Realism According to Mach, Carnap and Godel

IFSR Newsletter 1987 No. 1 (15) Summer
Lecture sponsored by the Depts. of Systems Theory and of Philosophy, Johannes Kepler University, Linz,
29 Jan. 1987; held by ECKEHART KOHLER, Institute for Advanced Studies, Vienna, and Institute for Statistics and Computer Science, University of Vienna
1. According to Mach’s monism, physical objects are just as real as mental objects (dual nature of elements). Therefore, as no elements are absolutely fundamental, they can in principle always be analyzed as theoretical complexes of other elements.
2. But “complexes” are mathematical functions (of elements), which in turn were conceived of by Mach as subjective operations (anthropomorphic finitism); therefore a) restriction of empirical concept-formation capability (differentials and other transfinite concepts are “fictions”) and hence of the concept of reality, although b) elements and their complexes taken prima facie as subjective are re-objectified by considering them to originate in socially and biological (i.e. evolutionarily) anchored methods of gaining knowledge.
3. Carnap’s “Principle of Tolerance” readmits all the concept-formation capability of classical mathematics, but at the cost of the indefiniteness of their interpretation (whether concepts are syntactical-nominalistic or subjective, etc.). However Carnap’s pragmatic conventionalism is otherwise compatible with Mach’s evolutionary utilitarianism. Carnap’s prima facie subjectivist conventionalism becomes re-objectified, like Mach’s method, through the use of pragmatic criteria.
4. Godel defends an apparently absolute realism for mathematics and postulates an intuitive perception (a 6th sense) for it. (An intentionally theological standpoint is required for the foundation of mathematics: the objectivity of mathematical rules lies in the validity of god-like, i.e. transfinite procedures.)
5. But Godel’s standpoint seems to coincide with Carnap’s after all, as Godel emphasizes the fallibilism of mathematical intuition, allowing even its probabilistic interpretation – which necessarily results in a utilitarian foundation for mathematics, comparable to a pragmatic conventionalism.
6. Since utilitarian foundations always depend on historically contingent interests and informational states, they are always subject to further critism and revision when necessary; but they can nevertheless (or perhaps for that very reason) be extremely robust – like democracy! Conclusion: the subjective/objective distinction is of little consequence – what’s important is the dependability of the source of information; on the other hand, if realism is defined as absolutism, then there are two alternatives. Either a) the revisibility of “knowledge” and of conceptual schemes is regarded as incompatible with realism and hence the acceptance of fallibilism renders realism false. Or b) realism is regarded as compatible with revisions so long as these tend to a robust issue in the limit, in which case accepting the hypothesis of robustness renders realism true. But the latter is a good working hypothesis, because it facilitates individual and interpersonal dealings (Boltzmann’s “ZweckmaBigkeit”).

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