On non-denoting

Some singular terms denote, or refer to, something, while others do not; for instance, “the US president” denotes Joe Biden and, famously, “the present king of France” denotes nothing. How should we deal with non-denoting terms? As is well-known, Frege (1892), Meinong (1904) and Russell (1905) offer three paradigmatic approaches. According to Meinong, these terms are denoting after all, as they refer to non-existent objects; given this ontological commitment to such objects, Meinong is not an actualist. In contrast, both Frege and Russell are actualist and for them non-denoting terms indeed refer to nothing. For Frege, however, they have a sense and their lack of reference makes it the case that many sentences involving them are neither true nor false, whereas for Russell there are no senses and no truth value gaps. In several previous works, following Cocchiarella (1982, 1989) and Landini (1990), I offered a view that combines Russell’s 1905 actualism without truth value gaps with the denoting concepts of an earlier Russell (1903). Here I defend this view from criticisms by Mario Alai, with some comparison to Alai’s approach to these matters.