{"id":11321,"date":"2010-09-16T19:18:45","date_gmt":"2010-09-16T19:18:45","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/09\/16\/varzi-sums-and-wholes\/"},"modified":"2010-09-16T19:18:45","modified_gmt":"2010-09-16T19:18:45","slug":"varzi-sums-and-wholes","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/09\/16\/varzi-sums-and-wholes\/","title":{"rendered":"Varzi, Sums, and Wholes"},"content":{"rendered":"

Achille C. Varzi, "The Extensionality of Parthood and Composition," The Philosophical Quarterly<\/em> 58 (2008), p. 109:<\/font><\/p>\n

\n

Suppose we have a house made of Tinkertoy pieces.  Then the house qualifies as a sum of those pieces: each piece is part of the house and each part of the house overlaps at least one of the pieces . . . . Are there other things that qualify as the sums of those pieces?  UC says there aren't; the house is the only candidate: it is the<\/em> sum of those pieces.<\/font><\/p>\n<\/blockquote>\n

UC is Uniqueness of Composition<\/em>:  <\/font><\/p>\n

\n

UC  If x and y are sums of the same things, then x = y,<\/font><\/p>\n

where<\/font><\/p>\n

(1) x is a sum of the zs =df<\/sub> The zs are all parts of x and every part of x has a part in common with at least one ofthe zs. <\/font><\/p>\n<\/blockquote>\n

Perhaps commenter John, who knows some mereology and the relevant literature on material composition, can help me understand this.  What I don't understand is what entitles Varzi to assume that the Tinkertoy house — 'TTH' to give it a name — is identical to a classical mereological sum.  I do not deny that there is a sum of the parts of TTH.  And I do not doubt that this sum is unique.  Let us name this sum 'TTS.'  (I assume that names are Kripkean rigid designators.)  What I do not understand is the justification of the assumption, made near the beginning of his paper, of the identity<\/em> of TTH and TTS.  TTH is of course a whole of parts.  But it doesn't straightaway follow that TTH is a sum<\/em> of parts.<\/font><\/p>\n

Please note that 'sum' is a technical term, one whose meaning is exactly the meaning it derives from the definitions and axioms of classical mereology.  'Whole' is a term of ordinary language whose meaning depends on context.  It seems to me that one cannot just assume that a given whole of parts is identical to a mereological sum of those same parts.<\/font><\/p>\n

I am not denying that it might be useful for some purposes  to think of material objects like TTH as sums, but by the same token it might be useful to think of material objects as (mathematical)  sets of their parts.  But surely it would be a mistake to identify TTH with a set of its parts.  For one thing, sets are abstract while material objects are concrete.  For another, proper parthood is transitive while set-theoretic elementhood is not transitive.  <\/font><\/p>\n

Of course, sums are not sets.  A sum of concreta is itself concrete whereas a set of concreta is itself abstract.  My point is that, just as we cannot assume that that TTH is identical to a set, we cannot assume that TTH is identical to a sum.<\/font><\/p>\n

What is the 'dialectical situation' when it comes to the dispute between those who maintain that TTH = TTS and those who deny this identity?<\/font><\/p>\n

It seems to me that the burden of proof rests on those who, like Varzi, identify material objects like TTH with sums especially given the arguments against the identity.  Here is one argument. (a) Taking TTH apart would destroy it, (b) but would not destroy TTS.  Therefore, (c) TTH is not identical to TTS.  This argument relies on the wholly unproblematic Indiscernibility of Identicals as a tacit premise:  If x = y, then whatever is true of x is true of y, and vice versa.  Because something is true of TTH — namely, that taking it apart would destroy it — that is not true of TTS, TTH cannot be identical to TTS.<\/font><\/p>\n

The simplicity and clarity of modal discernibility arguments like this one cast grave doubt on the opening assumption that TTH is a sum.  I am not saying that Varzi and Co. have no response to the argument; they do.  My point is that their response comes too late dialectically speaking.  If you know what a sum is, you know that the identity is dubious from the outset: the discernibility arguments merely make the dubiousness explicit. Responding to these arguments strikes me as too little too late; what the identity theorist needs to do is justify his intitial assumption as soon as he makes it.<\/font><\/p>\n

My main question, then, is this.  What justifies the initial assumption that material particulars such as Tinkertoy houses are mereological sums?  It cannot be that they are wholes of parts, for a whole needn't be a sum.  TTH is a whole but it is not a sum.  It is not a sum because a sum is a collection that is neutral with respect to the arrangement or interrelation of its parts, whereas it is essential to TTH that its parts be arranged house-wise.<\/font><\/p>\n

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

Achille C. Varzi, "The Extensionality of Parthood and Composition," The Philosophical Quarterly 58 (2008), p. 109: Suppose we have a house made of Tinkertoy pieces.  Then the house qualifies as a sum of those pieces: each piece is part of the house and each part of the house overlaps at least one of the pieces . … Continue reading “Varzi, Sums, and Wholes”<\/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":[21,346,86],"tags":[],"class_list":["post-11321","post","type-post","status-publish","format-standard","hentry","category-aporetics","category-identity-and-individuation","category-wholes-and-parts"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11321","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=11321"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11321\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=11321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=11321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=11321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}