Cook's distinctions

Charge (via Sainsbury and Tye): mathematical models idealize away the vagueness of ordinary language. Therefore, we cannot use mathematical models to capture or study vagueness itself. (Is that the goal of the vagueness literature?)

Cook thinks we can solve the problem we face by making a distinction between mathematicaldescriptions (bad) and mathematical models (good).

"On the traditional view of the role of formalization," Cook writes, "[Tye's and Sainsbury's criticisms] are devastating."

Unsurprisingly, though, the distinction between the alternative, `model' view (of math and logic) and the traditional `description' view is, well, vague. The description view says that`every aspect' of the model is meant to `correspond to something actually occurring.' (Can we really quantify over aspects? Or things occurring? Isn't this a bit like quantifying over `things about you' when I say there's something I like about you?)

The `description view' is the negation of this: there are admittedly aspects of the model which do not correspond to something actually occurring.

Cook also offers a third view, the `instrumentalist view of logic', which is really just a more extreme version of the model view. (`Nothing' corresponds.)

Aspects are divided into the representors and the artefacts (12-13).