Results 21  30
of
59
Information processing, computation, and cognition
 JOURNAL OF BIOLOGICAL PHYSICS
"... Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree veheme ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation ’ and ‘information processing ’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theoryneutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism/computational neuroscience on the other. We defend the relevance to cognitive science of both computation, at least in a generic sense, and information processing, in three important senses of the term. Our account advances several foundational debates in cognitive science by untangling some of their conceptual knots in a theoryneutral way. By leveling the playing field, we pave the way for the future resolution of the debates ’ empirical aspects.
Global semantic typing for inductive and coinductive computing
 Logical Methods in Computer Science
"... ..."
The ChurchTuring Thesis as an Immature Form of the ZuseFredkin Thesis (More Arguments in Support of the “Universe as a Cellular Automaton” Idea)
"... In [1] we have shown a strong argument in support of the "Universe as a computer " idea. In the current work, we continue our exposition by showing more arguments that reveal why our Universe is not only "some kind of computer", but also a concrete computational ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In [1] we have shown a strong argument in support of the &quot;Universe as a computer &quot; idea. In the current work, we continue our exposition by showing more arguments that reveal why our Universe is not only &quot;some kind of computer&quot;, but also a concrete computational model known as a &quot;cellular automaton&quot;.
Extension of embeddings in the recursively enumerable degrees
"... The extension of embeddings problem for the recursively enumerable degrees R = (R;!; 0; 0 0) asks for given finite partially ordered sets P ` Q with least and greatest elements, whether every embedding of P into R can be extended to an embedding of Q into R. Many of the landmark theorems giving an a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The extension of embeddings problem for the recursively enumerable degrees R = (R;!; 0; 0 0) asks for given finite partially ordered sets P ` Q with least and greatest elements, whether every embedding of P into R can be extended to an embedding of Q into R. Many of the landmark theorems giving an algebraic insight into R assert either extension or nonextension of embeddings. We extend, strengthen, and unify these results and their proofs to produce complete and complementary criteria and techniques to analyze instances of extension and nonextension. We conclude that the full extension of embeddings problem is decidable.
2010b]: ’The metatheory of firstorder logic: a contribution to a defence of Principia Mathematica
"... iv ..."
(Show Context)
Extensions, Automorphisms, and Definability
 CONTEMPORARY MATHEMATICS
"... This paper contains some results and open questions for automorphisms and definable properties of computably enumerable (c.e.) sets. It has long been apparent in automorphisms of c.e. sets, and is now becoming apparent in applications to topology and dierential geometry, that it is important to ..."
Abstract
 Add to MetaCart
This paper contains some results and open questions for automorphisms and definable properties of computably enumerable (c.e.) sets. It has long been apparent in automorphisms of c.e. sets, and is now becoming apparent in applications to topology and dierential geometry, that it is important to know the dynamical properties of a c.e. set We , not merely whether an element x is enumerated in We but when, relative to its appearance in other c.e. sets. We present here
Church’s Thesis
"... In this project we will learn about both primitive recursive and general recursive functions. We will also learn about Turing computable functions, and will discuss why the class of general recursive functions coincides with the class of Turing computable functions. We will introduce the effectively ..."
Abstract
 Add to MetaCart
(Show Context)
In this project we will learn about both primitive recursive and general recursive functions. We will also learn about Turing computable functions, and will discuss why the class of general recursive functions coincides with the class of Turing computable functions. We will introduce the effectively calculable functions, and the ideas behind Alonzo Church’s (1903–1995) proposal to identify the
Gödel on Intuition and on Hilbert’s finitism
"... There are some puzzles about Gödel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the con ..."
Abstract
 Add to MetaCart
There are some puzzles about Gödel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, Gödel’s writings represent a smooth evolution, with just one rather small doublereversal, of his view of finitism. He used the term “finit ” (in German) or “finitary ” or “finitistic ” primarily to refer to Hilbert’s conception of finitary mathematics. On two occasions (only, as far as I know), the lecture notes for his lecture at Zilsel’s [Gödel, 1938a] and the lecture notes for a lecture at Yale [Gödel, *1941], he used it in a way that he knew—in the second case, explicitly—went beyond what Hilbert meant. Early in his career, he believed that finitism (in Hilbert’s sense) is openended, in the sense that no correct formal system can be known to formalize all finitist proofs and, in particular, all possible finitist proofs of consistency of firstorder number theory, P A; but starting in the Dialectica paper
1 DEFINABILITY IN THE REAL UNIVERSE ∗
"... Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics w ..."
Abstract
 Add to MetaCart
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.”
Beyond Turing Machines ∗
, 907
"... www.cstruct.org This paper discusses ”computational ” systems capable of ”computing” functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite descriptions by interacting with their environme ..."
Abstract
 Add to MetaCart
www.cstruct.org This paper discusses ”computational ” systems capable of ”computing” functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite descriptions by interacting with their environment. 1