The quote from Kelvin is false on its face because it can’t pass its own test. That is, the categorical assertion “when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind,” should be applied to the assertion itself. Yet, we immediately see there is nothing quantifiable or measurable about the assertion—hence, per Kelvin’s own rules, his assertion is “meagre and unsatisfactory.”
Can modern information theory assign a value (or values) to the information “content” of Kelvin’s assertion or deal with Shannonesque entropy of a signal carrying that information? Sure. But information is *not* the same thing as meaning or intentionality—far from it. Information can be quantified because it depends on some material substrate.
Somehow, Mozart’s 21st piano concerto must be conveyed by symbols—whether scribbled on paper in ink or coded into a *wav or *mp3 file. But the symbols (expressed materially) are *not* the concerto itself because symbols (in this case, technically stated, “conventional signs”) are not the reality itself. Symbols/signs are a subservient reality that intentionally point to a greater reality beyond themselves. Meaning and intentionality are completely removed from and independent of any material substrate—which means these are in no way measurable.
Is that a problem? Not in the least. Why? Because quantifiability neither imposes validity nor is it a basis for judging whether something is “meagre and unsatisfactory”—unless, of course, one is an ontological reductionist who, among other things, reifies mathematical formalisms. Indeed, Baron Kelvin’s own deeply committed Christian faith is anything but “quantifiable” or “measurable”. So what? This in no way undermines Christian—or any faith. The “scientific method” (a species of the broader “epistemic cycle”) is not quantifiable in its meaning, intentionality, and operational validity. So what? This in no way undermines the wonderful epistemic tool the scientific tool is.
My point is, Baron Kelvin should have been more careful and nuanced by avoiding categorical assertions. This further implies the author should have been more careful by avoiding the assertion, “In fact, it [knowledge] is a *condition* for that articulation...” Nope. As Einstein is widely attributed to have quipped, “Not everything that can be counted counts, and not everything that counts can be counted.”