Computability and human symbolic output

• Authors: Megill Jason , Melvin Tim
• Languages of publication: EN

Abstracts

EN

This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is finite. But then, given fundamental results in recursion theory, the set will also be recursive, recursively enumerable, axiomatizable, and could be the output of a Turing machine. We then argue that it is impossible to produce a string of symbols that humans could possibly produce but no Turing machine could. Moreover, we show that any given string of symbols that we could produce could also be the output of a Turing machine. Our arguments have implications for Hilbert’s sixth problem and the possibility of axiomatizing particular sciences, they undermine at least two distinct arguments against the possibility of Artificial Intelligence, and they entail that expert systems that are the equals of human experts are possible, and so at least one of the goals of Artificial Intelligence can be realized, at least in principle.

Keywords

EN

Computability theory; Turing machines; axiomatization of sciences; artificial intelligence

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2014
• Volume: 23
• Issue: 4
• Pages: 391–401

Dates

published

2014-12-01

online

2014-04-30

Contributors

author

Megill Jason

• Carroll College, Department of Philosophy, Helena, Montana, USA

author

Melvin Tim

• Carroll College, Department of Mathematics, Helena, Montana, USA

References

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Identifiers

DOI

10.12775/LLP.2014.009