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--- 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