Richard, I had been confused by your footnote against the set theoretic concept of contradiction in Biology Under the Influence; what you say here makes the point well and compellingly. I am wondering whether you have read Andreas Wagner's Paradoxical Life; it seems that ideas that you stated in Dialectical Biologist are being rediscovered.
There is another sense of contradiction, recently articulated by Andrew Collier in his short and stimulating book on Marx: "two demands, both necessary for the successful working of the same system, but mutually incompatible." I think here of Marx's analysis of the development of contradictions of the falling profit rate, especially the famous paragraph that begins with capital being identified as the true barrier to itself. What does Marx mean? Here's a quick take, but I'd be happy to hear other interpretations. The system requires the valorization of the extant capital and encourages ceaseless productivity growth which proves necessary to relieve the relentless upward pressure on the value composition of capital that growth of the technical composition of capital engenders (especially on the assumption that unit values remain constant). In other words, the system requires (and encourages or 'incentivizes') the cheapening of capital and wage goods but the system also requires that the extant capital be allowed to valorize itself. These are both structural tendencies, yet they may prove to be incompatible. And the system may collapse under the weight of the contradiction. The value destroyed by the new cheaper capital and wage goods may be so great as to undermine the profitable accumulation that those new commodities should make possible. I am interested in how Marx understands contradiction in his theoretical work. This chapter is an important one to study as is Marx's analysis of the polar opposition between and mutual assumption of commodities and money. Yours, Rakesh The following considerations might be helpful: 1. "contradiction", in its etymology "speaking against" was a process unfolding in time, negating a proposition in order to get beyond it. 2. Formal logic removes the temporal dynamic aspect to make it a formal, structural relation. 3. The formal logical statement "implies" is a static, set-theoretic relation but is a detemporalized equivalent to "leads to" (in time). 4. In real systems, variables change(except at equilibrium, a set of measure 0!). That is, A leads to not-A. If there is an eventual equilibrium, this is equivalent to proof by contradiction. In living systems, social systems, eco-systems etc there is permanent change ( A always leads to (implies!) not-A.These may be periodic or chaotic . The terror of early computer programmers was to get into an endless (and expensive) loop, which was equivalent to contradiction in the program. In formal logic, you may not (but can) hold to contradictory propositions at the same time . In dialectical logic, two propositions may be separately false but jointly true; health is socially determined, and you are responsible for your health. Either one alone can result in passivity but jointly can result in self-care and collective action... 5. You can create formally disjunct mathematical sets, but with real things no division of a whole world into mutually exclusive categories really holds. Environmental/genetic, physical/psychological, biological/social, etc interpenetrate, and furthermore it is when we recognize their interpenetration that we get the exciting new insights. All of these and other aspects of contradiction make it an important tool in science. ========================= Richard Levins ________________________________________________ YOU MUST clip all extraneous text when replying to a message. Send list submissions to: [email protected] Set your options at: http://lists.econ.utah.edu/mailman/options/marxism/archive%40mail-archive.com
