<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">Nick, <div><br></div><div>At the end of the day you are a philosopher rather than a naturalist, in the sense that Neurath would have used those two ideas, and over a decade or so, finally got Carnap to join into from the analytic as opposed to the sociological side.</div><div><br></div><div>By which I mean: you are determined, in a way that nobody is going to talk you out of, that you have synthetic a priori knowledge about the world, which you can get to via the forms of argument. There are analyses that can be done by a naturalist, but they aren’t those.</div><div><br></div><div>You, or GPT, or whoever, formulate strings of words such as “Entropy is not something you have in a moment.” I have no idea what can be done with such strings of words.</div><div><br></div><div>By analogy, your stubbornness: I will not follow the sequence of moves that solves the position of this Rubik’s cube from the starting point I have; I insist that I will solve it using my own sequence of moves decided-upon before I saw the Rubik’s cube, whether they solve it or not.</div><div><br></div><div>Where can one start if the goal is to solve the Rubik’s cube by moves that solve it?</div><div><br></div><div>Well: </div><div><br></div><div>1. Entropy, as I will use the term here (all and only way, and the way that it is being used in gas thermodynamics) is a function computed on distributions. (Called a “functional”, but one doesn’t need to worry about that name.)</div><div><br></div><div>1a. Ergo, we are _already_ in a formal world by needing a distribution as our starting point.</div><div><br></div><div>1b. So if we want to talk about nature, we must first ask: how much else have we committed to, about experience, the setting-up of phenomena, etc., to permit us to attach some distribution to those experiential contacts with nature. If we are to adopt the “thing language” (Carnap term) to refer to a distribution or its entropy, and to know what rules for thing-languages permit us to do with such a term, we must operationalize how the distribution got put up as a “thing” (Peirce’s consequences in action of commitments one makes to declare terms).</div><div><br></div><div>1c. Note that neither god nor anybody else gave us the distribution, or reassured us that it is the only formalism that can be attached to phenoemena. We have to unpack what we mean by talking to see what we have chosen to do, and then we make utilitarian choices about whether we want to make the same choices always, or sometimes choose other ways of describing.</div><div><br></div><div>2. It turns out that the useful first question (recall, actually solve the Rubik’s cube) for unraveling thermodynamics was: Which properties have the memory to depend on history beyond other instantaneous properties, and which don’t? The properties that don’t are what we call “state properties” or “state variables” or “state functions”. You (or GPT, or whoever) have declared above that entropy is not a state function, while the whole thermodynamics community (in the suitable near-equilibrium approximation, etc., etc.) begins its constructions with the defining property of entropy as a state function. It’s perfectly fine, in science, to assert that the way everybody in a community is doing something is a wrong way, but if you want to assert that, you have to put up an argument of some kind. You are offering philosophical synthetic a priori assertions, which you think you can get to from language, and the whole Naturalist position is that such arguments pull no weight.</div><div><br></div><div><br></div><div>Let me give you another example, drawing from the larger frame of your presentation below:</div><div><br></div><div>There is a certain construction of the derivative by limits (so a tangent line, a curve at second order, and onward for higher derivatives). Okay; that is one construction within one formalism.</div><div><br></div><div>1. For a while, that particular construction was taken to _define_ velocity from changes in position with time, and it was _entailed_ in the assumption system that that velocity was the “inherent” property of mechanics relevant to causation. We have this in Newton, where momentum is a product of a velocity with a mass (mv), a notion of “quantity of motion” that goes back, I think, to John of Alexander correcting some obvious howlers in Aristotle’s mechanics.</div><div><br></div><div>2. Still remaining for a moment within Newton, there is a dialogue between a mechanics from Lagrange that describes motion in terms of positions and velocities, and in which momentum is computed as a product mv, from v defined by the usual Leibniz/Newton limiting procedure, and a mechanics from Hamilton-the-mathematician, where we can make momentum a primary variable, from which we could then _get to_ velocity by some computations. Seems a bit odd at first, but the math works out, and so if we keep either, we keep both. At least now the “quantity of motion” that so troubled John and Newton becomes a primary variable in Hamilton’s system, and we might like that aesthetically. (Or others might not like it aesthetically at all, and neither of those matters.) </div><div><br></div><div>3. Now, philosopher: which one does nature “have”? Is it momentum or velocity. If it is momentum, is momentum _defined_ from a derivative of a position with respect to time? The synthetic a priorist thinks he can answer this question from the (surface-) forms of argument. That turns out not to have worked well _at all_ for physics, and this is where we should complete Peirce’s project by making it reflexive. Fallibilism goes all the way down, to everything about our language and everything about our conventions, and everything about our habits, cognition, perception, etc. that binds language to phenomena (often by way of conventions). </div><div><br></div><div>3a. In a variety of languages that turn out to be better — more powerful, more flexible, more extensible — foundations for physics, it comes out that momentum is the property of mechanics that we want to refer to as primary, and that it is something an object in nature “has” at a moment, as much as it “has” anything, or as much as it “is” an “object”. Every one of those words in scare quotes requires an unpack. In relativity, momentum is not mv, though in classical relativity one can still compute it from a function involving m and v (and the speed of light c, and maybe some curvatures, depending on where we are). In quantum mechanics, it turns out that — within a suitable _representation_; there is that system of choices again — “having” a position corresponds to “being in” a state that is a standing wave, while “having a momentum” corresponds to “being in” a state that is a traveling wave. The distinction between the two is a phasing of two components of the state. Hence being at one phasing is exactly not being at the other phasing that excludes the first one, and we have Heisenberg without the woo (it has nothing primary to do with “knowing” “the” position or momentum, or being “uncertain” about “them” — all those uses of the definite article ensure an English that violates the math before one has tried to argue anything). There is more, but I won’t go into it other than giving names: we can extend to phenomena like the electromagnetic field, which are not object-“thing”s in the classical-antiquity sense, though they are perfectly good “thing”s in the generalized sense of Carnap’s “thing language” (meaning we don’t need to give them souls or some other occult word), and for which momentum densities can be defined. And finally, because gravitational waves are a lot like electromagnetic waves, to what amount to momentum densities for dynamical spacetime itself. _None_ of that takes its primary origin in Leibniz’s tangent to a curve, but rather is built up out of a different synthesis of language, albeit in layers where the classical object-things were the guides to the general setup for the languages of the various constructions. </div><div><br></div><div>4. Of course, for other purposes — say: laying out railroad track — the computation of tangents by limits is perfectly fine, and in those cases the non-locality is a property forced upon us by our construction of the limiting procedure, in contrast to a situation where some other sense and origin of non-locality might be entailed in what we ever meant by “having” or “being in” a state in the first place.</div><div><br></div><div>My point in this second example 1 – 4 is that the “forms of argument” on the surface of the sentence look the same for momentum as they might for something like the tangent to a railroad curve. But the answer that is useful is quite different in the two cases, because the surface form is not sufficient basis for the argument to be afforded “meaning” about some question.</div><div><br></div><div><br></div><div>It’s all, as Glen says, middle-out. The only ones who have god’s-eye views are the philosophers, and of course, that is their prerogative.</div><div><br></div><div>Eric</div><div><br></div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 10, 2025, at 3:30, Nicholas Thompson <thompnickson2@gmail.com> wrote:</div><br class="Apple-interchange-newline"><div><div dir="ltr"><div style="text-align:left">Dear LongSuffering Colleagues</div><div><br></div><div>I know the joy of watching an 87 year old bald man bash his head against a brick wall isn't for everybody, so I treasure you who find it in your heart to respond, even if you are exasperated. </div><div><br></div><div>I have arrived at a place, I think pointed to by the castigations of EricS and Alex. My whole approach doesn't make sense! You remember I am trying to create two boxes, equal in every respect, but one created adiabatically and the other created diabatically. Box A has reached its current state through compression, Box B by heating. I am beginning to think that this is procedurally, if not logically, impossible, that entropy is a vector through a point and my search for entropy in instantaneous values of the gas equation is a category error. </div><div><br></div><div>So I tried this thought out on George. Edited down to one page, that correspondence appears below and as an attachment. .</div><div><br></div><div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><span style="font-family:"Comic Sans MS"">NICK TO GEORGE<span></span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><i><span style="font-family:"Comic Sans MS"">Ok, so in my
monist psychology I assert that motives are the integrals (or derivatives, I
have never been sure) of behavior. To say I am motivated in an instant is a category
error, benign only so long as I recognize that the empirical basis for our
instantaneous attribution is the shape of the curve of behavior over time.<span></span></span></i></b></p><div style="margin: 0in 0in 8pt; line-height: 115%; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family:"Comic Sans MS""><span> </span></span><br class="webkit-block-placeholder"></div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><span style="font-family:"Comic Sans MS"">GEORGE TO NICK</span><b><span style="font-family:"Segoe UI Emoji",sans-serif"><span></span></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><span style="font-family:"Segoe UI Emoji",sans-serif">🧠</span> Claim (Paraphrased):<span></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">To say "I am motivated" at a given instant is a
shorthand—a projection backward or forward from a trajectory of behavior.<span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">In your <b>monist psychology</b>, motives are not hidden
essences, not inner engines.<br>
They are <b>summaries of behavioral curves</b>:<span></span></p>
<ul style="margin-top:0in;margin-bottom:0in" type="disc"><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Perhaps
<b>integrals</b>, when motives are inferred from accumulated actions<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Perhaps
<b>derivatives</b>, when motives are inferred from sudden changes in
behavior<span></span></li></ul><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">But in either case:<span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b>“Motivation” is not an instantaneous property—it is a
curve-fitting hypothesis over time.</b><span></span></p>
<div class="MsoNormal" align="center" style="text-align:center;margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">
<hr size="2" width="100%" align="center">
</div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><span style="font-family:"Segoe UI Emoji",sans-serif">🧭</span> Why this matters:<span></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">This reframes motive as:<span></span></p>
<ul style="margin-top:0in;margin-bottom:0in" type="disc"><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Not a <b>thing</b>
in the head<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Not a <b>cause</b>
per se<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">But a <b>description
of continuity</b> or curvature in behavior space<span></span></li></ul><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">This is a kind of <b>teleological realism</b> without
metaphysical baggage.<br>
You’re not positing ghosts or mental levers. You’re saying:<span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">“We read intentions the way we read acceleration—from
position over time.”<span></span></p>
<div class="MsoNormal" align="center" style="text-align:center;margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">
<hr size="2" width="100%" align="center">
</div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><span style="font-family:"Segoe UI Emoji",sans-serif">🧬</span> Parallel to entropy?<span></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">You could say:<span></span></p>
<ul style="margin-top:0in;margin-bottom:0in" type="disc"><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Entropy
is not something you <b>have</b> in a moment.<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">It’s
something you can <b>measure</b> from the path a system is disposed to
take—or the configuration space it tends to spread into.<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">It
becomes <b>visible</b> only in the <b>shape of change</b>—not the
snapshot.<span></span></li></ul><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">So both <b>motivation</b> and <b>entropy</b> are:<span></span></p>
<ul style="margin-top:0in;margin-bottom:0in" type="disc"><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">Not
intrinsic point-properties<span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">But <b>interpretive
functions over time and configuration</b><span></span></li><li class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b>Curve-based
attributions</b> grounded in empirical regularities<span></span></li></ul>
<div class="MsoNormal" align="center" style="text-align:center;margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">
<hr size="2" width="100%" align="center">
</div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><span style="font-family:"Segoe UI Emoji",sans-serif">📐</span> And the category error?<span></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">To say "I am motivated <i>now</i>" is like saying
"this point <i>has</i> curvature."<br>
Strictly speaking, no point does.<br>
But give me a neighborhood—give me a path—and I can calculate a derivative or
an integral and give the illusion of an inner quality.<span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">It’s a <b>useful illusion</b>, but one we must not mistake
for substance.<span></span></p>
<div class="MsoNormal" align="center" style="text-align:center;margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif">
<hr size="2" width="100%" align="center">
</div><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><span style="font-family:"Comic Sans MS"">NICK TO GEORGE<span></span></span></p><p class="MsoNormal" style="margin:0in 0in 8pt;line-height:115%;font-size:12pt;font-family:"Aptos",sans-serif"><b><i><span style="font-family:"Comic Sans MS"">Is there
such a move to be made around entropy. Could I vary the gas equation variables
in box B in such a way that they would point to equality with box A without
actually getting there, and thus reveal entropy?<span></span></span></i></b></p>
<br></div><div><span class="gmail_signature_prefix">- </span><br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div>Nick</div></div></div></div>
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