Download [42.] on formally undecidable propositions within capitalism and

SILVAN MÜHLEMANN (BERNE, SEPTEMBER 2015)
[42.] ON FORMALLY UNDECIDABLE PROPOSITIONS
WITHIN CAPITALISM AND RELATED SYSTEMS
THEOREM OF CAPITALIST INCOMPLETENESS (T5): Within each economicpolitical system that is sufficiently complex to create money as a
means of accounting, the maxim “To save is (essentially):= not to
invest” is formally undecidable. (This implies the consequence (T6): namely that (T5) is also
undecidable; but if it’s true, that (T5) is undecidable, then the proposition p „to save is (essentially) := not to invest”
is undecidable as well; therefore it is true that p is undecidable. Hence (T5) may only be true, but undecidable.)
ABSTRACT: The theorem (T5) shall be made plausible by a strict analogy to Gödels
First Incompleteness Theorem and simultaneously we’ll proof the legitimacy of
analogical inference as such. First the theorems (T1): Law of identity, (T2): Law of noncontradiction, (T3): Tertium non-datur as well as (T4): the Law of sufficient reason are
being deduced, and then the fact that theorem (T3) and (T4) are contradicting
each other. The Tertium non datur (T3), the most fundamental axiom of arithmetic,
states that each mental operation is either +(A) or –(A), but nothing in between/
nothing third. By abstraction – the formalism of arithmetic – sufficient reason, i. E. the
nature of the thing “A” itself, is systematically excluded from reasoning. That,
however, means that the particular or the concrete (in the Aristotelian-Hegelian
sense) or the constant/ dependent variable y is equated with the general or
abstract or the independent variable x such that→ y = f(x). Mathematical inference
is therefore not different from proceeding by analogy (symbolism as such). As shown
by Kubota (2015)1 and contrary to Andrews (2002)2, Gödels First Incompleteness
Theorem cannot be proven syntactically (without giving rise to contradictions) by
means of a pure object logic, but only through a semantical meta-theory (symbol
interpretation). Similarly, within capitalism, the meta-system of calculation
(accounting) based on money represents – and substitutes – the system of natural
calculation, i. E. calculation as such. In a way then, money is more mathematical
than mathematics itself, because it gives mathematics a taste of its own medicine of
formalization. From the existence of money as a general commodity (“general
equivalent” as Marx would have it, but that is a non-sense expression), it may be
both inferred that saving – the particular use of money – is the same as investing –
the general use of money, as well as the contrary. Therefore the proposition named
by theorem (T5) is undecidable (but not necessarily true, while (T5) is necessarily true).
Conclusively, we state that the currently practiced government politics of austerity in
Europe is unfounded, if not misguided, and a return to the Keynesian paradigm
would be more appropriate to handle the contemporary crisis.
Kubota, Ken. Gödel Revisited. Some more doubts Concerning the Formal Correctness of
Gödel’s Incompleteness Theorem. Owl of Minerva Press GmbH, Berlin 2015
2 Andrews, Peter B. An Introduction to Mathematical Logic and Type Theory: To Truth Through
Proof. Second Edition. Dordrecht/Boston/London: Kluwer Academic Publishers 2002
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