Publication 5339

Diettrich O. (1994) Is there a theory of everything? Bulletin of the Institute of Mathematics and its Applications 80: 166–170. Fulltext at https://cepa.info/5339
It is widely understood in physics that evaluation criteria for empirical theories are determined by what is called the objective structures of an outside and real world, and on this basis, discussions ensue as to whether our scientific efforts to condense observations into theories will eventually result in a “theory of everything” (Feynman 1965, Hawking 1979, Barrow 1990, Chalmers 1982) reflecting precisely these structures. “Unless one accepts that the regularities (we perceive) are in some sense objectively real, one might as well stop doing science” (Davies 1990a). I.e., reality is seen as a prerequisite for a non arbitrary and reasonable development of theories. Without reality “anything goes” – which is the downright unacceptable in physics. On the other hand, if regularities are objective in the sense that they depend on the structures of an objective outside world, it remains unclear why mathematics which obviously does not include any information on these structures is nevertheless so helpful in describing them in such a way that purely mathematical extrapolations will lead to correct predictions. This is the old question about “the unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960), or, as Davies (1990b) put it, “why the universe is algorithmicly compressible” (i.e. why the obviously complex structure of our world can be described in so many cases by means of relatively simple mathematical formulae). This question is closely linked to why induction and, therefore, science at all, succeeds. It is difficult to avoid asking whether mathematics, as the outcome of human thinking has its own specificity which, for what ever reason, fits to the specificity of what man would see or experience. As long as this question is not comprehensively answered science may explain much – but not its own success. But how can such entirely disparate categories as perceiving and thinking be linked with each other? This question will be discussed here in the context of a new constructivist version of evolutionary approaches to epistemology (Diettrich 1991, 1993), which will lead to a revised notion of reality, as well as to some rather unexpected links between the phenomena of non-classical physics and the mathematical findings of Gödel.

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