Sellars, Second-order Quantification, and Ontological Commitment
Sellars [1960. ‘Grammar and existence: A preface to ontology’, Mind, 69 (276), 499–533; 1979. Naturalism and Ontology, Reseda, CA: Ridgeview Publishing Company] argues that the truth of a second-order sentence, e.g. [Inline formula], does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come to understand sentences of a second-order language wherein the truth of sentences of the form [Inline formula] do not require there to be abstract entities. In addition to this, as Sellars [1979. Naturalism and Ontology, Reseda, CA: Ridgeview Publishing Company] notes, a formal account of quantification is required that does not make use of the apparatus of sequences. Both a translation of [Inline formula] and a formal account of quantification are provided by this paper.
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