David Corfield suggests that modality has to do with *ranges of variation*. This seems extremely helpful. He connects Brandom’s notion of *ranges of counterfactual robustness* with mathematical analyses of variation. Corfield approvingly cites Brandom’s argument that in order to successfully apply empirical concepts at all, we must *already* be able to apply modal concepts like possibility and necessity. This always seemed right to me, but the talk about possible worlds made me worry about what sounded like impossibly strong quantification over infinities of infinities. Corfield also points out that Saul Kripke originally cautioned against uncareful extension of his possible-worlds talk.

It now seems to me that Brandom’s counterfactual robustness and Corfield’s mathematically analyzable variation together can be taken as an *explanation* for modal notions of necessity that previously seemed to be simply posited, or pulled out of the blue. Modality suddenly looks like a direct consequence of the *structure* of ranges of variation. Previously, I associated both structure and Brandom’s modally robust counterfactuals with Aristotelian potentiality, so this fits well.

Corfield also relates this to work done by the important 20th century neo-Kantian, Ernst Cassirer, on *invariants* behind the various systems of Euclidean and non-Euclidean geometry. He points out that Cassirer thought similar concerns of *variation and invariance* implicitly arise in ordinary visual perception, and connects this with Brandom’s thesis that modality is already there in our everyday application of empirical concepts.

The British Empiricist David Hume famously criticized common-sense assumptions about causality and necessity, preferring to substitute talk about our psychological tendencies to associate things that we have experienced together. Hume pointed out that from particular facts, no *knowledge* of causality or necessity can ever be derived. This is true; no knowledge of *necessity* could arise from acquaintance with particular facts. But if necessity and other modalities are *structural*, as Corfield suggests, they do not *need* to be inferred from particular facts, *or* to be arbitrarily posited.

The kind of necessity associated with structural determination is quite different from unconditional *predestination*. I want to affirm the first, and deny the second. Structural determination only applies within well-defined contexts, so it is bounded. If we step outside of the context where it applies, it no longer has force. (See also New Approaches to Modality; Free Will and Determinism.)

Leibniz is more familiar to me than Kripke, so when I hear “possible worlds”, I have tended to imagine complete alternate universes *à la* Leibniz. “Worlds”, however, could be read much more modestly as just referring to Corfield’s *ranges of variation*.