For quite a while, the favourite Cambridge example of a collective plural predication has been ‘Alex and Tim are writing a book’ (said with a teasing tone, as it was a long drawn out business). But our example will, at last, have to change. For the book is now published, as Plural Logic, out from OUP. Here’s their blurb as a taster (if you don’t already know some of their earlier papers on plurals):
Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms (‘Whitehead and Russell’, ‘Henry VIII’s wives’, ‘the real numbers’, ‘the square roots of -1’, ‘they’), plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’), and plural quantification (‘some things’, ‘any things’). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; in other words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration.
I in fact saw a late draft of the book which Alex and Timothy kindly asked me to comment on, which I did with enthusiasm here and scepticism there, so I’ll be really interested to discover how this final published version works. It wouldn’t be appropriate for me to write a formal review in one of the journals, even if asked, as I wouldn’t have the requisite distance. But that certainly won’t stop me giving some informal thoughts here over the next few weeks. Watch this space, then: and meanwhile, get yourselves a copy of the book!
Re this book and the plural logic section in your ‘Teach Yourself Logic’, I’ve seen another book that discusses plural quantification and plural logic: Understanding the Many, by Byeong-uk Yi.
I remember it as interesting, but haven’t looked at it for quite a while (my copy is around somewhere, but I can’t find it).
Love the cover, but I confess the connection between Alice and plural logic escapes me. Perhaps you can shed some light on the issue, or should we just go ask Alex and Tim?
‘So Alice said “Who cares for you? You’re nothing but a pack of cards!” So they were all very angry, and flew up into the air, and came tumbling down again, all over Alice, just like a shower of rain.’ The quote is on the back cover, and it seems that Lewis Carroll is treating ‘pack of cards’ as having plural denotation (‘you are …’, ‘they were …’), in accord with Alex and Tim’s view of such terms. [Ok, a bit of a tenuous link, but makes for a nice cover!]