Related papers: Strong Determinism vs. Computability
Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
One of the central aims of neuroscience is to reliably predict the behavioral response of an organism using its neural activity. If possible, this implies we can causally manipulate the neural response and design brain-computer-interface…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
Contemporary quantum mechanical description of nature involves two processes. The first is a dynamical process governed by the equations of local quantum field theory. This process is local and deterministic, but it generates a structure…
The theory of addition in the domains of natural (N), integer (Z), rational (Q), real (R) and complex (C) numbers is decidable, so is the theory of multiplication in all those domains. By Godel's Incompleteness Theorem the theory of…
I wish to discuss a large, interwoven set of topics pointed at in the title above. Much of what I say is highly speculative, some is testable, some is, at present, surely not. It is, I hope, useful, to set these ideas forth for our…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
The Mind-Body Problem, which constitutes the starting point for a large part of the speculations about consciousness and conscious experience, can be re-stated in an equivalent way, using the `brain duplication' argument described in this…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…
Can a problem undecidable with classical resources be decidable with quantum ones? The answer expected is no; as both being Turing theories, they should not solve the Halting problem - a problem unsolvable by any Turing machine. Yet, we…
Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement"…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
We show that the modern quantum mechanics, and particularly the theory of decoherence, allows formulating a sort of a physical metatheory of consciousness. Particularly, the analysis of the necessary conditions for the occurrence of…
As neuroscientific theories of consciousness continue to proliferate, the need to assess their similarities and differences - as well as their predictive and explanatory power - becomes ever more pressing. Recently, a number of structured…
Are intelligent machines really intelligent? Is the underlying philosophical concept of intelligence satisfactory for describing how the present systems work? Is understanding a necessary and sufficient condition for intelligence? If a…