Assume that doubt is meaningfully defined. Or let's say we define doubt as , both the statement under doubt, and it's complement can be true or false, we do not know, the uncertainty exists.
Imagine an ultimate doubter.
In this scenario, the doubter can doubt everything, including him being in doubt.
The doubter can make the sentence “I doubt that I am doubting”.
This sentence does not break reasoning.
Let me explain how.
I doubt (A), that I am doubting(B).
These are two different levels of doubt. This is a self referential doubt.
Doubting that “I am doubting”, does not mean that the doubter is not doubting. Doubting entails both the possibilities, “I am doubting”, can be true, or “I am doubting” can be false.
So the chain of recursion goes something like this:
“I am doubting”, is True. (1) “I doubt(A), that I am doubting(B)”, is also True. (2)
But, in (2), (B) is true under doubt or statement (A), and since (B), is in doubt, it is not as True as (1).
Again, the order of statements matter quite a lot.
Consider the sentence,
“I doubt (A), that I am not doubting(C)” (3), for example
This(C) is false, since we have already established in (A) that we are doubting, so it’s complement in a sense, that “I doubt, that I am doubting”, has to be True.
Or, am I wrong somewhere in logic? ( I get my obvious current mistake, but trying to reword it meaningfully)