Gregg I am sorry for the overly personal attack. I read with interest the latter part of your post concerning metonymy, which did seem to contrast with my (perhaps mis)reading of the discussion of mathematical functions, with or without a name.
I found it strange that Sandro responded to your message with "I'm probably done now. " - it struck me that Sandro was on a roll that I found creative. In particular you said: [[ metonymy […] already accounts for the way RDF properties and classes are construed by RDF Semantics; we can just do the same thing for graphs. ]] which, if we could flesh that out, would achieve the goals I think. Then an RDF property is not a set of pairs, and an RDF class is not a set of resources, and a named graph is not a set of triples … but there is one step of indirection which you are referring to as being a metonym. How to say that in a simple ways seems to be the issue Jeremy J Carroll Principal Architect Syapse, Inc. On Sep 19, 2013, at 11:25 AM, Gregg Reynolds <d...@mobileink.com> wrote: > On Wed, Sep 18, 2013 at 1:33 PM, Jeremy J Carroll <j...@syapse.com> wrote: > > Something of an aside … > > On Sep 18, 2013, at 1:29 AM, Gregg Reynolds <d...@mobileink.com> wrote: > >> The suggestion that a pair of mathematical entities with exactly the same >> extension are not equal doesn't help - it reads like an attempt to redefine >> mathematics. > > > Gregg > > I think you misunderstand mathematics ... > > It's called the Extensionality Axiom. If x and y have the same elements, > then x is equal to y. According to Ciesielski, it's one of the two most > basic axioms of set theory. You may object that set theory does not exhaust > mathematics, but I remind you that we're talking about a technical > specification whose audience consists of working programmers who are > virtually guaranteed to take this axiom for granted. So if you're going to > claim it does not hold, you have some explaining to do. > > > I attach two pictures. > > The first is my copy, of Jones' copy of a diagram in a book in the vatican > library which is a tenth century, maybe fifth generation, copy of a diagram > drawn by Pappus of Alexandria in the 4th century, which may in turn have been > a (n-th generational) copy of a diagram drawn by Euclid a few hundred years > earlier. > The copy in the vatican library, has, according to Jones, got a mistake in > it: which he corrected, assuming it to be a copyist's error and not an error > of Pappus or Euclid. > > All these copies will have minor variations .. such as angles and distances > and sizes being slightly different > > In some sense there is one diagram, even the one with a mistake in it, which > refer to the same mathematical concept. In another sense there are multiple > diagrams - the one in this e-mail is even in some sense different from the > one at > http://oriented.sourceforge.net/images/jones139.jpg which is bitwise > identical. The intent of the two pictures is quite different - within this > e-mail I am discussing the meaning of pictures, on that website I am > interested mainly to compare and contrast with my own picture, the second > picture here, which, I boldly assert is a picture of the same mathematical > concept as Pappus' original picture. (My picture and Pappus' original form > the same arrangement of pseudolines in the projective plane - concepts which > had not been invented when Pappus drew his picture) > > And you would be wrong. That's a matter of (bad) historical judgment, not > mathematics. If you see your contemporary mathematical concept in a tenth > century diagram, its because you put it there. It's a variation on the > Fallacy of Anachronism. You might find Quentin Skinner's "Meaning and > understanding in the history of ideas" enlightening. You can find a copy on > the web. If not email me privately and I'll send you a copy. Another > fascinating account of how this happens is "Lengths, widths, surfaces: a > portrait of old Babylonian algebra and its kin" by Jens Høyrup. He shows how > the scholars who first reconstructed Babylonian mathematics radically misread > the texts in spite of their brilliance, because they treated their own > historically situated concepts of mathematics for timeless universals and > therefore read them into texts written by people who had no such ideas. > > ... > > The point of all this is that even in mathematics we need to be able to talk > about the very human tasks relating to copying and changing and making my own > copy … where notions such as identity move from being obvious to being really > very subtle. > > No, the point is that mathematicians make bad historians. > > Sandro is trying to understand the notion of identity that Pat and I see as > obvious when it comes to graph naming, and by way of technical questions > trying to probe the subtleties > > Which I assure you I completely understand. I made a good faith effort to > contribute to the conversation, to which you responded with an ad homimen > attack. Nice. I wonder if you even bothered to read my post.
