David Corfield Lassiter, Graded Modality

Daniel Lassiter, Graded modality, OUP,

Any way to get this to work with mode theory? Seems to be proposing that even apparent non-scalar modalities are secretly so reliant. What if continuous logic were the key? Grading there.

Introduction

p. xiii, study graded modals beyond those which are grammatically inert.

My strategy, then, is to develop a semantics for the complicated modals—in particular, the ones that are clearly gradable, such as likely, certain, and good – and then to use the conclusions reached in this way to infer the hidden structure behind the less revealing auxiliary modals, by examining their logical relationships with the gradable modals.

p. xiv

when we are theorizing about the lexical semantics of modals, the tradition has been to focus on the analogy with quantifiers such as some, all, and none and to try to graft on gradable modals as an afterthought. Instead, I suggest, our leading analogy should be to scalar adjectives such as big, small, empty, full, and enormous.

Chap. 1

Consider graded scalars on their own terms, not like

SOME- and ALL-quantifiers are upward monotone

(B implies C, then some A is B implies some A is C, I guess, so dependent sum as functor)

Even non-gradables (must, might) have scalar semantics.

Different scales: fully open, lower closed, upper close, fully closed. (p. 14)

(Is it enough to have an object of values $[0,1]$ as just one object, or do we need continuous logic?)

we should give up the venerable assumption that modals are a complicated sort of quantifiers. Instead, I argue, thecommonalities between gradable and modal expressions are due to the fact thatboth have a semantics built around scales. (p. 18)

Chap. 2

Different kinds of scale: ordinal, ratio, interval. One issue is that real numbers have many structures. (Due to being the unique complete ordered field, terminal archimedean field?) So some idea to take invariants for all relevant homomorphisms. (So why not restrict language?)

Miscellaneous thoughts

When MacIntyre mentions the difference between good as adjectival attribute, and as qualifying what to do (good jam vs it is good to feed the poor), the first seems merely relative to a type, the second is across types (not a good way to feed the poor, but it is better than leaving them to starve). But is this not good in the type of ‘achievements to aim for now’? Perhaps there’s the Collingwood point that it’s not a type of replaceable entities, good jam is any of a number of jam. It would be good to X is closer to duty.