October 28th, 2018 8:43 AM
AGAIN: OPERATIONS (REAL) VS SETS (IDEAL) – CANTOR AS AN EXAMPLE OF THE PROBLEM IN MATHEMATICS AND BY EXTENSION EVERYTHING.
—“Ok but Cantor’s work is specifically set-theoretic, not analytical. Also, an infinite sum is by definition a sum over a countable set. So cantor’s notions are in fact relevant for this.”—Alex Pareto
Yes it is a sacred cow because people who are (knowingly or unknowingly) mathematical platonists are just as indoctrinated into superstitious nonsense as people who are indoctrinated into platonism proper, and people indoctrinated into theology. They know how to DO what they do (meaning make arguments with the objects, relations, and values of their vocabulary and grammar) but they don’t know how and why what they do functions.
Frequencies are the scientific description and infinities (sizes) the fictional (imaginary) description. The difference is that those of us who work in the sciences, where we CANNOT engage in Platonism, because that is the purpose of science: to prevent such ‘magical’ speech, and instead force us to undrestand the causal relations between reality and our speech.
So in this case a number consists of nothing more than the name of a position. That’s it. Mathematics consists of the vocabulary and grammar of positional names. Nothing more. Period.
We generate positional names by the process of positional naming. We can scientifically describe that process as did Babbage, Turing, and Computer Science (consisting of nothing but addition), with gears, or the positional equivalent of gears (positional names), or the electronic-switch(memory) of positional names, and use these gears to produce positional names and operations on positional names at varying speeds. We can also tell a ‘story’ about those things (a fiction) which is what we do with literary, symbolic, and set mathematics. And then we can tell a fairy tale about sets, as if they are an equivalent to red riding hood.
But no matter what we do, operationally, (scientifically) all we can do is produce a series of positional names faster or slower than another series of positional names.
Ergo, there exists only one name “infinity” for “unknown limit of operations” and different rates (frequencies) by which we generate positional names, using any set of operations with which we produce positional names.
This is why mathematics ‘went off the rails’ into fictionalism despite Poincare’s and others efforts at the beginning of the 20th century. Math is just the use of positional names which have only one property: position, and therefore only ONE constant relation: position.
All logic consists of the study of constant relations, and as such mathematics provides the most commensurable language of constant relations, since it has only ONE constant relation: position.