{"id":11426,"date":"2010-07-31T12:49:55","date_gmt":"2010-07-31T12:49:55","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/07\/31\/a-problem-with-the-multiple-relations-idea\/"},"modified":"2010-07-31T12:49:55","modified_gmt":"2010-07-31T12:49:55","slug":"a-problem-with-the-multiple-relations-idea","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/07\/31\/a-problem-with-the-multiple-relations-idea\/","title":{"rendered":"A Problem With the Multiple Relations Approach to Plural Predication"},"content":{"rendered":"

Consider<\/font><\/p>\n

1. Sam and Dave are meeting together.<\/font><\/p>\n

2. Al, Bill, and Carl are meeting together.<\/font><\/p>\n

3. Some people are meeting together.<\/font><\/p>\n

Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting together.'  So it is natural to try to analyze (1) and (2) using relational predicates.  (1) becomes<\/font><\/p>\n

1R. Meeting(Sam, Dave)   In symbols: Msd<\/font><\/p>\n

But if 'meeting' is a dyadic (two-place) predicate, then we should expect (2) to give way to<\/font><\/p>\n

2R. Mab & Mbc & Mac.<\/font><\/p>\n

Unfortunately, (2R) is true in circumstances in which (2) is false.  Suppose there are three separate meetings.  Then (2R) is true and (2) false.  To get around this difficulty, we can introduce a triadic relation M* which yields as analysans of (2):<\/font><\/p>\n

2R*. M*abc.<\/font><\/p>\n

But then we need a tetradic relation should Diana come to the meeting.  And so on, with the result that 'meeting together' picks out a family of relations of different polyadicities.  But what's wrong with that?  Well, note that (1) and (2) each entail (3) by Existential Generalization in the presence of the auxiliary premise 'Al, Bill, Carl, Dave, and Sam are people.'  <\/font><\/p>\n

But then we are going to have difficulty explaining the validity of the two instances of Existential Generalization.  For the one instance features a dyadic meeting relation and  the other a triadic.  If two different relations are involved, then what is the logical form of (3) — Some people are meeting together — which is the common conclusion of both instances of Existential Generalization?  If 'meeting together picks out a family of relations of different 'adicities, then (3) has no one definite logical form.<\/font><\/p>\n

Does this convince you that the multiple relations approach is unworkable?<\/font><\/p>\n

REFERENCE:  Thomas McKay, Plural Predication<\/em> (Oxford 2006), pp. 19-21.<\/font><\/p>\n

<\/font> <\/p>\n","protected":false},"excerpt":{"rendered":"

Consider 1. Sam and Dave are meeting together. 2. Al, Bill, and Carl are meeting together. 3. Some people are meeting together. Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting … Continue reading “A Problem With the Multiple Relations Approach to Plural Predication”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[408,108,84],"tags":[],"class_list":["post-11426","post","type-post","status-publish","format-standard","hentry","category-language-philosophy-of","category-logica-docens","category-predication"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/comments?post=11426"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11426\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=11426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=11426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=11426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}