## Thursday, 3 January 2013

### Deontology's Royal Road to Beenakker's boundary

This is a link to an interesting paper suggesting that any deontology can be collapsed into a Consequentialism by an appropriate weighting of Utilities but not vice versa  thus generating an asymmetry in favour of the latter.
An obvious rejoinder is that you can have a Deontology specified thus
1) first compute all possible Consequentialist solutions be they rule, act or whatever.
2) find something better than any of them.
However, there is one sort of Consequentialism, which I've just this moment invented, which goes something like 'discontinuously assign very high Utility to particular ordinal Utilities which have interesting mathematical properties, like Pi or e, such that what is maximized relates to something to do with  doing the Consequentialist calculus itself. In this case the deontology suggested above fails because something at step 1 encounters a halting problem.

Now as a matter of fact, not theory, it is the case that talk about Consequentialism vs Deontology is only interesting in so far as it drives maths or provides a concrete model for cool axiom systems arising from other fields.

The author of the paper linked to above writes-
A consequentialiser who cannot account for the diﬀerence between act and rule consequentialism has not succeeded to deliver a theory that deserves the label ‘consequentialism’. However,only cardinal consequentialism can account for this distinction. Rule consequentialism presupposes that one is able to calculate averages (or at least sum up the utility of diﬀerent consequences into a sum total) and this requires that we measure utility on a cardinal scale.
Is it the case that Rule Consequentialism (R.C) is constrained in the manner specified? Who is to say that, so long as R.C. doesn't throw away information, that single valued averages are necessary? Suppose a fractal captures the information rather than an average. It would have been news to many, prior to the Seventies, that fractals were in fact rankable on a cardinal scale on the basis of dimensionality. How do we know that the same thing is not true of other, currently exotic or unknown, mathematical objects which capture information?

I suppose this is just a sort of slapdash prelude to the realization that here as elsewhere what appears to be a Philosophical problem dissolves at Beenakker's boundary.