Related papers: Informal Physical Reasoning Processes
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
We give an effective procedure that produces a natural number in its output from any natural number in its input, that is, it computes a total function. The elementary operations of the procedure are Turing-computable. The procedure has a…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis:…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such systems, the strong representation of primitive recursive…
It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions.The Theory of Logical Openness connects the Physics of system/environment relationships…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
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…
We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
Turing Machines are universal computing machines in theory. It has been a long debate whether Turing Machines can simulate the consciousness mind behaviors in the materialistic universe. Three different hypotheses come out of such debate,…
The "easy" problem of cognitive science is explaining how and why we can do what we can do. The "hard" problem is explaining how and why we feel. Turing's methodology for cognitive science (the Turing Test) is based on doing: Design a model…
The no-supervenience theorem limits the capacity of physicalist theories to provide a comprehensive account of human consciousness. The proof of the theorem is difficult to formalize because it relies on both alethic and epistemic notions…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…