--- abstract: "The value of syntax is controversial:\r\nsome see syntax as defining us as species,\r\nwhile for others it just facilitates communication.\r\nTo assess syntax\r\nwe investigate its relation to problem resolving.\r\nFirst we define a problem theory from first principles,\r\nand then we translate the theory concepts to mathematics,\r\nobtaining the requirements\r\nthat every resolution machine has to implement.\r\nSuch a resolution machine will be able to\r\nexecute any possible resolution, that is,\r\nany possible way of taking a problem expression\r\nand computing the problem solutions.\r\nTwo main requirements are found:\r\n1) syntax is needed to express problems,\r\n that is, separate words are not enough, and\r\n2) the resolution machine has to be as powerful\r\n as lambda calculus is, that is, \r\n it has to be Turing complete.\r\nNoting that every device that can generate\r\nany possible syntax, that is,\r\nany possible syntactically correct sentence\r\nof any possible, natural or artificial, language,\r\nhas to be Turing complete,\r\nwe conclude that syntax and problem resolving\r\ncan use the same components, as, for example,\r\nsentences, functions, and conditionals.\r\nThe implication to human evolution is that\r\nsyntax and problem resolving should have\r\nco-evolved in humans towards Turing completeness.\r\n" altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - papa@ramoncasares.com creators_name: - family: Casares given: Ramón honourific: '' lineage: '' date: 2014-02-24 date_type: completed datestamp: 2014-03-11 11:55:42 department: ~ dir: disk0/00/00/92/09 edit_lock_since: ~ edit_lock_until: 0 edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 9209 fileinfo: /9209/1.hassmallThumbnailVersion/Syntax-20140225.pdf;/9209/1/Syntax-20140225.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: ~ item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'syntax evolution, problem resolving, Turing completeness' lastmod: 2014-05-02 11:51:22 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE referencetext: "[Abelson and Sussman 1985] Harold Abelson, Gerald Sussman, Julie Sussman, \"Structure and Interpretation of Computer Programs\"; The MIT Press, Cambridge MA, 1985, ISBN 978-0-262-01077-1.\r\n\r\n[Arbib 1987] Michael Arbib, \"Brains, Machines, and Mathematics\", Second Edition; Springer-Verlag, New York, 1987, ISBN 978-0-387-96539-0.\r\n\r\n[Bickerton 2009] Derek Bickerton, \"Adam's Tongue: How Humans Made Language, How Language Made Humans\"; Hill and Wang, New York, 2009, ISBN 978-0-8090-1647-1.\r\n\r\n[Casares 1993] Ramón Casares, \"Ingeniería del aprendizaje: Hacia una teoría formal y fundamental del aprendizaje\"; Universidad Politécnica de Madrid, 1993 (in Spanish).\r\n\r\n[Casares 1999] Ramón Casares, \"El problema aparente: Una teoría del conocimiento\"; Visor Dis., Madrid, 1999, ISBN 978-84-7774-877-9 (in Spanish).\r\n\r\n[Casares 2010] Ramón Casares, \"El doble compresor: La teoría de la información\"; www.ramoncasares.com, 2010, ISBN 978-1-4536-0915-6 (in Spanish).\r\n\r\n[Casares 2012] Ramón Casares, \"On Freedom: The Theory of Subjectivity\"; www.ramoncasares.com, 2012, ISBN 978-1-4752-8739-4.\r\n\r\n[Chomsky 1959] Noam Chomsky, \"On Certain Formal Properties of Grammars\"; in Information and Control, Volume 2, Issue 2, pp. 137-167, June 1959.\r\n\r\n[Chomsky 2000] Noam Chomsky, \"New Horizons in the Study of Language and Mind\"; Cambridge University Press, Cambridge, 2000, ISBN 978-0-521-65822-5.\r\n\r\n[Church 1935] Alonzo Church, \"An Unsolvable Problem of Elementary Number Theory\"; in American Journal of Mathematics, Vol. 58, No. 2 (Apr., 1936), pp. 345-363. Presented to the American Mathematical Society, April 19, 1935.\r\n\r\n[Hauser, Chomsky, and Fitch 2002] Marc Hauser, Noam Chomsky, Tecumseh Fitch, \"The Language Faculty: Who Has It, What Is It, and How Did It Evolved?\"; in Science 298, pp. 1569-1579, 2002.\r\n\r\n[Kenneally 2007] Christine Kenneally, \"The First Word: The Search for the Origins of Language\"; Penguin Books, New York, 2008, ISBN 978-0-14-311374-4.\r\n\r\n[Turing 1936] Alan Turing, \"On Computable Numbers, with an Application to the Entscheidungsproblem\"; in Proceedings of the London Mathematical Society, Volume s2-42, Issue 1, pp 230-265, 1937. Received 28 May, 1936. Read 12 November, 1936.\r\n" relation_type: [] relation_uri: [] reportno: ~ rev_number: 15 series: ~ source: ~ status_changed: 2014-03-11 11:55:42 subjects: - bio-evo - comp-sci-lang - ling-syntax succeeds: ~ suggestions: It requires a good understanding of computing theory. sword_depositor: ~ sword_slug: ~ thesistype: ~ title: Resolution Machinery type: preprint userid: 22782 volume: ~