Resumen de Henkin on Nominalism and Higher-Order Logic
In this paper a proposal by Henkin of a nominalistic interpretation for secondand higher-order logic is developed in detail and analysed. It was proposed as a response toQuine’s claim that second and higher-order logic not only are (i) committed to the existenceof sets, but also are (ii) committed to the existence of more sets than can ever be referredto in the language. Henkin’s interpretation is rarely cited in the debate on semantics and on-tological commitments for these logics, though it has many interesting ideas that are worthexploring. The detailed development will show that it employs an early strategy of using sub-stitutional quantification in order to reduce ontological commitments. It will be argued thatthe perspective adopted for the predicate variables renders it a natural extension of Quine’snominalistic interpretation for first-order logic. However, we will argue that, with respect toQuine’s nominalistic program and his notion of ontological commitment, (i) still holds andthus Henkin’s interpretation is not nominalistic. Nevertheless, it will be seen that (ii) is ad-dressed successfully and this provides further insights on the so-called “Skolem Paradox”.Moreover, the interpretation is ontologically parsimonious and, in this respect, it arguablyfares better than a recent proposal by Bob Hale.
