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2014 | 23 | 4 | 391–401
Article title

Computability and human symbolic output

Title variants
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.
Year
Volume
23
Issue
4
Pages
391–401
Physical description
Dates
published
2014-12-01
online
2014-04-30
Contributors
author
  • Carroll College, Department of Philosophy, Helena, Montana, USA
author
  • Carroll College, Department of Mathematics, Helena, Montana, USA
References
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  • Megill, J., T. Melvin, and A. Beal, “On some properties of humanly known and humanly knowable mathematics”, Axiomathes (forthcoming).
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  • Searle, J., “Minds, brains and programs”, Behavioral and Brain Sciences, 3 (1980): 417–457. DOI: 10.1017/S0140525X00005756
  • Wang, H., Popular Lectures on Mathematical Logic, Mineolam NY: Dover 1981.
  • Wightman, A.S., “Hilbert’s sixth problem: Mathematical treatment of the axioms of physics”, pages 147–240 in Mathematical Developments Arising from Hilbert Problems (ed. by F.E. Browder), Symposia in Pure Mathematics, Amer. Math. Soc., Providence, RI 1976.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-1fa6cd6b-8a4b-471a-a780-ab0aa87693ce
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