Thursday, February 23, 2006

Diminishing and Non-Diminishing Qualifications

Consider the following two inferences:

(1) The car is rubber with respect to its tires; therefore the car is rubber.

(2) The man is blond with respect to his hair; therefore the man is blond.

The first is obviously a bad inference (assuming we are not understanding the conclusion in a peculiarly restricted way); while the second is obviously a good inference. The difference between the two has to do with the nature of the qualification. The qualification in the first is what we can call a 'diminishing qualification'; the qualification in the second is what we can call a 'non-diminishing qualification'. Diminishing qualifications make the inference from the qualified version ('The car is rubber with respect to its tires') to the unqualified version ('The car is rubber') illegitimate, because the qualification 'diminishes' or restricts what would otherwise be the natural application of the predicate. In a non-diminishing qualification, however, the qualification doesn't restrict the natural application of the predicate. 'With respect to his hair' clarifies, perhaps, the way in which a man is blond; but it does not restrict the way in which a man is blond.

This distinction between diminishing and non-diminishing qualifications has relevance to the analysis of reduplicative propositions. The failure to make the distinction is also at the heart of a number of sophisms.

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