Twenty Fregean Ways to Quantify Over Frege's Senses

This paper continues my discussion with Michael Dummett on Frege’s senses, published in The Philosophy of Michael Dummett and further developed in Diametros. In his reply to my original paper, Dummett came to agree with me that senses are neither objects nor functions, since they have a categorially different kind of linguistico-metaphysical function to perform. He then asks how we might quantify over senses, if they are neither objects nor functions. He discusses two main options, and finds one unviable and the other “very un-Fregean.” I then offer a Fregean or neo-Fregean option in my rejoinder. And I still hold that this way out will do the job, or is at least plausible enough that the burden of persuasion is on those who disagree. But I hope to show in this paper that on a more complete examination of Frege, there are at least twenty Fregean or neo-Fregean ways out, with the one I proposed being option (17).