{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lectures-on-jacques-herbrand-as-a-logician","title":"Lectures on Jacques Herbrand as a Logician","arxiv_id":"0902.4682","date":"2009-02-26","proceeding":null,"authors":["Claus-Peter Wirth","Joerg Siekmann","Christoph Benzmueller","Serge Autexier"],"abstract":"We give some lectures on the work on formal logic of Jacques Herbrand, and\nsketch his life and his influence on automated theorem proving. The intended\naudience ranges from students interested in logic over historians to logicians.\nBesides the well-known correction of Herbrand's False Lemma by Goedel and\nDreben, we also present the hardly known unpublished correction of Heijenoort\nand its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's\nFundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we\ncarefully investigate Herbrand's notion of intuitionism in connection with his\nnotion of falsehood in an infinite domain. We sketch Herbrand's two proofs of\nthe consistency of arithmetic and his notion of a recursive function, and last\nbut not least, present the correct original text of his unification algorithm\nwith a new translation.","url_abs":"http://arxiv.org/abs/0902.4682v5","url_pdf":"http://arxiv.org/pdf/0902.4682v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"lectures-on-jacques-herbrand-as-a-logician","repo_url":"https://github.com/thejohncrafter/flows","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":"formal-logic","task_name":"Formal Logic"},{"task_slug":"lemma","task_name":"LEMMA"},{"task_slug":"translation","task_name":"Translation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}