# The limits of (atomistic) mathematics

July 2, 2014 4 Comments

Lars Syll draws attention to a recent seminar on ‘Confronting economics’ by Tony Lawson, as part of the Bloomsbury Confrontations at UCLU.

If you replace his every use of the term ‘mathematics’ by something like ‘atomistic mathematics’ then I would regard this talk as not only very important, but true. Tony approving quotes Whitehead on challenging implicit assumptions. Is his implicit assumption that mathematics is ‘atomistic’? What about Whitehead’s own mathematics, or that of Russell, Keynes and Turing? He (Tony) seems to suppose that mathematics can’t deal with emergent properities. So What is Whitehead’s work on Process, Keynes’ work on uncertainty, Russell’s work on knowledge or Turing’s work on morphogenesis all about?

Hi Dave, this is a great talk by Tony Lawson. You may be interested to know that in our book “Holonomics: Business Where People and Planet Matter” we provide a view of systems and wholeness which takes a phenomenological and hermeneutical perspective, moving away from an analysis using mathematical modelling and into the meaning of systems, both ecological as well as economical.

Just as Lawson mentions, we also discuss ontology and the nature of being. You can read the first few chapters on-line here: http://www.florisbooks.co.uk/book/Simon-Robinson/Holonomics/9781782500612

Thanks. You point to some severe limitations of (conventional) ‘analysis using mathematical modelling’. I accept that some people have a very narrow view of analysis, mathematics, and modelling, but it seems to me that Whitehead et al reached very similar conclusions using ‘modern’ analysis using mathematical modelling and that economics, for example, could benefit from re-acquainting itself with this material. So shouldn’t we be taking a broader view of ‘analysis’, ‘mathematics’ and ‘modelling’, and linking it in to the material that you review and extend?

Absolutely. I would be really interested to hear your thoughts on Whitehead. While I do have a couple of his books, I have not studied his work in-depth. I have more gone down the Gadamer – Wittgenstein route which I do also believe would be highly complementary to Whitehead.

Simon, judging by Wikipedia, Gadamer took the view that ‘truth’ and ‘method’ are at odds with each other. Whitehead et al suppose that mathematics can reveal mathematical truths, and that in some cases one can develop an effective method. On the other hand, they also reveal the limits of mathematical methods.

I think the difficulty comes in things like financial mathematics, whose results may be ‘mathematically true’ yet false ‘in practice’. So I guess the question is ‘true to what’?

Whitehead introduces the notion emergence. Emergent properties, structures and behaviours are not predictable, and so one cannot have a method for predicting them. But there is often some ‘supra-theory’ which allows one to say something useful, short of having a conventional ‘mathematical model’.