My eye was caught by this new paper ‘Against Fregean Quantification’ by Bryan Pickel and Brian Rabern. From the Abstract:
There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. …
Now, the treatment of quantification in my IFL is Frege-flavoured, in the way that Benson Mates’s classic treatment was. So I need to work out whether I should feel challenged by the arguments here. At a first pass, my hunch is not. But I’ll certainly put this on my list of things to worry about when I get back to reworking IFL for a third-and-last edition! And if inspiration strikes, I may return to it here rather sooner.
The paper’s headline news is also available in a somewhat lugubrious 27 minute YouTube video.