11
Feb
08

Fully rational systems are closed systems

Consider two kinds of systems that we have identified:

(DFN-RATIONAL-SYSTEM-v.1.0) A system is a rational system to the extent that its contents are deducible from its axioms.

(DFN-CLOSED-SYSTEM-v.1.0) A closed system is a system whose content does not depend on any variables exogenous to it.

It is clear from Lukacs’ writing that he considers these two concepts to be connected in a certain way: he believes that a fully rational system must be closed.

Here is an argument for why he must be right:

  1. Suppose a system, S is fully rational.
  2. S is entirely deducible from its axioms (by (DFN-RATIONAL-SYSTEM-v.1.0)).
  3. That means that S’s contents do not depend on anything except that which is contained in its axioms.
  4. Anything contained in the axioms of S is endogenous (not exogenous) to S.
  5. Hence, S does not depend on any variables exogenous to it (by 3 and 4)
  6. S is closed. (by (DFN-CLOSED-SYSTEM-v.1.0))

One day I’d like to make this argument more formal, but for now I think it will suffice to let me make the following statement with confidence:

(RATIONAL->CLOSED) If a system is fully rational, then it is closed.

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