Pietro Enrico di Prampero


The development of a scientific theory (T) can be separated into successive phases: i) Fantasy, to conceive T ii) Analysis to couch T into formal language iii) Action, to apply in practice the predictions of T. The history of human powered flight, in which case the three phases are stretched over several thousand years, allow us to better appreciate their intrinsic characteristics. Fantasy, dating back to the myth of Ikarus, must be experimentally testable, as indeed were Daedalus' wings. Analysis must state in quantitative terms the laws governing the matter at stake. Action, from Leonardo’s unsuccessful attempts to the crossings of the British Channel in 1979 and of the arm of the sea separating Crete from mainland Greece in 1988, has the aim of shaping the world according to our will. The kernel of any “proper” T is a formal system wherein a set of operational rules allows us to manipulate a set of symbols, representing the objects of T, on the bases of a limited number of axioms. In such formal systems, "theorem" is a string of symbols that can be arrived at in a finite number of steps from the axioms, applying the canonical operational rules. However, as Kurt Gödel showed in 1931, it is possible to demonstrate that, within a sufficiently powerful formal system, there exists demonstrably true strings of symbols that are not theorems. Thus, even in an ultra-powerful theory of everything, there will still be truths that can not be arrived at within the theory.

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