Do Accelerating Turing Machines Exist?
Paradoxes and Logical Possibilites
DOI:
https://doi.org/10.37467/revtechno.v13.5005Keywords:
Accelerating Turing Machines, Super-task, Paradoxes, Existence, Logical Possibility, Modal Analysis, Philosophy of ComputationAbstract
Accelerating Turing Machines (ATMs) are devices capable of executing super-tasks. However, the mere exercise of definition has generated several paradoxes. This paper will define the notions of super-task and ATM in a comprehensive way and will clarify what should be understood in a formal-logical context when asking about the existence of an object. Following the distinction between logical and physical possibilities, the paradoxes will be dissolved and it will be concluded that ATMs are possible and exist as abstract objects.
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