PLEASE TRY TO BE SMARTER ABOUT APPLIED MATHEMATICS THAN I AM. IT’S EASY. I AM GL

PLEASE TRY TO BE SMARTER ABOUT APPLIED MATHEMATICS THAN I AM. IT’S EASY. I AM GLAD PEOPLE DO THAT SO I DON”T HAVE TO. BUT DO NOT TRY TO BE SMARTER ABOUT THE FOUNDATIONS OF MATH (OR TRUTH) THAN I AM. OK?

> Curt Doolittle :

A priori consist of trivial examples of hypotheses. The deductive consist of trivial examples of the a priori.

There exists only one epistemic method:

observation > free association > wayfinding > hypothesis > self criticism > theory > market criticism > law.

The non-contradictory, the a priori and the deductive are simply trivial cases.

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>Robert Mosimann :

If such a simplistic view of the a priori and epistemic methods were true then

Provide the observational evidence to establish the axioms of mathematics such as

The axiom of infinity

The Power set axiom

The Generalized Continuum Hypothesis.

How about the law of Contradiction itself

Etc

Only someone not knowing much science or mathematics would consider the a priori and deductive cases to be trivial.

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Curt Doolittle:

You’re kidding me.

Let’s just take the first one.

“I promise that I observe that the method of constructing positional names that we commonly refer to as ‘natural numbers’, can be performed without limit, other than practical limit, and as such I can deduce that at least that single set of positional names satisfies the criteria of limitlessness independent of applied context that we commonly represent with the symbol *infinity*.”

Ergo: “I can truthfully claim, as a general rule of scale independence – meaning that by removing the dimensions of time, space, operations, and cost, at least one condition of infinity is possible.”

This is a trivial observation.

The Continuum Hypothesis is the most interesting because it’s stated pseudo-scientifically and appears profound. But if stated scientifically (meaning informationally complete) then it’s also trivial:

“I promise that I observe that the method of constructing position names beginning with the natural numbers all ratios thereof, that the rate of production of some positional names (numbers) will vary per operation.”

Or the law of contradiction.

“I promise that I observe that when I name a set of properties, relations, and values (category), that if I refer to (testify) a different set of properties, relations and values(category) by the same name I engage in either error or deception (falsehood).”

These are trivial statements dressed upon pseudo-scientific garb, because of the remnants of archaic platonism in the field.

The foundation of mathematics is trivial: correspondence and non-correspondence. Dimensions included, or dimensions ignored. The only challenge in mathematics is in applied math: like chess, the learning of observable patterns of transformations.

Each dimension of reality we can speak of (identity, logical, empirical, operational(existential), rational, reciprocal, and fully accounted), and each dimension of constant relations (mathematics) we can speak of (identity, number(name), arithmetic(quantity), geometry(space), calculus(motion), and algebraic geometry (pure relations), can only be tested (proved) by appeal to the subsequent dimension. (No system of logic can prove itself). Hence the necessity of axiom of choice..

Anyway. If there is anyone living who understands these matters better than I do, I would love to know. But as far as I know, there isn’t.

Cheers.