> there are serious intimations of
> non-linearity in Marx, especially 'Grundrisse'
The Grundrisse records, even more obviously than Capital itself, Marx's adoption from Hegel of the ontological idea of social relations as "internal relations" in a form that means that, as relations change, the identities of related things will not be maintained to the degree required for algebraic - linear or non-linear - representation.
As I pointed out some time ago in explaining Keynes's opposition to the use of algebra in economics, this implication of internal relations for the use of algebra is spelled out in the following argument of Whitehead.
>
> "Before we finally dismiss deductive logic [as the method of 'philosophy'
> understood as 'the search for premises'], it is well to note the function of
> the 'variable' in logical reason. In this connection the term variable is
> applied to a symbol, occurring in a propositional form which merely
> indicates any entity to which the propositional form can be validly applied,
> so as to constitute a determinate proposition. Also the variable, though
> undetermined, sustains its identity throughout the arguments. The notion
> originally assumed importance in algebra, in the familiar letters such as x,
> y, z indicating any numbers. It also appears somewhat tentatively in the
> Aristotelian syllogisms, where names such as 'Socrates,' indicate 'any man,
> the same throughout the argument.'
> "The use of the variable is to indicate the self-identity of some use of
> 'any' throughout a train of reasoning. For example in elementary algebra
> when x first appears it means 'any number.' But in that train of reasoning,
> the reappearance of x always means 'the same number' as in the original
> appearance. Thus the variable is an ingenious combination of the vagueness
> of any with the definiteness of a particular indication.
> "In logical reasoning, which proceeds by the use of the variable, there
> are always two tacit presuppositions - one is that the definite symbols of
> composition can retain the same meaning as the reasoning elaborates novel
> compositions. The other presupposition is that this self-identity can be
> preserved when the variable is replaced by some definite instance. Complete
> self-identity can never be preserved in any advance to novelty. The only
> question is, as to whether the loss is relevant to the purposes of the
> argument. The baby in the cradle, and the grown man in middle age, are in
> some senses identical and in other senses diverse. Is the train of argument
> in its conclusions substantiated by the identity of vitiated by the
> diversity?" (A.N. Whitehead, Modes of Thought, p. 107)
>
> In the case of the use of algebra to represent human behaviour, the
> maintenance of the requisite degree of self-identity (of the same "meaning")
> of the "variables" in behavioural relations requires the maintenance of the
> requisite degree of self-identity in the individuals whose behaviour the
> algebra is to be used to represent. (This, by the way, is only one of the
> requirements the material must meet for algebra to be validly applicable to
> it.)
Ted