Quine's Individuals

Publisher Summary This chapter focuses on the Quine's individuals. Professor Quine has suggested that in relation to the theories of membership, it can be possible to allow for the existence of nonclasses or individuals by interpreting the formula “x Є y” as synonymous with “x = y”—in the case that y is an individual. The fact that the situation did not arise in the course of one particular development is not a conclusive argument. However, it seems clear that Professor Quine does not imagine such a deduction is possible nor would anyone else believe this. Nothing supports belief like proof, and it will be the purpose of this chapter to demonstrate that if Quine's axioms are consistent. For these purposes, the chapter imagines NF formulated in first-order logic with identity and with the descriptive operator. The proof given in the chapter for NF is finitary and in no doubt a similar argument can be applied to ML.