The failure of post modern philosophy is a failure of the scientific method.

[surreptitious57]

Pi is not infinite Pi is irrational

In practice its as finite as your best approximation

An irrational number has an infinite number of digits or decimal places
All approximations of pi are finite because they can never be complete

For to express pi to infinity would require infinite time and even then you would never get to the end
Not even if you had a quantum computer calculating at the speed of light forever would you get there

However this is not necessary because irrational numbers are determined mathematically not empirically

[Logik]

An irrational number has an infinite number of digits or decimal places

In theory.

All approximations of pi are finite because they can never be complete

In practice.

For to express pi to infinity would require infinite time and even then you would never get to the end
Not even if you had a quantum computer calculating at the speed of light forever would you get there

Indeed. Because you don't live in a theoretical universe.

However this is not necessary because irrational numbers are determined mathematically not empirically

Mathematicians live in theoretical world. Pi is not determined. Pi is defined.
We defined it. As the proportion of a circle's radius to its diameter.

Circles don't exist in the practical universe. They are only mental abstractions.
Numbers don't exist in the practical universe. They are only mental abstractions.

Tools.

[Eodnhoj7]

I claim that infinity is not a useful concept for a finite mind.

You want me to define "finiteness"? Limits.

Limited time.
Limited energy.
Limited observations.
Limited decisions.
Limited samples/experiments.
Limited sets.
Limited number of integers.
Limited precision.

Bounded rationality.

And describe "x" (with "x" observing all the "axioms" the axiom of "limit" is connected to...rofl; law 2 and 3) without going into an limited regress.

Second, are these the only "phenomenon" which have limits? If they are not, then your finite definition is irrational.

Nonsense. If you insist on completeness then the prime triad is also incomplete.

If there are infinite axioms, please go ahead and list them. Not some of them. All of them.

I'll drink some wine while you get on with it.

False, the prime triad is axiomatic as it is grounded in assumption. All axioms are assumed with proof being the connection of assumptions also being assumed as all proof as the connection of axioms exist as axioms in themselves connected to further axioms.

The prime triad is complete as "assumed".

The prime triad is also incomplete as "unassumed" in the respect it exists through all further axioms. As unassumed/incomplete it still requires further assumed axioms to observe it...hence it becomes self-referening.

This contradictory state observes the prime triad as a contradiction. However all contradiction is assumed "polarity" where one axiom exists in a differential state to another axiom. Hence even "division", which sets the foundation for contradiction, is "assumed" and we are left with the prime triad as again complete.

The prime triad observes progressive completion.