We have the 5 Peano Axioms for the natural numbers. The 5th axiom is the principle of induction. If a set contains 0 and contains the successor of each natural number in it, then it contains all natural numbers. This is a principle of proof.

What is the difference between saying the 5th axiom is a principle of proof and saying it is a principle of faith?

If proof is an axiom, then why can’t faith be an axiom? Why is not a proof by the proof axiom equivalent to faith from the faith axiom? Are they not parallel?

The proof axiom and the faith axiom are parallel.

Do we choose a system of axioms? A system like the Peano Axioms is something we choose? Or something that we accept?

Do we really go around choosing which math axioms we believe? Or we just believe them? In practice, we just believe them.

So they are axioms of faith. They are convenient to human existence so we accept them?

So if the axiom of God or axiom of Faith is convenient to human existence, we accept them as well?

Numbers are on an equal footing as God?

Turn it around. We find that for the existence of the numbers, 0,1,2, etc. we need an axiom. Do we then turn around and say because we need an axiom, we doubt numbers exist? Not at all. We never doubt their existence. So why do we not come to doubt them when we find their existence requires an axiom that can’t be proved?

Then why should we doubt God’s existence because we find it needs an axiom that must be proved?

We use number axioms because they are convenient to our knowledge of numbers.

So why do we not use a God axiom because it is convenient to our knowledge of the universe? Or of moral things? Or moral practice?

Applications justify the number axioms? I.e. works?

Then why don’t works justify the Faith Axiom?

Is it really a choice? Do we really choose whether to believe the axioms of math? Have we met a person who chooses not to believe them?

Is belief in God likewise determined for us? By an act of Grace?

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## About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition.
President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.