Truthmakers, Partial Content, and Logical Subtraction

16 July 2016

Workshop on Steve Yablo's 'Aboutness'

In this talk I show how various desirable formal features of partial content and logical subtraction are sensitive to whether we understand them in terms of recursive truthmakers (as favoured by Fine and van Frassen) or reductive truthmakers (which Yablo prefers). In particular if we think of partial content in terms of reductive truthmakers (which when dealing with propositional languages correspond to the minimal partial valuations generated by the prime implicants of a formula) then both partial content and logical subtraction fail to be closed under uniform substitution. When characterised in terms of recursive truthmakers both of these notions are closed under uniform substitution. Prima facie, this suggests that if we want to think of either of these notions as holding in virtue of logical form, then we had best understand them in terms of recursive truthmakers.