Commensurability 4.0

Actually, in strengthening the demarcations between the different levels of commensurability, I no longer consider any level viable below level 3. Level 3 now denotes the impossibility in principle of non-coercive agreement, due to fundamental divergence of basic assumptions. It is now, therefore, a proper Kuhnian account of Kuhnian incommensurability. In order to contain a level below 3, therefore, one would have to be saying that at this level, the possibility of forming cogent arguments for or against the claim in question is impossible. Yet this cannot be the case if we are meant to understand any one dispute as simply involving the truth-value of a specific claim (as I do). Let's suppose for the sake of a reductio ad absurdum that a level 4 dispute is in fact possible. If you cannot form a cogent argument that proposition A is true, say, then this ipso facto constitutes a commenusurately cogent argument that not-A is true, and therefore falls under a level 2, not a level 4, debate. In other words, the supposition that level 4 debate is possible is shown to be logically contradictory. The fact that a cogent argument cannot be made on one side of the debate is itself evidence of a commonality of assumptions making level 2 debate possible.

This is a major revision of version 3.1, and therefore will be called version 4.0.