How to understand "that" in the sentence?

Question

The original text (except for the beginning and ending brackets):

[...] One should have the courage to think uncomfortably, since it is only by rejecting the convenient that one can come to think the truth.

Not, after all, that there is any such thing as truth. At best we can approach to some relative approximation. On the other hand, there is surely such a thing as untruth. [...]

My qustion is on the boldfaced "that."

Please note there should be a tab space before "Not". That sentence is the beginning of a new paragraph.

Can "that" be dropped, making the sentence as:

Not, after all, there is any such thing as truth.

Or is it a conjunction in an elided sentence, something like :

　[I would argue] that there is not any such thing as truth after all. At best we can approach to some relative approximation.

Answer 1

"Not that" is an idiomatic phrase and needs to be used in its entirety. It's used to diminish the importance of or contradict the statement that comes before it.

Examples:

He lost ten pounds, not that it matters because he still can't fit into his pants.

She's wearing a sweater, not that it's cold out.

He graduated from Harvard, not that is why he was hired.