---
abstract: "Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, \"This formula is unprovable-in-the-system\". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that \"This formula is unprovable-in-the-system\" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula \"This formula is unprovable-in-the-system\" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula \"This formula is unprovablein- the-system\" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, \"This formula is unprovable-in-the-system\" is true. Goedel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines."
altloc:
  - http://users.ox.ac.uk/~jrlucas/mmg.html
chapter: ~
commentary: ~
commref: ~
confdates: ~
conference: ~
confloc: ~
contact_email: ~
creators_id: []
creators_name:
  - family: Lucas
    given: J.R.
    honourific: ''
    lineage: ''
date: 1961
date_type: published
datestamp: 1998-07-24
department: ~
dir: disk0/00/00/03/56
edit_lock_since: ~
edit_lock_until: ~
edit_lock_user: ~
editors_id: []
editors_name: []
eprint_status: archive
eprintid: 356
fileinfo: /style/images/fileicons/text_html.png;/356/1/lucas.html
full_text_status: public
importid: ~
institution: ~
isbn: ~
ispublished: pub
issn: ~
item_issues_comment: []
item_issues_count: 0
item_issues_description: []
item_issues_id: []
item_issues_reported_by: []
item_issues_resolved_by: []
item_issues_status: []
item_issues_timestamp: []
item_issues_type: []
keywords: "goedel's theorem, computation, computability, symbolsystems, computationalism, cognitivism, machines, mind, provability, mental models, Penrose, Searle"
lastmod: 2011-03-11 08:53:51
latitude: ~
longitude: ~
metadata_visibility: show
note: ~
number: ~
pagerange: 112-127
pubdom: TRUE
publication: Philosophy
publisher: ~
refereed: TRUE
referencetext: ~
relation_type: []
relation_uri: []
reportno: ~
rev_number: 8
series: ~
source: ~
status_changed: 2007-09-12 16:26:54
subjects:
  - cog-psy
  - comp-sci-art-intel
  - phil-logic
  - phil-mind
  - phil-sci
succeeds: ~
suggestions: ~
sword_depositor: ~
sword_slug: ~
thesistype: ~
title: 'Minds, Machines and Goedel'
type: journalp
userid: 63
volume: 36
<script src="//archive-bar.soton.ac.uk/archive-bar.js"></script>