Quantifiers: Naturalness and Restrictiveness
According to ontological pluralism proposed by Kris McDaniel, we should include pairs of at least two restricted quantifiers when talking about ontology. This version of ontological pluralism relies on the notion of naturalness. More specifically, the emphasis is on natural predicates, rather than natural properties. As stated by the proponents of this thesis, restricted quantifiers are more natural than unrestricted one. It is claimed that even if we consider unrestricted quantifiers relevant for ontology, restricted quantifiers must be taken as more primitive and more natural. The talk about naturalness is a component of McDaniel’s ontological pluralism which I shall call “restricted is natural” (RN). I defend the opposite thesis: “unrestricted is natural“ (UN).
After accepting everything a proponent of RN might say about natural predicates, I will claim that we still need to consider properties as pertinent for quantifier naturalness. Quantifiers, being logical operators, have many properties. I will argue that some of those properties yield restrictive and unrestrictive behaviour of quantifiers. I will further show that no quantifier, no matter how restricted it may be, can be devoid of unrestrictive properties. The ubiquity of unrestrictiveness regarding quantifiers is the main part of my attack on RN. Moreover, it will be shown that restrictiveness lacks this ubiquity since there are quantifiers that don’t have restrictive properties in any way. The conclusion is that UN is a better theory than RN, which poses a problem for some ontological pluralists.
June 20th, 17:25 / Aula 0A