> rigor and logical coherence are the same thing

Well, you are the one who introduced the term "rigor" into the discussion, but you didn't define it so I had to infer what you meant, and the only clue I had to go on is that, whatever you meant, it was at odds with "practicality". So I assumed that "rigor" meant something like, "thoroughly and explicitly attending to all of the details of an argument, defining all the terms, making all the assumptions and logical reasoning steps explicit" or something like that. So sweeping some of the details of rigor under the rug in service of "practicality" was an acceptable transgression.

On the other hand, I am the one who introduced the term "logical coherence" so I'm the one who gets to say what it means: a logically coherent argument is one which is not based on any transparent contradictions or logical fallacies. On this view, rigor and logical coherence are orthogonal. You can have a rigorous argument that is not logically coherent (here is an example: https://math.hmc.edu/funfacts/one-equals-zero/), and you can have a logically coherent argument that is not rigorous. You can even have an argument that is both rigorous and logically coherent but is nonetheless wrong. But a logically incoherent argument cannot be correct. Logical coherence is necessary but not sufficient for correctness.

It doesn't really matter. What matters is that "rigor", on your view, is something that can be casually sacrificed on the alter of "practicality". Logical coherence is not. If you sacrifice logical coherence you abandon all pretense of hewing to logic and reason, and your position is no longer worthy of serious consideration or rebuttal beyond the observation that it is logically incoherent.

What makes your position logically incoherent is that you are taking a position on what it takes to truly "understand" the second law, but you are unable even to define the word "temperature". Your first attempt was literally a joke, and your second was based on a logical contradiction. And BTW, when I pointed this out, your response began with "You are kinda right :D"

No, I'm not "kinda right". I am right, full stop, no smiley. Your stated position includes both P (there are no perfect insulators) and NOT P (it is possible for two systems to be in thermal equilibrium with each other). And this is not an inference, you were absolutely adamant about both of these things:

> [P]erfect insulators do not exist" is not a statement about how difficult it is to solve some engineering problem. It is an absolute statement with certainty equal to that of "√2 is irrational" or "you can not solve the halting problem".

> According to the zeroth law of thermodynamics, if bodies A and B are in thermal equilibrium (no heat transfer) and bodies B and C are in thermal equilibrium, then A and C are also in thermal equilibrium. Use this equivalence property to tag all bodies that belong to the same equivalence class. This tag is your measure of temperature. It is an arbitrary (ordered) scale.

I don't need to know anything else to know that what you are saying is wrong, just as I don't need to know the details of a perpetual motion machine design to know that it won't work. (Though it certainly doesn't hurt to further observe that what you are saying is at odds with the SI definition of the Kelvin, to say nothing of the fact that I can accurately predict how much electricity it will take to boil a cup of water.)

BTW...

> It is truly silly to share a pop-sci blurb from NIST in this situation.

That citation was more for the benefit of lurkers than it was for you. You have clearly buried any desire to seek the truth under layers of defensiveness that are far beyond my ability to penetrate.

NIST is quite literally in the business of defining physical quantities in ways that allows them to be accurately measured, and also of communicating to the public how their work is done. If you think it is "silly" to cite one of their official publications in the context of a discussion of the pedagogy of the second law, well, all I can say is that I feel sorry for your students. I really urge you to try to develop a little more empathy for your audience, because if you don't you are going to do a tremendous amount of damage.