Do you see the contradiction?
No, because a logical reasoning process is not necessarily a formal logical argument.
logical
Logical describes something that comes from clear reasoning. Using a fire extinguisher to put it out a fire is a
logical step. Trying to put it out with gasoline is not.
The adjective
logical is rooted in the Greek word
logos, which means "reason, idea, or word." So calling something logical means it's based on reason and sound ideas — in other words, thought out with mathematical precision and removed from emotion. Sounds strict and boring, but it's the orderliness and consistency of logic that helps you write a great argument or figure out how to solve a problem.
Logical - Definition, Meaning & Synonyms
You have now a step in your logical reasoning process that is neither an axiom nor proven or in evidence.
Your logic has a hole.
Just because a reasoning process is logical that does not mean it is being presented as a formal logical argument.
Let me explain by citing an example.
If the premise Baha’u’llah was a Messenger of God is true, then the conclusion God exists must be true.
However, since I can never prove the premise Baha’u’llah was a Messenger of God is true, I cannot conclude that God exists is true.
And that is why I am not presenting a formal logical argument.