Sound and Fury

Signifying nothing

Use and abuse of mathematical language.

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I have complained about the misuse of mathematical language before. Philosophy of biology is a serial offender here. But I recently came across a really good use of maths concepts to convey an idea. In John Dupre’s paper Natural kinds and biological taxa he explains the apparent reasonableness of thinking of species as natural kinds as follows:

If it were possible to map individual organisms on a multidimensional quality space, we would find numerous clusters or bumps. In some parts of biology these clusters will be almost discrete

Now there is obviously no suggestion we do this. But it is a really neat way to get across the idea that members of a species really do have a lot in common, and it is fair enough to imagine species as being natural kinds.

Speaking of maths concepts in biology, I spent a while this afternoon thinking about the “sameness relations” Dupre uses to build classifications of animals. I struck upon the cool fact that if you demand that your relations be equivalence relations, then the classification will automatically have lots of nice kinds of consistency, because equivalence classes will always partition the space! I thought that was pretty cool.

Also today we were talking about the difference between Whitehead’s process philosophy and a more conventional ontology taking onbjects to be primitives. I started thinking of it in terms of category theory. So processes are arrows (maps morphisms whatever you want to call them.) and objects are objects. Now, I believe there is an alternative way of starting category theory which takes only the arrows as primitives, and defines objects in terms of special arrows: the identity maps. I then started thinking about taking just objects as primitives and defining arrows as ordered pairs of objects. (I don’t know if this is really legitimate…) So then I started thinking that maybe the two kinds of ontology weren’t really that different in that what you take to be basic doesn’t really matter. But maybe I was missing the point of the debate because category theory was clogging up my brain.

I also started thinking about logic and how some of the operators are interdefinable. So if you have NOT and then one of AND, OR and CONDITIONAL (and possibly BICONDITIONAL?), then you can define all the operators in terms of that. So normally you’d just take all of the symbols on board at the start. Because it doesn’t really make a difference in the end.

So I suppose my mind works in quite a mathematical/logical way. Does that make it strange that I dislike the misuse of maths language? Or does that make it more understandable? I don’t really know.

p.s. Dupre should have an accent and I could put in the logical symbols instead of AND etc. But I’m feeling lazy. Sue me.


Written by Seamus

May 6, 2008 at 8:43 pm

Posted in maths, philosophy, science

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