Pallmann has responded to me again. He remarks that my criticisms have verged on the bizarre. Perhaps I have been unclear. To rectify this, I will recount our dialectic here and hopefully eliminate any misunderstandings.

Pallmann has stated and implied in his videos that Aristotle’s TA is unsound because it does not rule out competing perspectives on logic. For example, Aristotle’s TA is consistent with paraconsistent logic, even though it is used to defend classical logic. In other words, Pallmann accuses Aristotle’s TA of underdetermination.

So Pallmann submits his own method of justifying classical logic, one aimed at avoiding this underdetermination issue. We’ll get to that in a moment. First, it needs to observed that Pallmann’s objection to Aristotle’s TA is ambiguous.

Does Pallmann mean to say that because we know non-classical logics are possible, Aristotle’s TA fails? Or does Pallmann mean to that even though we know non-classical logics are impossible, Aristotle’s TA isn’t a good way to deal with them?

My objection has assumed the former, but it needn’t do so. I’ll expand my response into two prongs, a strong and a moderate objection. If Pallmann’s argument includes as a premise the possibility of non-classical logics, the strong objection applies. If he rather means to say Aristotle’s TA does not rule out non-classical logic and so fails to justify classical logic, then the moderate objection applies.

The strong objection goes like this. Pallmann’s argument (against Aristotle’s TA) has as a premise the possibility of non-classical logic. So if his argument is sound, then Pallmann suffers the same underdetermination he projects on Aristotle. This is a straightforward case of self-refutation. So it’s probable that this just isn’t what Pallmann meant – hence all the confusion in our dialogue so far.

To understand the moderate objection, let’s first clarify how Pallmann intends to justify classical logic. Pallmann submits a justification that is intended to avoid the underdetermination that plagues Aristotle’s justification of classical logic. What does Pallmann’s justification have that Aristotle’s doesn’t?

Analyticity. Pallmann suggests that classical logic is just analytically true, like that a square has four sides or that a bachelor is unmarried. Therefore, by merely ruminating on the concept of logic, we arrive inevitably at its classical version.

The moderate objection goes like this. Pallmann’s appeal to analyticity does not favor one system of logic any better than another. A dialetheist is perfectly capable of asserting that dialetheism is analytically true. A trivialist is perfectly capable of asserting that trivialism is analytically true. Repeat for relevant logic, intuitionism, and the whole host of other systems that have been outlined in the history of philosophy. In a great twist of irony, Pallmann’s analyticity-justification is, at best, in the same underdetermined boat as Aristotle’s TA, and at worst, is just subjectivism parading as conceptual analysis.

To illustrate this point, imagine two logicians, John and Jill. Jill claims dialetheism is analytically true. John claims the same for classical logic. How should we adjudicate who has the right concept? In fact, why even suppose that either of them has rightly conceived logic at all? On Pallmann’s naive epistemology, all we could do is add further claims to analyticity!

Is multiplying assertions really the best justification Pallmann’s epistemology has? Maybe not. In the end, I suspect Pallmann will resort to his direct acquaintance narrative. And of course, the dialetheist, trivialist, et al, are welcome to take up the same narrative.

Of course, all this amounts to is people appealing to their own imagination – their own ideas of logic. We have a word for this: subjectivism. It’s not only intellectually vacuous, but in the case of inference, a well-documented fallacy.

To sum-up, the strong objection is that Pallmann would be critiquing his own attempt to justify classical logic even as he critiques Aristotle’s attempt. The moderate objection is that Pallmann’s alternative not only face the same underdetermination, but reduces to a case of drooling subjectivism.