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Implementation Is Semantic Interpretation: Further Thoughts
 Journal of Experimental and Theoretical Artificial Intelligence
, 2005
"... This essay explores the implications of the thesis that implementation is semantic interpretation. Implementation is (at least) a ternary relation: I is an implementation of an ‘Abstraction ’ A in some medium M. Examples are presented from the arts, from language, from computer science and from cogn ..."
Abstract

Cited by 4 (3 self)
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This essay explores the implications of the thesis that implementation is semantic interpretation. Implementation is (at least) a ternary relation: I is an implementation of an ‘Abstraction ’ A in some medium M. Examples are presented from the arts, from language, from computer science and from cognitive science, where both brains and computers can be understood as implementing a ‘mind Abstraction’. Implementations have side effects due to the implementing medium; these can account for several puzzles surrounding qualia. Finally, an argument for benign panpsychism is developed.
Mathematical knowledge
, 2007
"... Abstract The original proof of the fourcolor theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depe ..."
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Abstract The original proof of the fourcolor theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computationintensive custombuilt software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary customwritten code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the fourcolor theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system.