Sentence examples for plural quantification of from inspiring English sources
More generally, we may attempt to introduce plural quantification of any finite level.
Others, such as Lewis's (1991), resort to the machinery of plural quantification of Boolos (1984).
For this application of plural quantification to work, PFO must be applicable to all kinds of concrete objects, and it must be ontologically innocent, or at least not committed to any entities that share those features of abstract objects that are found to be nominalistically objectionable.
Non-structural states of affairs do not supervene on their atomic conjuncts individually, but jointly, a claim that, it appears, must be understood via plural quantification: for any non-structural state of affairs s, there are some states of affairs such that (a) s supervenes on them and (b) something is one of them if and only if it is atomic and s includes it.
The idea is to pay the ontological price of a mere first-order theory and then use plural quantification to get for free (a theory with the force of) the corresponding monadic second-order theory.
In both cases, we interpret plural quantification in terms of quantification over non-empty sets of individuals in the domain $D$.
One class of applications of plural quantification aim to make ontological bargains in the philosophy of mathematics.
In particular, a number of philosophers have attempted to use plural quantification as an ingredient of nominalistic interpretations of mathematics.
In the next section, where various applications of plural quantification will be discussed, I will carefully note which strains of the notion of logicality our theories PFO and PFO+ must possess for the various applications of them to succeed.
Like in the case of second-order logic, we may provide at least two sorts of models for the theory of plural quantification.
As we saw in Section 2.1 Boolos defined an interpretation of the theory MSO of monadic second-order logic in the theory PFO of plural quantification.
