Øystein Linnebo (University of Oslo) Non-instantial generality: What it is and why we need it

What features of reality are responsible for the truth of a universal generalization? The orthodox answer proceeds via the instances of the generalization. Everything is F because a is F, b is F, and so on, plus (perhaps) the fact that these are all the objects. I show that the orthodoxy needs to be supplemented with (wholly or partially) non-instantial explanations. E.g., we can explain why everything crimson is red or why every object has a singleton set without invoking any instances of these generalizations. Although non-instantial generality is familiar from mathematical intuitionism, I divorce the idea from the intuitionistic philosophy and show how it can be put on a robustly realist footing (say, in terms of Finean essences). With non-instantial generality on board, all the truths of intuitionistic (but not classical) first-order logic turn out to have a trivial truthmaker.

The talk will describe the truthmaker analysis of non-instantial generality developed in my “Generality explained”. Some more recent developments will also be discussed, especially an extension of my analysis of non-instantial generality to the framework of metaphysical grounding, as well as some applications of the analysis in philosophy and the foundations of mathematics.

Matteo Plebani  (University of Turin) Variations on a theme from Linnebo

I will use Linnebo’s notion of non-instantial generality to shed some light on Wittgenstein’s tantalizing claim that “the generality required in mathematics is not an accidental generality” [T 6.031]. I will also compare the type of truthmaker semantics presented in Linnebo’s “Generality explained” with Kleene realizability semantics.

Francesca Boccuni (Vita-Salute San Raffaele University, Milan) Frege’s proof of referentiality 

In this talk, I will investigate a novel reading of Frege’s proof of referentiality (and its failure) based on so-called generic generality. First, I will explain what the latter amounts to, and, secondly, I will motivate why it is apt to capture Frege’s conception of quantification. I will then compare the reading of Frege’s proof of referentiality in terms of generic generality to its traditional readings. Finally, I will comment on a few consequences of applying generic generality to Frege’s conception of quantification.

Alice van't Hoff (University of Vienna) Against higher-order unrestrictedness

Generality absolutists argue that it is possible to quantify absolutely unrestrictedly over everything that there is. A challenge to their view arises if we take seriously the possibility of genuinely higher-order quantification. An influential proposal, first put forward by Timothy Williamson, however, suggests that to conclude on this basis against generality absolutism would be premature. Williamson's claim is that higher-order quantification in our object language is only a threat to generality absolutism if we, misleadingly, adopt a first-order metalanguage. I argue, though, that this approach is subject to a counter-example: intuitively, quantification in many-sorted languages need not be absolutely general. Yet both higher-order and many-sorted systems may involve multiple distinct quantifiers and there are, I claim, no differences of the kind relevant to a quantifier's unrestrictedness that distinguish these two versions of quantifier pluralism. This suggests, contra Williamson and others, that higher-order quantification is a threat to generality absolutism, at least insofar as we take quantification of this kind ontologically seriously.