Definitions:

Objective = exists independent of anyone's mental state

Subjective = does not exist independent of anyone's mental state

Terminology:

MP = Modus Ponens

MPF = MP is flawless

MV = mental verification that MPF

Argument Part 1:

Let's take MP as an example,

1) A

2) A → B

3) ∴ B

To mentally verify that MPF, you need to think very carefully... but to do so, you must use memory.

1) Your memory is fallible

2) Your memory is fallible → your MV may be wrong

3) ∴ Your MV may be wrong

Argument Part 2:

Let's assume that your memory did not fail you... but you still had to execute a process of thought when thinking very carefully.

1) Your thought process is fallible

2) Your thought process is fallible → your MV may be wrong

3) ∴ Your MV may be wrong

Argument Part 3:

Let's assume that your thought process executed correctly.

Still, MP is not necessarily flawless because "your MV" does not equal "MPF".

"Your MV" is a subjective idea.

"MPF" is an objective claim (of fact).

Therefore "your MV" does not equal "MPF".

Argument Part 4:

We cannot yet use "Your MV necessarily implies that MPF" because it carries with it the burden of proof which has not yet been satisfied, congruent to its generalized form "Your subjective idea that an objective claim is a fact necessarily implies that that objective claim is a fact".

Argument Part 5:

Therefore we may never know whether MP has a flaw.

Therefore MP may have a flaw.

Since MP is a part of propositional logic,

Conclusion:

Propositional logic may have a flaw.

Questions:

1) Is the conclusion true by default? If no, why not?2) I've used propositional logic in this argument, so does the conclusion still hold?

3) In my argument, I assumed that the flawlessness property of propositional logic is objective, is that correct? Why or why not?