I’m guessing you disagree with Elizier’s thoughts on Reductionism, then?
The 7-denialists are making a circular argument with your first defence of their posistion. Circular arguments aren’t self-evidently wrong, but they are self-evidently not evidence as there isn’t justification for believing any of them. The argument for conventional modus ponens is not a circular argument.
The second argument would be that the 7-denialists are making an additional assumption they haven’t proven, whilst the Foundationalist Skeptic starts with no assumptions. That there is an inconsistency in 7 being prime needs demonstrating, after all. If you redefine Prime to exclude 7 then it is strictly correct and we don’t have a disagreement, but we don’t need a different logic for that. (And the standard defintition of Prime is more mathematically useful)
Finally, the Foundationalist Skeptic would argue that they aren’t using something to prove itself- they are starting from no starting assumptions whatsoever. I have concluded, as I mentioned, that there is a problem with their posistion, but not the one you claim.
I’m guessing you disagree with Elizier’s thoughts on Reductionism, then?
The 7-denialists are making a circular argument with your first defence of their posistion. Circular arguments aren’t self-evidently wrong, but they are self-evidently not evidence as there isn’t justification for believing any of them. The argument for conventional modus ponens is not a circular argument.
The second argument would be that the 7-denialists are making an additional assumption they haven’t proven, whilst the Foundationalist Skeptic starts with no assumptions. That there is an inconsistency in 7 being prime needs demonstrating, after all. If you redefine Prime to exclude 7 then it is strictly correct and we don’t have a disagreement, but we don’t need a different logic for that. (And the standard defintition of Prime is more mathematically useful)
Finally, the Foundationalist Skeptic would argue that they aren’t using something to prove itself- they are starting from no starting assumptions whatsoever. I have concluded, as I mentioned, that there is a problem with their posistion, but not the one you claim.