This question appeared in a previous question.
Should I write "it stands without reason that accuracy is of utmost importance" or "it stands to reason that accuracy is of utmost importance?"
The latter is the only I can find in online dictionaries.
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The common idiom is "It stands to reason", meaning "It makes sense" or "It is expected". I've never seen any other variant, and at least some internet resources show the same.
There is a confusion in this question, over possible meanings of “reason”.
Your suggested usage “it stands without reason” implies the meaning of “it stands without requiring a reason”. This is the colloquial use of “reason” as an excuse or apologetic defense of some factual claim.
I agree with other answers that this is uncommon and unclear usage: “without reason” would imply the claim is indefensible, because it has no reason supporting it. This is pretty much the opposite of your intended meaning.
The common idiom “it stands to reason” implies the meaning “it stands when challenged by reason”. This is the primary use of “reason” as the process of critical inquiry and rational thinking about claims.
So this usage connotes a factual claim that, when others challenge it using the process of critical inquiry and demand for supporting one's claims – that is, when others use reason to interrogate it – the claim stands (does not fall) to this challenge.
"It stands to reason that ..." Is basically a synonym for "Based on the reasoning provided, ...". For example,
He treated you like dirt! It stands to reason that you're having second thoughts!
"It stands without reason that ..." I have always understood to mean, "It needs no explanation that ...". For example,
It stands without reason that he should treat you like a princess.
But as we have seen, this idiom doesn't appear in any significant usage on the Internet so it could be a regionalism or just my own mistake. If it were my paper, I would use "it needs no explanation".