Trope theory: Identity of indiscernables? interaction of concurrance sums?

[Greg_G47]

We're just getting into trope theory in my philosophy class and I've got a couple questions about it. The first is regarding Black's apparent proof that there can be two numerically distinct objects with entirely identical properties. This proof would force the existence of "bare particulars".

 

First, some reasons why I'm not a fan of bare particulars:

For one thing, how do we assign properties to an "object" which cannot be accessed or referenced by any kind of index (as this would be a property). Also what happens with a bare particular if all properties are removed? If I were to obliterate my textbook by colliding it with its equivalent mass of antimatter converting it to photons, what would happen to the associated bare particular? In addition, the requirement of having particulars lying in wait for future objects creates the rather unattractive consequence of an entirely predetermined timeline.

 

Now, the problem with the argument that forces their existence. To say that the location of the two spheres in black's possible world is identical is making a comparison from two frames of reference simultaneously. This simply can't be done. It has consequences such as objects moving paralell to each other diverging or Grandpa REALLY managing to walk uphill both ways to and from school. Extended to a radially symmetrical mirrored universe, the direction to the center (or the -r) direction must be reversed. Again, to make moving objects identical in all properties requires comparison from 2 opposed frames of reference at once. Finally, there's the case of two disjoint identical universes. Either there is some extradimensional separation between the two, or we are reduced to the tautology of saying "if two numerically distinct universes identical in all respects exist than we can have objects which are numerically distinct and identical in all respects." Or "Imagine a world where I'm correct. In this world I am correct. QED." So the question is, What's really wrong with bundle theory? Is there a form of this argument against it without the apparent flaw mentioned above?

 

The second question is a little more general, a lot less long-winded and probably harder to answer. How is interaction between concurrance sums mediated? That is, how does one bundle of tropes operate on the tropes of another, what operations are permitted and why?

 

Written Oct 4 2005 by Greg Gilmour (I have a midterm coming up and if I write something similar in the essay that gets tagged by turnitin or some similar anti-plagarism software I want it on record that I wrote it!)

[UncleAl]

The first is regarding Black's apparent proof that there can be two numerically distinct objects with entirely identical properties.

If it isn't math, then any conclusion drawn is crap. That said,

 

http://www.mazepath.com/uncleal/handed.png

 

Here are stereograms of two objects. They are mathematically and in all other ways indistinguishable - except by comparison. (Given a regular tetrahedron, assign its four vertices or sides four different colors, and then do it mirror image).

 

Quantitating handedness is one of mathematics' really nasty probems. It can only be done by comparison. An isolated object cannot have its handedness described. ("Turn to the right" or "turn clockwise" is cheating. "Right" and "clockwise" are aribitrary assignments. You could globally reverse the labels and nothing would change. Ben Franklin labeling the electron "negative" was a really stupid if admittedly arbitrary thing to do. Wait until you do electric current in physics.)

 

http://www.mdpi.net/entropy/papers/e5030271.pdf

http://petitjeanmichel.free.fr/itoweb.petitjean.html

 

One can go the the other way, too - two numerically identical objects with entirely different properties. Get some adding machine tape. Make two Moebius bands, one with a clockwise half-twist and the other with a counterclockwise half-twist. Are they superposable? Of course not! But a Moebius band is a non-orientable surface. The two apparently dfferent constructions are indistinguishable. If they look different it is an artifact.

 

Google

"non-orientable surface" 755 hits

 

http://www.math.ohio-state.edu/~fiedorow/math655/yale/math.htm

 

As we say down in the trenches, "A non-orientable surface can not be embedded in three-space, but it can be immersed there." Philosophy? "Ack! Thbbft!" Mathematics! God is a geometer.

 

Have a nice midterm. Tell the teacher what he wants to hear - or go to war bloody and sincere. "8^>)

[Mercenaryend]

If it isn't math, then any conclusion drawn is crap.

 

Math is only a way to explain, and attemp to explain the unexplainable at the present of a thought....