Friday, September 12, 2008

Logical Judgment

Still moving, and with settling in and the like, posting will likely be light over the next week or two.

I've been looking into the theory of logical judgments, an area of logic that isn't much studied (at least as such) these days, but used to be considered quite important; so I was reading up on Kant's account of logical judgment, and, in particular, Robert Hanna's very good discussion of it in the SEP. I recently realized, although I don't think it was from Kant, that it makes at least a bit of sense to take judgment to be the quality of the predicate of the meta-proposition. That is, suppose we take a proposition,

All black cats are ninjas.

Assuming that this sentence is not intended to be ironic, the proposition expressed by it it has affirmative judgment. This is the same as to say,

The proposition, All Black cats are ninjas, is true

expresses a proposition with affirmative quality. If the proposition at hand is expressed by the sentence,

It is not the case that all black cats are ninjas,

then, assuming again that it is not ironic, it has negative judgment. This is as much as to say that

The proposition, All black cats are ninjas, is not true


expresses a proposition with negative quality. The result remains stable when we factor in modality, which is the part that really makes me think this way of looking at it has promise. If I say without irony,

It is possible that all black cats are ninjas
,

this judgment (affirmative problematic) can be understand us saying that

The proposition, All black cats are ninjas, is possibly true.

And so on for assertoric (of course, since we've already done those above) and apodictic judgments. And if that works, that means we can regard propositional modality as the predicate modality of the context proposition, what I called the 'meta-proposition' above. And this itself makes some sense in light of the relations between propositional modality and predicate modality. And it makes propositional modality reducible to predicate modality , which I think is a nice result, despite the widespread attachment to the idea of the fundamental character of propositional modality.

In any case, this is all roughly sketched in my mind right now; it's possible that I'll hit some serious wall at some point. But I'm liking the way things look so far. As far as I know, no one has suggested this so far; but given how many things in the history of logic have disappeared down some black hole in a dusty section of a library, I'm rather expecting to come across a case of someone having suggested something like it any day now.

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