I’m about to take my first of _four_ road trips in the next four weeks, so the blog will be quiet now and for a while. I’m off to Manitoba to talk about properties and quantities, and in particular why metaphysics should care more about quantities than properties. I’ll post the paper in a bit, but for now I just want to post a puzzle that’s somewhat central to the paper.

It’s rather difficult to figure out how to properly incorporate vector quantities into a systematic metaphysics. Lewis was given a bit of a working over on this point over issues to do with spinning spheres. But actually I think there is a problem here for everyone. Assume we have three objects as below with some fundamental vector-valued magnitude, with the direction of the vector given by the arrow. (Imagine these are homogenous 3D objects, and I’m showing you a 2D cross-section.)

If I’ve remembered enough grade school physics, simple bar magnets are like this, and we can imagine the arrow as pointing from the south pole to the north pole of the magnet. Since it turns out to matter that the objects are geometrically asymmetric, I call this the Asymmetric Magnets Problem.

!http://brian.weatherson.org/intrinsic.jpg 75%x75%!

What’s the problem? Well, there’s an intuitive case to be made that A and B are duplicates. You could ‘convert’ A to B by picking it up and spinning it around, and this ‘process’ intuitively takes an object into a duplicate object. (My argument that is is intuitive is that Euclid, and most of his readers for the first 2000 years, used such reasoning in the proof of proposition 4, and it seemed intuitive to all of them.) But it seems to convert A to C you’d have to redo its magnetic structure, or change its shape so the vector points towards the ‘pointy’ end, and either of those seems like an intrinsic change. So A and C are not duplicates.

The problem then is finding a theory of intrinsicness that delivers those results. If vector properties are intrinsic, then A and B are not duplicates, because they differ with respect to an intrinsic property. If vector properties are extrinsic, i.e. not intrinsic, then there aren’t any intrinsic differences between A and C, so they are duplicates. To make the paradox here explicit, we can write out the claims that seem true about the case as an inconsistent pentad.

# A and B are duplicates
# A and C are not duplicates
# Duplicates are objects that share all their intrinsic properties, and have their parts stand in the same intrinsic relations
# If vector properties are intrinsic, and 3, then A and B are not duplicates
# If vector properties are not intrinsic, and 3, then A and C are duplicates

I think the one to give up is 5, but writing out a full theory on which 5 is false, and the others are all true, is non-trivial. And 5 might not be the false one. So for now I’ll just leave this as a puzzle, and I’ll post my preferred (somewhat radical) solution in a while.