemistry)</a>> *Li* and atomic number <<a href="https://en.wikipedia.org/wiki/Atomic_number">https://en.wikipedia.org/wiki/Atomic_number</a>> 3. It is a soft, silvery-white alkali metal <<a href="https://en.wikipedia.org/wiki/Alkali_metal">https://en.wikipedia.org/wiki/Alkali_metal</a>>. Under standard conditions <<a href="https://en.wikipedia.org/wiki/Standard_temperature_and_pressure">https://en.wikipedia.org/wiki/Standard_temperature_and_pressure</a>>, it is the least dense metal and the least dense solid element. Like all alkali metals, lithium is highly reactive <<a href="https://en.wikipedia.org/wiki/Reactivity_(chemistry)">https://en.wikipedia.org/wiki/Reactivity_(chemistry)</a>> 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<br></div><div style="font-family:Arial;">>> <<a href="https://en.wikipedia.org/wiki/Luster_(mineralogy)">https://en.wikipedia.org/wiki/Luster_(mineralogy)</a>>, but moist air corrodes <<a href="https://en.wikipedia.org/wiki/Corrosion">https://en.wikipedia.org/wiki/Corrosion</a>> it quickly to a dull silvery gray, then black tarnish. It never occurs freely in nature, but only in (usually ionic) compounds <<a href="https://en.wikipedia.org/wiki/Chemical_compound">https://en.wikipedia.org/wiki/Chemical_compound</a>>, such as pegmatitic <<a href="https://en.wikipedia.org/wiki/Pegmatite">https://en.wikipedia.org/wiki/Pegmatite</a>> 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 <<a href="https://en.wikipedia.org/wiki/Brine">https://en.wikipedia.org/wiki/Brine</a>>. Lithium metal is isolated electrolytically <<a href="https://en.wikipedia.org/wiki/Electrolysis">https://en.wikipedia.org/wiki/Electrolysis</a>> from a mixture of lithium chloride <<a href="https://en.wikipedia.org/wiki/Lithium_chloride">https://en.wikipedia.org/wiki/Lithium_chloride</a>> and potassium chloride <<a href="https://en.wikipedia.org/wiki/Potassium_chloride">https://en.wikipedia.org/wiki/Potassium_chloride</a>>.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> On Sun, Jan 8, 2023 at 3:21 AM glen <<a href="mailto:gepropella@gmail.com">gepropella@gmail.com</a> <mailto:<a href="mailto:gepropella@gmail.com">gepropella@gmail.com</a>>> wrote:<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> 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 <a href="https://en.wikipedia.org/wiki/Moment_(mathematics)">https://en.wikipedia.org/wiki/Moment_(mathematics)</a> <<a href="https://en.wikipedia.org/wiki/Moment_(mathematics)">https://en.wikipedia.org/wiki/Moment_(mathematics)</a>>)?<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> While we're on the subject, Martin Davis died recently: <a href="https://logicprogramming.org/2023/01/in-memoriam-martin-davis/">https://logicprogramming.org/2023/01/in-memoriam-martin-davis/</a> <<a href="https://logicprogramming.org/2023/01/in-memoriam-martin-davis/">https://logicprogramming.org/2023/01/in-memoriam-martin-davis/</a>> 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.<br></div><div style="font-family:Arial;">>> <br></div><div style="font-family:Arial;">>> On 1/7/23 15:20, David Eric Smith wrote:<br></div><div style="font-family:Arial;">>> > Nick, the text renders.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > 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.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > 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.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > 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.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > 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<br></div><div style="font-family:Arial;">>> pools and<br></div><div style="font-family:Arial;">>> > 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”.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > Speaking or thinking in an orderly way about that seems to have many technical as well as modal aspects.<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > Best,<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> > Eric<br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> ><br></div><div style="font-family:Arial;">>> >> On Jan 7, 2023, at 5:05 PM, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a> <mailto:<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>> <mailto:<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a> <mailto:<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>>>> wrote:<br></div><div style="font-family:Arial;">>> >><br></div><div style="font-family:Arial;">>> >> */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. 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