Hewitt, Carl (2019) For Cybersecurity, Computer Science Must Rely on the Opposite of Gödel’s Results. [Preprint]

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Abstract

This article shows how fundamental higher-order theories of mathematical structures of computer science (e.g. natural numbers [Dedekind 1888] and Actors [Hewitt et. al. 1973]) are cetegorical meaning that they can be axiomatized up to a unique isomorphism thereby removing any ambiguity in the mathematical structures being axiomatized. Having these mathematical structures precisely defined can make systems more secure because there are fewer ambiguities and holes for cyberattackers to exploit. For example, there are no infinite elements in models for natural numbers to be exploited. On the other hand, the 1st-order theories of Gödel’s results necessarily leave the mathematical structures ill-defined, e.g., there are necessarily models with infinite integers.
Cyberattackers have severely damaged national, corporate, and individual security as well causing hundreds of billions of dollars of economic damage. A significant cause of the damage is that current engineering practices are not sufficiently grounded in theoretical principles. In the last two decades, little new theoretical work has been done that practically impacts large engineering projects with the result that computer systems engineering education is insufficient in providing theoretical grounding. If the current cybersecurity situation is not quickly remedied, it will soon become much worse because of the projected development of Scalable Intelligent Systems by 2025 [Hewitt 2019].
Gödel strongly advocated that the Turing Machine is the preeminent universal model of computation. A Turing machine formalizes an algorithm in which computation proceeds without external interaction. However, computing is now highly interactive, which this article proves is beyond the capability of a Turing Machine. Instead of the Turing Machine model, this article presents an axiomatization of a universal model of digital computation (including implementation of Scalable Intelligent Systems) up to a unique isomorphism.

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Item Type:	Preprint
Creators:	Creators Email ORCID Hewitt, Carl carlehewitt@gmail.com
Keywords:	categorical theories, strong types, Scalable Intelligent Systems, Alonzo Church, Kurt Gödel, Richard Dedekind
Subjects:	Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Artificial Intelligence > Classical AI Specific Sciences > Computer Science Specific Sciences > Cultural Evolution
Depositing User:	Prof. Carl Hewitt
Date Deposited:	09 May 2019 20:57
Last Modified:	09 May 2019 20:57
Item ID:	15989
Subjects:	Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Artificial Intelligence > Classical AI Specific Sciences > Computer Science Specific Sciences > Cultural Evolution
Date:	3 May 2019
URI:	https://philsci-archive.pitt.edu/id/eprint/15989

Available Versions of this Item

• For Cybersecurity, Computer Science Must Rely on the Opposite of Gödel’s Results. (deposited 06 May 2019 15:55)
  • For Cybersecurity, Computer Science Must Rely on the Opposite of Gödel’s Results. (deposited 07 May 2019 17:04)
    • For Cybersecurity, Computer Science Must Rely on the Opposite of Gödel’s Results. (deposited 09 May 2019 20:57) [Currently Displayed]

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