James > I attach a (slightly updated0 version of the paper that was > the background of what I said at Linz/Hagenberg.
Thanks for this! It makes a lot of sense to me as a 'working mathematician with pragmatic interests in computer aided maths research but a normally healthy scepticism about the utility of reducing real-world maths to strict logic'. With this hat on I am currently not agreeing with your conclusions about the necessity of 'uniqueness' at the end. It seems to me that, pragmatically if not formally, it is no more difficult to make a 'human check' on the 'mathematical consistency' of two practical definitions than it is to check that there are no cycles in 'the dependency graph' starting a definition or that a recursive definition gives a computable function. Thus I would allow multiple definitions but insist that they are compatible. Moving on, one could usefully insist on a _mathematical_ proof of all of such things: compatibility, non-cyclicity, finiteness etc. Or not! chris PS: the distinction between a 'mathematical definition' and 'an evaluation method' can often be, pedagogically, very subtle and perhaps needs to be better understood by the creators of the descriptive parts of the MathML CDs. _______________________________________________ Om3 mailing list [email protected] http://openmath.org/mailman/listinfo/om3
