Related papers: Strong Determinism vs. Computability
This article presents a formal model demonstrating that genuine autonomy, the ability of a system to self-regulate and pursue objectives, fundamentally implies computational unpredictability from an external perspective. we establish…
On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…
This article addresses the question of when physical laws and their consequences can be computed. If a physical system is capable of universal computation, then its energy gap can't be computed. At an even more fundamental level, the most…
The relationship between brains and computers is often taken to be merely metaphorical. However, genuine computational systems can be implemented in virtually any media; thus, one can take seriously the view that brains literally compute.…
We analyse so-called computable laws, i.e., laws that can be enforced by automatic procedures. These laws should be logically perfect and unambiguous, but sometimes they are not. We use a regulation on road transport to illustrate this…
It has been proposed that human physical reasoning consists largely of running "physics engines in the head" in which the future trajectory of the physical system under consideration is computed precisely using accurate scientific theories.…
Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational…
The existence of a non-algorithmic side of the mind, conjectured by Penrose on the basis of G\"odel's first incompleteness theorem, is investigated here in terms of a quantum metalanguage. We suggest that, besides human ordinary thought,…
Human consciousness has been a long-lasting mystery for centuries, while machine intelligence and consciousness is an arduous pursuit. Researchers have developed diverse theories for interpreting the consciousness phenomenon in human brains…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…
In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…