LET ME SlMPLlFY TO FIRST PRINCIPLES: “Mathematics is a simple language (Grammar of continuous recursive disambiguation), consisting of one noun(Positional Name), one operation (Addition-Subtraction), and one agreement (Equality).
This is the most reductive (simple) language possible. The combination of arbitrary correspondence (what the number refers to), and ordinality(position in the order), produce context independence and scale-independence. There are no context-independent and scale-independent measurements in physics (or in any aspect of reality).
Likewise, this is why mathematics fails at the very small (quantum background), and very large (economics): because causal density is not reducible to a generalization in either case. Meaning all of mathematics is fundamentally statistical (reductive). As such, as we have complained, by criticizing Cantor for over a century, there are no in?nities. Only unachievables and unknowns.
In other words, never mix mathematical LANGUAGE (?ction) with physical MEASUREMENTS (description).
The fact that mathematicians dont’ know the foundations of mathematics as other than sets (language) and philosophers don’t know that all sophistry consists of failure to respect the ?rst rule of grammar (continuous recursive disambiguation to the point of unambiguity (identity)), is a symptom of one of the many catastrophic failures in the intelligentsia and academy in the pre-war period, and the ‘credentialism’ in the academy in the postwar period.
There is no evidence that the number of people contributing to primary knowledge has increased since 1900. This should terrify us. And we should ask why. And this simple example, in this paragraph illustrates why: verbalism(idealism(sophistry)) vs action(existence (testimony)).
(And yes, I know this is word salad for those that don’t understand the problem. There are however a number of us who do.)