Incorrect. Our reasoning has much to do with our ideals and reasoning is the start of reaching a logical conclusion.
One man looks at the sky day after day and also observes the night sky and reaches the conclusion that everything revolves around the earth.
Another man does the same thing using a telescope to observe the other planets and seeing how all the planets move in relation to each other. He concludes that the earth rotates.
Both are logical, one is wrong.
Actually NONE of the two are logical in the form you presented them.
But i think I understand what you want to say.
As I said already logic deals with formal sentences and their conclusiveness.
I think we are not so far apart as you might believe but the difference nontheless is crucial.
Reasoning is what you actually talk about, namely thinking about how things could be or are. For that reasoning we use logic. Logic however is only a ruleset for determining if an assembly of arguments and statements is in itself conclusive without regard to some "outer" truth.
In your example (and in order to understand what i have said last time).
The men observing the sky have different initial assumptions or premisses that you didnt state of course.
Man 1:
1) Earth stands fixed (Premisse)
2) I see the sky moving in relation to earth
3) Ergo: the sky moves
Man2:
1) the sky is fixed (premisse)
2) I see the sky moving in relation to earth
3) Ergo: The earth rotates.
BOTH are logically sound arguments. The problem in both cases lies within the premisse.
Thats why i stated that logic is unrelated to "ideals".
Logic is only the set of rules by which you evaluate the formulations 1-3.
Its not what you use in order to make a statement about the premisses.
Another example perhaps:
Logically correct you can state:
a) All froos are beags
b) Tom is a froo
c) Ergo he is a beag.
Thats correct and still totally nonsense because there exist no definition or term for froo or beag.
You can of course logically conclusively formulate that for example Jesus was born to the virgin mary.
1) The Bible is literaly correct
2) the Bible states Jesus was born to the virgin Mary
3) Ergo: Jesus was born to the virgin Mary
All however rests with the premisse.
If one were to ask now how to proove that the premisse is true we would fall into a circular problem however.
You can also logically conclusively formulate that for example God doesnt exist.
Thats where the question of completeness gets interesting.
I accept a different set of facts than you but that does not make my logic incorrect, it means that I am applying different criteria to my reasoning.
Let me try to find a consensus here ok?
What you perhaps mean (and i would agree) is that you use different premisses and assumptions than me and using your assumptions you can still formulate a logically sound argument. I would not in general contradict this. Of course one can "reason" within his own set premisses.
The question is very often how good the premisses are.
And my claim here would be that the premisses you use and the ones that others use are not equal in quality.