14 research outputs found

    A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

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    There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\'emeti and D\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis.Comment: 27 pages, 5 figures. Forthcoming in Synthese. Matches published versio

    In Defense of a Constructive Truth Concept

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    I address some major critical arguments against a constructive truth concept and intuitionist logic. I put the notions of in principle possibilities and valid constructions (mathematical proofs) under scrutiny. I argue that the objections against a constructive account of truth miss target, thus they are not decisive. Eventually, constructivism is at least as cogent and natural a stance as realism

    In Defense of a Constructive Truth Concept

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    I address some major critical arguments against a constructive truth concept and intuitionist logic. I put the notions of in principle possibilities and valid constructions (mathematical proofs) under scrutiny. I argue that the objections against a constructive account of truth miss target, thus they are not decisive. Eventually, constructivism is at least as cogent and natural a stance as realism

    Π˜Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ ΠΈ матСматичСскоС ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ (ИВММ-2019) : ΠΌΠ°Ρ‚Π΅Ρ€ΠΈΠ°Π»Ρ‹ XVIII ΠœΠ΅ΠΆΠ΄ΡƒΠ½Π°Ρ€ΠΎΠ΄Π½ΠΎΠΉ ΠΊΠΎΠ½Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠΈ ΠΈΠΌ. А. Π€. Π’Π΅Ρ€ΠΏΡƒΠ³ΠΎΠ²Π°, 26βˆ’30 июня 2019 Π³. Π§. 1

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    Π‘Π±ΠΎΡ€Π½ΠΈΠΊ содСрТит ΠΈΠ·Π±Ρ€Π°Π½Π½Ρ‹Π΅ ΠΌΠ°Ρ‚Π΅Ρ€ΠΈΠ°Π»Ρ‹ XVIII ΠœΠ΅ΠΆΠ΄ΡƒΠ½Π°Ρ€ΠΎΠ΄Π½ΠΎΠΉ ΠΊΠΎΠ½Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠΈ ΠΈΠΌΠ΅Π½ΠΈ А.Π€. Π’Π΅Ρ€ΠΏΡƒΠ³ΠΎΠ²Π° ΠΏΠΎ ΡΠ»Π΅Π΄ΡƒΡŽΡ‰ΠΈΠΌ направлСниям: ΠΈΠ½Ρ‚Π΅Π»Π»Π΅ΠΊΡ‚ΡƒΠ°Π»ΡŒΠ½Ρ‹ΠΉ Π°Π½Π°Π»ΠΈΠ· Π΄Π°Π½Π½Ρ‹Ρ…, ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ, матСматичСскоС ΠΈ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅. Для спСциалистов Π² области ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ ΠΈ матСматичСского модСлирования.ВСкст Π½Π° рус. ΠΈ Π°Π½Π³Π». яз
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