Sunday, April 15, 2012

Not proven, not guilty

I have been leafing through Ueberweg's System of Logic, which is an interesting nineteenth-century and Teutonic look at that subject.  Very few logic text books would now mention Hegel's logic, for example.  He has an interesting discussion of the principle of Excluded Middle, the one that says any sentence, or its negation must be true.  He claims (p. 263) that the principle may be invalid in certain instances. For example, 'not proven' fills an obvious gap between 'guilty' and 'not guilty'.

Surely not.  What does 'not proven' mean?  It means not proven to be guilty.  'It is proved that' is an operator on the proposition 'x is guilty', not a third truth value filling the gap between sentence and negation. What an elementary mistake, or have I missed something?

Brandon said...

It's a reference to the Scotch verdict; in certain kinds of cases in Scottish law a jury would refuse to return a verdict either of guilty or not guilty, and would instead return a verdict of not proven. Thus it means, roughly, "guilty enough that 'not guilty' is inappropriate but not meeting requirements for 'guilty' and therefore requiring acquittal." Thus the three verdicts are:

proven guilty
not proven guilty
proven not guilty

Edward Ockham said...

Yes of course, but the point is still that "It is not proved that P' is not a third value between

P
not P

Brandon said...

Ueberweg is not taking negation sententially here; he is talking about predicate negation.

In the Scotch verdict case, the negation is not classical and in context cannot be. A verdict doesn't return an assessment of fact; it returns an assessment of proof. The contrast between 'Guilty' and 'Not Guilty' with regard to verdicts is never a contrast between P and not-P, full stop, and therefore the negation here isn't classical. The proposition is not 'X is guilty' but 'X receives the guilty verdict', which is (with minor assumptions) equivalent to 'X is proven to be guilty according to standards of law'. This means that the predicates are modally qualified; the negation itself is affected by this -- hence the difference between proven-not and not-proven.

The ultimate background here is Kant's antinomies (which is what Hegel et al. are modifying), in which Kant argues that certain positions typically seen as contradictories are actually contraries, and can be seen to be such when one removes false assumptions, and thus the 'Scotch verdict' analogy is actually quite good one for describing Kant (and, mutatis mutandis, most German dialectical philosophers). Ueberweg goes on to make this point about the switch from contradictory to contrary opposition in his later criticism, of course; but the people he is talking about think that when we are dealing with any actual concepts you only get contradictory opposition by arbitrary and artificial assumptions: i.e., that negation in real discourse is contrariety, and we only make it contradictory by purely artificial stipulation.

Edward Ockham said...

>>Ueberweg is not taking negation sententially here; he is talking about predicate negation.

You may well be right, however the translation says 'judgments opposed as contradictories (p.260). Predicate negation is contrary only.

I concede, however, that immediately after the example is given 'A is B' and 'A is not B', the latter of which could be read as either predicate (contrary) or sentential (contradictory) negation.

I don't know enough about Hegel to say anything useful here.

Edward Ockham said...

Nice to see you here at Beyond Necessity, by the way.

Stan said...

Couldn't one say that 'not proven that x is not guilty'? When some agent is not proven guilty, it doesn't follow that the person is not guilty. It may be the case that a person may also be not proven not guilty.

I believe you're correct to express concern over Ueberweg's view. Just because a person's guilt (or innocence) is not proven does not suggest that the principle of excluded middle is 'invalid'. The lack of evidence might mean that we are incapable at a time to prove guilt (or innocence), not that there's a so-called third position.

Brandon said...

Perhaps -- this is purely a guess -- what is being presupposed is an account of logical judgment, which sometimes was seen as the 'form' of the proposition, and so would include both sentential and predicate negation. And so the problem could be precisely the ambiguity between sentential and predicate negation.

I don't know about Hegel, but I seem to recall some later nineteenth-century philosophers in that line arguing that all negation is predicate negation -- we are always implicitly predicating everything of the All or the Absolute. (I might be misremembering; but it fits with other things.)

I actually read BN quite regularly; I just don't always have much to say.