On self-reference and self-description
pp. 189-197
in: Arturo Carsetti (ed), Functional models of cognition, Berlin, Springer, 2000Abstract
Let us assume that our world is discretely organized, and that it is governed by constructive, i.e., effectively computable, laws [1]. By that assumption, there exists a "blueprint", a complete set of rids or laws governing the universe. This seems unlike mathematics for which Gödel, Tarski, Turing and others proved that no reasonable (i.e., strong enough and consistent) formal system will ever be able to prove all true well-formed statements. Indeed, Chaitin showed that certain mathematical entities are as random as a sequence produced by the tossing of a fair coin [2, 3]. Hence, let us contemplate the assumption that, when it comes to an enumeration of laws and initial values, nature is finitely "shallow" while mathematics is infinitely "deep" [4].