Commensurability 2.0
The more I think about it, the more I do not like that existing account of commensurability I devised. I think that it is just too inconsistent with the way that that word is used elsewhere, particularly with its dictionary definition. For example, if both sides can agree that a view is false, then the view does not have agreeability. But one should still be able to say that it is at level 2, because both sides can agree on its truth or falsity. It is still measurable by the common standard of rational discourse, to the extent that people can reach non-coercive agreement about its truth or falsity.
Level 1, therefore, as triviality, should mean that a claim is trivially either true or false. That is, there should be an already existing convergence of opinion about its truth or falsity. Hence, "The pope is Catholic" is at level 1 because it is trivially true, but "The moon is made of green cheese" is also at level 1, because it is trivially false.
Level 3 is still a viable level of commensurability. It denotes claims where one cannot reach non-coercive agreement about their truth or falsity but one can form respectable arguments for or against them. A respectable view is one that is worth pursuing, even if only because it is not absurd, hence not to be dismissed offhand.
What, therefore, happens to level 4? I used to think that a view that was absurd was below level 4, but such views are now properly at level 1. As to what a view would be like that was at level 4, I think that one can still fruitfully consider the example of theism. One can debate whether theism is intellectually respectable, but various religious views seem not necessarily to be intellectually respectable; it is simply that that is not the point of them in the first place. They do not have to be respectable in order for someone to hold them without being given a hard time about it. This is because the views are still appreciable, in the sense that one can appreciate the reasons why one would hold such a view. An appreciable view, as such, seems somewhat beyond the pale of rationality because it is protected by human sympathy. Level 4, therefore, still seems to be a viable level of commensurability.
What happens to level 5, as comprehensibility? Well, views that are comprehensible but not appreciable are at level 1, as absurdities, and views that are comprehensible but appreciable are at level 4. Views that are incomprehensible are not at level 5, because level 5 is comprehensibility in the first place. I would imagine, therefore, that that means that level 5 is not longer a viable level of commensurability.
What happens to level 6, as thematicity? Well, bona fide views that are not comprehensible will be at level 6, but it will be impossible to tell this because they are not comprehensible, and non-views will not be at level 6 to begin with. It would seem, therefore, that thematicity is not a particularly useful level. Even if something were to be at level 6, this fact would be unverifiable, because if it were, it would be at a level higher than 6.
Therefore, under the new system, the bottom two levels are no longer useful, and should be scrapped. This leaves just four levels. The maximum limit for the new kind of commensurability is still 1, because one cannot get any more commensurable than an already existing convergence of opinion about something's truth or falsity. The minimum limit is still 4, because this defines what falls outside the pale of rationality to begin with. No level can be lower, because a view that lacked appreciability would be at level 1 as an absurdity.
Level 1, therefore, as triviality, should mean that a claim is trivially either true or false. That is, there should be an already existing convergence of opinion about its truth or falsity. Hence, "The pope is Catholic" is at level 1 because it is trivially true, but "The moon is made of green cheese" is also at level 1, because it is trivially false.
Level 3 is still a viable level of commensurability. It denotes claims where one cannot reach non-coercive agreement about their truth or falsity but one can form respectable arguments for or against them. A respectable view is one that is worth pursuing, even if only because it is not absurd, hence not to be dismissed offhand.
What, therefore, happens to level 4? I used to think that a view that was absurd was below level 4, but such views are now properly at level 1. As to what a view would be like that was at level 4, I think that one can still fruitfully consider the example of theism. One can debate whether theism is intellectually respectable, but various religious views seem not necessarily to be intellectually respectable; it is simply that that is not the point of them in the first place. They do not have to be respectable in order for someone to hold them without being given a hard time about it. This is because the views are still appreciable, in the sense that one can appreciate the reasons why one would hold such a view. An appreciable view, as such, seems somewhat beyond the pale of rationality because it is protected by human sympathy. Level 4, therefore, still seems to be a viable level of commensurability.
What happens to level 5, as comprehensibility? Well, views that are comprehensible but not appreciable are at level 1, as absurdities, and views that are comprehensible but appreciable are at level 4. Views that are incomprehensible are not at level 5, because level 5 is comprehensibility in the first place. I would imagine, therefore, that that means that level 5 is not longer a viable level of commensurability.
What happens to level 6, as thematicity? Well, bona fide views that are not comprehensible will be at level 6, but it will be impossible to tell this because they are not comprehensible, and non-views will not be at level 6 to begin with. It would seem, therefore, that thematicity is not a particularly useful level. Even if something were to be at level 6, this fact would be unverifiable, because if it were, it would be at a level higher than 6.
Therefore, under the new system, the bottom two levels are no longer useful, and should be scrapped. This leaves just four levels. The maximum limit for the new kind of commensurability is still 1, because one cannot get any more commensurable than an already existing convergence of opinion about something's truth or falsity. The minimum limit is still 4, because this defines what falls outside the pale of rationality to begin with. No level can be lower, because a view that lacked appreciability would be at level 1 as an absurdity.
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