[Marxism] Marx on Mathematics

[D OC]

The paper forwarded was Anthony Hartin was very interesting indeed. Marx seems to have anticipated both Boole's work on finite calculus and even operator theory which he seems to have described in dialectical terminology as 'strategies of action' (at least to some extent). My academic specialism is Mathematics - primarily analysis - and did not know Marx wrote anything substantial on it aside from his work on logic. So quite something to see this.

 

He correctly identifies underlying problems within Leibnitzian integration which were subsequently dealt with more advanced measure theory. His analytic approach prefigures some similar approaches to wider problems in the decades after his death. 

 

Also very interesting is how his concerns with the logical basis of infinitesmal theory is reflected in his aversion to simplistic mathematical modelling in Economics. The concept of infinitesmals like so many other assumptions underpinning modern economic theory can never really reflect the nature of the real economy (as Joan Robinson said they have substituted mathematics for thinking). Just consider what an infinitesmal increase in labour power represents. While this might seem pedantic to more vulgar economists - from a pure mathematical perspective it is critical. The differential cannot be defined. Perhaps it was this realisation that led him to review the definition of the limit.

 

Yet again the quality and intellectual rigour of Marx's thought stands out. The fact that he could spend such time reading back into Newton's early work (which is tremendously inaccessible particularly the more mathematical bits) is typical of the man. Newton's methods remain largely untapped today - his extensive proofs overhauled by modern methods. But there is likely concepts involved which will inform future studies. 

 

Marx's intellectual honesty and moral courage in tackling difficult issues remain an outstanding example to us all. That it has not been published until relatively recently is a shame. Furthermore his presentation of thought through the dialectic makes it very difficult to grasp what he was saying but it is very coherent - if at times slightly naive from a modern analytic perspective. 

 

The question for me is whether the mathematical books are in the Collected Works. If not, as it appears, why not? Also, what else is missing from the MECW? I would be grateful for any answers.

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