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Sometimes one man's modus ponens is another's modus tollens, but to a third it is modus delens, the method that erases or destroys: the argument from the premises to the conclusion is rejected.

Do you think any of the examples are better termed 'modus delens'?

I don't think those fit the pattern, although in discursive English it can be difficult to carve a line separating the A from the A ⊃ B. But modus delens is the right response to many arguments of conspiracy theorists and pseudoscientists who proceed from unobjectionable premises to fantastic conclusions by broken reasoning.

Could you say more about this? Googling “modus delens” appears to be fruitless, and it’s not immediately clear to me what you could mean.

I made up the name for a faux aura of mediaeval scholarship.

Modus ponens: I accept A and A ⊃ B, therefore accept B.

Modus tollens: I deny B and accept A ⊃ B, therefore deny A.

Modus delens: I accept A and deny B, therefore deny A ⊃ B.

Thanks. Yeah, that’s a good point. I wonder how common this sort of response is, relative to the others? (And how often it’s correct?)

The examples in the buckets error post have "modus delens" as the correct response. To take the diet example from the post, A = "diet worth being on", B = "zero studies suggesting health risks". Adam has stored in his brain, and Betty presents , so Adam's brain computes . The "protecting epistemology" move is to instead adamantly believe A ("I need to stay motivated!") which ends up rejecting what Betty said. But the desired response is to instead deny B but also accept A, and hence to deny the implication .

So in these buckets error examples, modus ponens corresponds to the "automatic" reasoning, modus tollens corresponds to the "flinching away from the truth" move, and modus delens corresponds to the "rational" move that avoids the buckets error.

I explained this more in a comment on the post.

I can't comment as to the relative frequency of this response and how often it's correct (this sort of question seems difficult to answer).