Related papers: Informal Physical Reasoning Processes
Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and G\"odel's Dialectica interpretation. In this paper we show that a great many intuitionistic set theories are closed…
This article presents an operationalized solution to the mind-body problem which relies on rigorously defined theoretical reasoning rather than philosophical argument. We identify a specific operation which is a necessary property of all…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over…
A physicalistic argument can support the idea that cognition is an emergent property driven by dissipation. This argument suggests that cognition arises not from any fiat desire to understand the world, but rather because a certain type of…
We introduce a simple natural deduction system for reasoning with judgments of the form "there exists a proof of $\varphi$" to explore the notion of judgmental existence following Martin-L\"{o}f's methodology of distinguishing between…
A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach…
Even though classic theories and models of discrete choice pose man as a rational being, it has been shown extensively that people persistently violate rationality in their actual choices. Recent models of decision-making take these…
We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…
This paper investigates $\exists\mathbb{R}(r^{\mathbb{Z}})$, that is the extension of the existential theory of the reals by an additional unary predicate $r^{\mathbb{Z}}$ for the integer powers of a fixed computable real number $r > 0$. If…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
The world has seen the emergence of machines based on pretrained models, transformers, also known as generative artificial intelligences for their ability to produce various types of content, including text, images, audio, and synthetic…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
Despite significant achievements and current interest in machine learning and artificial intelligence, the quest for a theory of intelligence, allowing general and efficient problem solving, has done little progress. This work tries to…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems…