Catálogo de publicaciones - libros

This chapter introduces some important epistemology. Without epistemology any inroad into the subject of (un)decidability and (in)determinism may result in confusion and incomprehensibility.

Empirical evidence can solely be drawn from operational procedures accessible to embedded observers. Embeddedness means that intrinsic observers have to somehow inspect and thus interact with the object, thereby altering both the observer as well as the object inspected.

The vision that self-reflexivity may, through self-intervention amounting to paradoxical situations, impose some restrictions on the performance and the capacity of physical agents to know their own states, is a challenging one. It has continued to present a source of inspiration.

Having explored the limits and the “negative” effects of the type of self-exploration and self-examination embedded observers are bound to we shall now examine the “positive” side of self-description. In particular, we shall prove that, at least for “nontrivial” deterministic systems (in the sense of recursion theory and, by the Church-Turing thesis, capable of universal computation), it is possible to represent a complete theory or “blueprint” of itself within these very systems.

According to his own narrative, and totally unaware of Saint Augustine of Hippo’s as well as Nicholas of Cusa’s (aka Nicolaus Cusanus’) notion of (Latin: ), the Baron Münchhausen pulled himself (and his horse) out of a mire by his own hair (Bürger, Münchhausen. Wunderbare Reisen zu Wasser und zu Lande, 1789, [88, Chap. 4]). (This story is not contained in Raspe’s earlier collections Raspe, The Travels and the Surprising Adventures of Baron Munchausen, 1877, [427].) In the following we shall be concerned with the question exactly why it is entirely hopeless to pursue the strategy suggested by the Baron Münchhausen; and why should one be concerned about this. More generally, is it (im)plausible to attempt to reach out into some external domain with purely intrinsic means; that is, by operational (from the point of view of intrinsic, embedded observers) capacities and means which cannot include any “extrinsic handle,” or Archimedean point?

While – depending on one’s subjective optimism or pessimism often, sometimes or rarely – it is possible to predict the future, certain forecasting tasks, in particular, when it comes to self-reference, are provable unattainable, and will remain so forever.

Induction is the inference of general rules “causing” and “generating” (in an algorithmic interpretation) physical behaviours from these very behaviours (without any extra assumptions) alone. Thus induction is “bottom up:” given the phenomena and how observers perceive them operationally, these observers somehow obtain the causes and rules which supposedly underlie these phenomena. Thereby we shall restrict ourselves to algorithmic methods of induction; others, such as intuition, guesses or oracles, or means other than intrinsic.

This Chapter enumerates a 200 of recursion theoretic undecidabilities not covered before.

The following speculations resemble Darwin’s and also Turing’s “inversion of reason” – that is, “competence without comprehension” – forcefully put forward by the atheistic philosopher Daniel Dennett in his phrase .

One of the biggest dangers in presenting quantum unknowns is ; a wasteful exercise in fruitless scholasticism and mysticism.