{"id":11234,"date":"2010-10-12T17:09:06","date_gmt":"2010-10-12T17:09:06","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/10\/12\/bundling-is-symmetrical-but-not-transitive\/"},"modified":"2010-10-12T17:09:06","modified_gmt":"2010-10-12T17:09:06","slug":"bundling-is-symmetrical-but-not-transitive","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/10\/12\/bundling-is-symmetrical-but-not-transitive\/","title":{"rendered":"Bundling is Symmetrical But not Transitive"},"content":{"rendered":"

Over the phone the other day, Peter L. suggested the following objection to the bundle-of-universals theory of ordinary particulars, 'BT' hereafter.  (I leave out of consideration for the nonce bundle-of-tropes bundle theories.)  I am not sure I understood what Peter was driving at.  But here is the gist of what I thought he was saying. <\/span><\/p>\n

1. Suppose x is a proper (spatial) part of y, y being a physical thing.  On BT, both y and x are bundles of universals.  Now it often happens that a whole has a property that is not had by all its parts.  Think of a rubber ball.  The ball is spherical (or spheroid, if you  insist).  But it has proper parts that are not spherical.  For example, its hemispheres are not spherical.  Nor are the cubes of rubber internal to it spherical.  (They too are proper parts of it on classical mereology. These cubes could be 'liberated' by appropriate cutting of the ball.) The ball is red, let us say, but beneath the surface it is black.  And so on.  in sum, wholes often have properties that their parts do not have.<\/span><\/p>\n

2.  On BT, property-possession is understood, not in terms of the asymmetrical relation of exemplification, but in terms of the symmetrical relation of bundling.  Accordingly, for a property to be possessed by something is not for it to be exemplified by this thing, but for it to be bundled with other logically and nomologically compossible properties.  Exemplification, the asymmetrical relation that connects a substratum to a first-level property is replaced by bundling  which is a symmetrical relation that connects sufficiently many properties (which we are assuming to be universals) so as to form a particular.  When the universals are bundled, the result is a whole of which the universals are ontological constituents, with the bundling relation taking over the unifying job of the substratum.  While bundling is symmetrical — if U1 is bundled with U2, then U2 is bundled with U1– ontological constituency is asymmetrical:  if U is an ontological constituent of B, then B is not an ontological constituent of U.<\/span><\/p>\n

3.  Given that the  ball is a bundle of universals, and that the ball is spherical, it follows that the ball has as one of its ontological 'parts' the universal, sphericality.  Now sphericality and cubicality are not broadly-logically compossible.  Hence they cannot be bundled together to form an individual.  But our ball has a proper part internal to it which is a cube.  That proper part has cubicality as a constituent universal.  So it seems a broadly-logical contradiction ensues:  the ball has as constituents both sphericality and cubicality, universals that are not compossible.<\/span><\/p>\n

4. An interesting objection!  But note that it assumes Transitivity of Bundling:  it assumes that if sphericality is bundled  with sufficiently many other Us to form a complete individual, and cubicality is bundled with one of these Us — say being made of rubber — then sphericality is bundled with cubicality. But it is well-known that bundling is not transitive.  Suppose roundness and redness are bundled in our ball, and redness and stickiness are bundled in a numerically distinct disk, but there is nothing that is both round and sticky. That's a possible scenario which shows that Transitivity of Bundling fails. From the fact that U1 is bundled with U2, and U2 with U3, one cannot infer that U1 is bundled with U3.  So from the fact that sphericality is bundled with rubberness, and rubberness with cubicality, it does not follow that sphericality is bundled with cubicality.<\/span><\/p>\n

The  bundle theory can accommodate the fact that a property of a whole needn't be a property of all its proper parts.  Or am I missing something?<\/span><\/p>\n

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

Over the phone the other day, Peter L. suggested the following objection to the bundle-of-universals theory of ordinary particulars, 'BT' hereafter.  (I leave out of consideration for the nonce bundle-of-tropes bundle theories.)  I am not sure I understood what Peter was driving at.  But here is the gist of what I thought he was saying.  1. … Continue reading “Bundling is Symmetrical But not Transitive”<\/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":[487],"tags":[],"class_list":["post-11234","post","type-post","status-publish","format-standard","hentry","category-constituent-ontology"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11234","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=11234"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11234\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=11234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=11234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=11234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}