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

Haim Gaifman
Columbia University
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
Categories (categorize this paper)
ISBN(s) 0022-362X
DOI 10.2307/2678427
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,379
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

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.

View all 9 citations / Add more citations

Similar books and articles

Heterologicality and Incompleteness.Cezary Cieśliński - 2002 - Mathematical Logic Quarterly 48 (1):105-110.
On Some Much Maligned Remarks of Wittgenstein on Gödel.Charles Sayward - 2001 - Philosophical Investigations 24 (3):262–270.
On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
Gödel's Incompleteness Theorems and Computer Science.Roman Murawski - 1997 - Foundations of Science 2 (1):123-135.
Gödel’s Incompleteness Theorems and Physics.Newton C. A. Da Costa - 2011 - Principia: An International Journal of Epistemology 15 (3):453-459.
The Scope of Gödel’s First Incompleteness Theorem.Bernd Buldt - 2014 - Logica Universalis 8 (3-4):499-552.
A Note On Interaction And Incompleteness.Damjan Bojadžiev - 2003 - Logic Journal of the IGPL 11 (5):513-523.


Added to PP index

Total views
495 ( #18,620 of 2,519,686 )

Recent downloads (6 months)
6 ( #116,860 of 2,519,686 )

How can I increase my downloads?


My notes