KARL JASPERS FORUM

N71 (response to N70, Riegler)

A HILBERT-PROGRAM FOR CONSTRUCTIVISM ?
by Herbert FJ Müller
19 August 2006, posted 2 Sept 2006

[1]
Alexander Riegler's question about a possible 'Hilbert-Program' for constructivism is an interesting idea, which merits consideration. Since about 1900 Hilbert had wanted, in protest against duBois-Reymond's 'ignorabimus' proposition of 1872, to establish a complete contradiction-free logical system, based on axioms, as the basis for mathematics (and this was similar to proposals for mathematical-logical-epistemological systems by Russell and Whitehead, and by the members of the Vienna Circle). But in 1931 Gödel showed these undertakings to be impossible : if conceptual systems are free of contradictions they are incomplete. Feyerabend (1999) in effect extended this insight by writing that logical systems only exist as 'interruptions' of an irrational background.

[2]
Awareness of these historical developments, together with the constructivist position, may help to find a way to address this situation. All mental (for instance logical) structures are created within the mind (ongoing experience, consciousness); the mind is encompassing (Jaspers) and therefore cannot itself be encompassed by structures. Thus all structures, including those of mathematics, of logic, as well as of ontology-metaphysics, are working-structures; we create them as needed and use them to the extent that they work.

[3]
To postulate complete structures for all of reality necessarily implies an erroneous assumption : either that structures exist mind-independently, or that ongoing experience can be structured (or both). Instead of postulating a complete conceptual coverage of experience, and later finding that this cannot be done (as it happened historically), we can start from the knowledge that the center and agency of experience cannot be structured, and that the structures are its tools, created and used under its guidance. To talk here about a 'Hilbert-Program" would be misleading since Hilbert wanted a complete system; if at all, it would have to be a 'H-P around a Negative Center'.

[4]
Does this confirm the 'ignorabimus' thesis of duBois-Reymond ? Probably not : that term concerned mainly the question of knowledge of metaphysics-ontology, and of 'consciousness', all of which nowadays still trigger much discussion, but are undecideable in principle, so long as they are treated as mind-independent (it makes no sense to see human structures like words, triangles, imaginary numbers, or also ongoing experience, the mind, itself, as 'existing' mind-independently). Acknowledging that the center of experience cannot become structured, and that mind-and-world-structures are our (subjects') subject-inclusive ad-hoc working-tools - that are knowable as such - can become a start-point for discussion of concepts in constructivism and other fields.

[5]
Riegler asks : who would work on such a 'program' ? Preferably a revision of concepts in epistemology would be explicitly accepted by a group of workers (for instance constructivists) as their long-term task. Then one could dedicate a section of a journal to deal with it, asking some experts to write opinions about one proposition or question each time. That could be followed by a more general discussion, open to all members of the group, and perhaps to the general public.

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Reichenberger AA, Grenzen des Wissens ? Der Ignorabimusstreit.

http://www2.uni-siegen.de/~ifan/ungewu/heft11/reichenberger11.htm

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Herbert FJ Müller