Journal of Philosophy 97 (8):462 (2000)

Authors
Haim Gaifman
Columbia University
Abstract
In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and more forceful. Yet the argument fails in an interesting and revealing way. And it leaves a remainder: if some computer does in fact simulate all our mathematical reasoning, then, in principle, we cannot fully grasp how it works. Gödel’s result also points out a certain essential limitation of self-reflection. The resulting picture parallels, not accidentally, Davidson’s view of psychology, as a science that in principle must remain “imprecise”, not fully spelt out. What is intended here by “fully grasp”, and how all this is related to self-reflection, will become clear at the end of this comment
Keywords Analytic Philosophy  Contemporary Philosophy
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ISBN(s) 0022-362X
DOI 10.2307/2678427
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On Ontology and Realism in Mathematics.Haim Gaifman - 2012 - Review of Symbolic Logic 5 (3):480-512.
On the Depth of Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Philosophia Mathematica.
Remarks on the Gödelian Anti-Mechanist Arguments.Panu Raatikainen - 2020 - Studia Semiotyczne 34 (1):267–278.
Proving Unprovability.Bruno Whittle - 2017 - Review of Symbolic Logic 10 (1):92–115.

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