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.