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

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

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

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

Информационные технологии и математическое моделирование (ИТММ-2019) : материалы XVIII Международной конференции им. А. Ф. Терпугова, 26−30 июня 2019 г. Ч. 1

Сборник содержит избранные материалы XVIII Международной конференции имени А.Ф. Терпугова по следующим направлениям: интеллектуальный анализ данных, информационные технологии, математическое и компьютерное моделирование. Для специалистов в области информационных технологий и математического моделирования.Текст на рус. и англ. яз