Where Does The Idea Of Infinity Come From?

Kane,

Mathematics consists in a deflationary vocabulary, grammar, and syntax, with some conflationary vocabulary for the purposes of verbal convenience.

The content of that vocabulary consists of names of positions (Nouns), and Operations (verbs). The grammar provides a very limited means of organizing those nouns and verbs. The syntax provides hints for organizing operations and vocabulary within the grammar.

We use glyphs to represent a positional names.

We use decimal systems (or other bases) to generate positional names.

All numbers(positional names) consist entirely of names of positions with constant relations.

Using names for positions to pair off any item of any category, creates categorical independence.

Using names for positions forces constant relations, and scale independence,.

Using positional name then yields correspondence under categorical independence, and scale independence while preserving constant relations.

Positional names provide perfect commensurability.

All operations on numbers (positional names) are reducible to addition or subtraction of positions.

All positional names other than the natural numbers (base positional names) must be produced through functions.

We use inflationary grammar (conflation) to label reducible and non-reducible functions to numbers – a verbal convenience.

We use the deflationary grammar of mathematics to remove scale dependence – thereby creating the requirement for limits.

We use the deflationary grammar of mathematics removes time-to-perform any operation (Function) – thereby creating the requirement for infinity.

We restore scale dependence and eliminate infinity in any and every application of mathematics. By restoring pairing off (context) we eliminate both limits (minimums) and infinity (maximums)

In other words, as Babbage demonstrated, all computation can be produced through gears.

If you were to use gears to discuss infinity, you would find that different gear ratios produce new positional names at different rates.

All mathematical platonism is false (magic).

If mathematics were taught operationally, and as a sequence of technical problems of measurement that we needed to solve as we increased the scales of our perception and action, we would not lose so many people who become confused at the apparent ‘magic’ of the discipline.

This is the curse of mathematics profession. It is still operating with ‘magical’ or ‘priestly’ language.

When its a terribly simple discipline. The art of composing sentences (expressions) that describe phenomenon in the language of constant relations (mathematics), should be no more difficult than learning any other language. Most of it is learning nuance. Just as learning all other languages requires a bit of nuance.