BW: Odd contrast, since disparity is a fact in reality, whereas analogy is a mental process. There's certainly plenty of divergence in evolution, but very little convergence. Communication facilitates a convergence of knowledge and understanding, but only rarely a new divergence. Dialectics are useful tools for resolving conflicting ideas, but nature doesn't do dialectics.
[GB: Of course, analogy and disparity are both mental processes. So analogy occurs when things are brought together and are considered to be similar and disparity occurs when things are brought apart and are considered to be dissimilar. Sorry, but evolution involves equal amounts of divergence and convergence. You are right that communication is a convergence (how could it be otherwise). As I have said before, it is definitely not true that nature doesn't do dialectics. In the infinite universe, things are always moving together or apart—pretty simple.]
BW: To the degree that it doesn't reflect reality, it is demonstrably false.
[GB: Of course.]
TSW: "... The third level is an attempt to compare the measurements themselves in an objective way."
BW: Pleased to see your commentary "evolving" to an appreciation of objectivity. It should be one of the primary "assumptions" of science, which is always seeking objective truths about reality, rather than vague, whimsical, arbitrary, or subjective impressions.
TSW: "... mathematize the comparison ..."
BW: I don't think math is the Sine Qua Non of objectivity. Yes, quantitative distinctions are important, but not at the expense of qualitative features. Mathematics is fine when it uses numbers, but it frequently adopts symbols to represent Westmiller Things, without defining them. For example, the "v" of velocity doesn't indicate whether the attribute is relative (translational) or objective (rotational). The frame of reference is missing and frequently confused. There are still many physicists who use "pure energy" terminology, as though it were disconnected from mass and velocity.
TSW: "Pi, for example, can be calculated at least a million more decimal places than it can be measured. The diameter and circumference of a real circle fluctuates over time; only the imagined, 'ideal' circle does not."
BW: I think Pi is a good argument against the existence of "real circles", or even "ideal" ones. I won't elaborate.
Your SIMAN coefficient sounds useful for some applications, but not for comparing Westmiller Things. What is the similarity index between gravity and acceleration? How "equivalent" are they?
TSW: David Bohm: "Because every kind of thing is defined only through an inexhaustible set of qualities each having a certain degree of relative autonomy, such a thing can and indeed must be unique; i.e. not completely identical with any other thing in the universe, however similar the two things may be."
BW: That defeats the entire purpose of a definition, which requires differentiation and integration. See the Ayn Rand commentary linked above for the "rules of correct definition", with which I agree.
[GB: Now you are starting to catch on. Because everything in the universe has an “inexhaustible set of qualities,” we need to tame the observed microcosmic and macrocosmic infinity through “definition.” In other words, we need to call “finis” to each xyz portion of the universe to be able to speak, think, or write about it. For instance, the categories clay, silt, sand, and gravel can only be defined through the application of arbitrary particle size limits. By convention, scientists and engineers have agreed upon what those limits should be. They have not been defeated by the inexhaustible particle size continuum!
BW: It is always possible that there are pigs that fly. If so, the definition of "pig" (or "electron") will remain the same, but we will have a new identity for a different animal, maybe called a "pyg", for flying pigs. See my prior notes about your claim that there are "three kinds of electron" (I couldn't find the Ernest Nagel citation anywhere on the net).
BTW: In UT [Bill’s Unimid Theory], electrons do have a slightly different shape, depending on their reference orbital shell or transmission context. But, they're all the same mass and configuration (of Unimids).
BW: Actually, it wasn't "intensity", but frequency. It didn't indicate that beta particles violated parity, but rather that neutrinos had two distinct spin configurations, prompting one to be labeled an "anti-neutrino". I hate the prefix, which implies that the object is the opposite of a neutrino, when it is just a "left-neutrino", which could be called a "leutrino", as distinct from a "reutrino".
TSW: "As a result, the comparisons that we make in science and in everyday life have a single criterion for validity: usefulness."
BW: Material efficacy is just a consequence of truth. It may be "useful" to imagine a Loving God, or even believe in one, but that doesn't make the conception valid.
BW: Finally, it's very strange that you would not discuss Einstein's Theories of Relativity in a chapter titled "Relativism". It certainly seems "relevant" to "relativism". Maybe I'll find something later in the book.