A second, paperback, edition of Plural Logic by Alex Oliver and Timothy Smiley is now out from OUP. As the cover says, it is ‘Revised and Enlarged’ – in fact it is almost fifty pages longer, with some new sections and a whole new chapter on Higher-Level Plural Logic. So you should certainly make sure that your library gets a copy.
I did read and comment on a version of the original edition pre-publication. But that was not at a good time for me, and I remember much less detail than I should: so I really want now to re-read the book. One reasons is that, in reworking my Introduction to Formal Logic, I want to excise unnecessary set talk, e.g. when giving the semantics of QL. So I want to remind myself how Oliver and Smiley handle this. And there is also a tenuous potential connection too between thinking about plurals and another interest, my on-the-back-burner introductory discussion of category theory. For I need to think through how far we can get in elementary category theory by conceiving of categories plurally rather than as set-like, thereby avoiding certain problems of ‘size’ hitting us too soon.
1 thought on “Plural Logic, again”
I think the pluralist alternatives to “unnecessary set talk” are often worse — further from natural English, or confusing in some way — than “light’ use of collective nouns such as “set”. So if you are determined to excise such talk, I think some care is needed to ensure that the chosen alternatives read as naturally as possible.
An example is from page 11 of IFL-2d: Some given propositions are consistent just if there is a logically possible situation in which they are all true together.
To me, that looks like wording that was chosen just to avoid saying “A set of propositions is consistent …”, rather than a natural, unforced way to express the definition in English.
Presumably “given” is present because “some propositions” doesn’t make it clear enough that it will be certain specific propositions in each case, and because “some propositions are P just if Q” can make it seem that some propositions are like that, but others aren’t. (Consider “some foods are edible only if cooked, but others can be eaten raw”.)
(I also end up wondering about the “just” in “just if”. Why isn’t it just “if”?)
I think this is a more natural way to put it: Propositions are consistent with each other if there is a logically possible situation in which they are all true together.
(Perhaps the “with each other” should be in parentheses to suggest that it should be understood but won’t always be stated explicitly.)