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The Kleene Symposium

North-Holland (1980)

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  1. Set theory and physics.K. Svozil - 1995 - Foundations of Physics 25 (11):1541-1560.
    Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible “solution of supertasks,” and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for physical applications are discussed: (...)
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  • (1 other version)What Is Nature-Like Computation? A Behavioural Approach and a Notion of Programmability.Hector Zenil - 2013 - Philosophy and Technology (3):1-23.
    The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment—the input—as reflected in a measure of programmability. This definition is intended to have relevance beyond the realm of digital computers, particularly vis-à-vis natural systems. This will be done by using an extension of a phase transition coefficient previously defined in an attempt to characterise the dynamical behaviour of cellular automata (...)
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  • Turing-, human- and physical computability: An unasked question. [REVIEW]Eli Dresner - 2008 - Minds and Machines 18 (3):349-355.
    In recent years it has been convincingly argued that the Church-Turing thesis concerns the bounds of human computability: The thesis was presented and justified as formally delineating the class of functions that can be computed by a human carrying out an algorithm. Thus the Thesis needs to be distinguished from the so-called Physical Church-Turing thesis, according to which all physically computable functions are Turing computable. The latter is often claimed to be false, or, if true, contingently so. On all accounts, (...)
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  • Choice sequences and informal rigour.A. S. Troelstra - 1985 - Synthese 62 (2):217 - 227.
    In this paper we discuss a particular example of the passage from the informal, but rigorous description of a concept to the axiomatic formulation of principles holding for the concept; in particular, we look at the principles of continuity and lawlike choice in the theory of lawless sequences. Our discussion also leads to a better understanding of the rôle of the so-called density axiom for lawless sequences.
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  • The church-Turing thesis and effective mundane procedures.Leon Horsten - 1995 - Minds and Machines 5 (1):1-8.
    We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number theoretic functions (...)
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  • Concrete Digital Computation: What Does it Take for a Physical System to Compute? [REVIEW]Nir Fresco - 2011 - Journal of Logic, Language and Information 20 (4):513-537.
    This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to (...)
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  • Quantum algorithms: Philosophical lessons.Amit Hagar - 2007 - Minds and Machines 17 (2):233-247.
    I discuss the philosophical implications that the rising new science of quantum computing may have on the philosophy of computer science. While quantum algorithms leave the notion of Turing-Computability intact, they may re-describe the abstract space of computational complexity theory hence militate against the autonomous character of some of the concepts and categories of computer science.
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  • Computability of String Functions Over Algebraic Structures Armin Hemmerling.Armin Hemmerling - 1998 - Mathematical Logic Quarterly 44 (1):1-44.
    We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a BSS-like (...)
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  • The Explanatory Role of Computation in Cognitive Science.Nir Fresco - 2012 - Minds and Machines 22 (4):353-380.
    Which notion of computation (if any) is essential for explaining cognition? Five answers to this question are discussed in the paper. (1) The classicist answer: symbolic (digital) computation is required for explaining cognition; (2) The broad digital computationalist answer: digital computation broadly construed is required for explaining cognition; (3) The connectionist answer: sub-symbolic computation is required for explaining cognition; (4) The computational neuroscientist answer: neural computation (that, strictly, is neither digital nor analogue) is required for explaining cognition; (5) The extreme (...)
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