tag:blogger.com,1999:blog-6642011.post114368242366267131..comments2023-10-29T10:32:36.914-04:00Comments on Philosophy, et cetera: Sparse PropertiesRichard Y Chappellhttp://www.blogger.com/profile/16725218276285291235noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6642011.post-1143744259298915892006-03-30T13:44:00.000-05:002006-03-30T13:44:00.000-05:00One other interesting question (at least to me) re...One other interesting question (at least to me) regarding sparse properties is whether there is a single set of sparse properties sufficient for explanation.<BR/><BR/>That is let us say hypothetically there is some Set S1 such that the members of S1 are the properties such that they are all "orthagonal" and yet describe all properties in our universe. Is it the case that there is no Set S2 with a <I>different</I> set of properties that does the same?<BR/><BR/>To make the mathematical analogy, consider the axis in Cartesian space {x,y}. Clearly there are infinite other orthagonal axis which could be used instead. Say {theta, r}. If sparse properties are equivalent to these orthagonal axis, does the same thing occur.<BR/><BR/>The second thing to wonder is whether they really need to be orthogonal. Perhaps there is some property in a sparse set that isn't fully orthagonal to some other property, but is needed to explain all other properties. Would that still count as sparse even if it is a minimal property set.<BR/><BR/>OK, maybe this is only of interest to me. But <I>way back</I> when I first got into thinking about properties in college it always seemed a big issue. One reason I wonder whether sparse properties are workable.Clark Goblehttps://www.blogger.com/profile/03876620613578404474noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-1143686300434885532006-03-29T21:38:00.000-05:002006-03-29T21:38:00.000-05:00First, it should be noted that most advocates of u...First, it should be noted that most advocates of universals have wanted sparse universals (the issue is discussed in Plato's "Parmenides", and may well have come up earlier). Perhaps the best known modern advocate of universals, David Armstrong, has always insisted on their sparseness.<BR/><BR/>However, while sparse properties may have appealed to the two most prominent philosophical Davids of recent times, I don't think they're tenable. We have no good reason to believe there are any fundamental or perfectly natural properties. At least, that's one of the conclusions of my (sadly as yet unfinished) dissertation; for published discussion of some of the issues which lead me to that conclusion, you might check out Jonathan Schaffer's stuff on infinite complexity.Anonymousnoreply@blogger.com