{"id":30,"date":"2020-01-29T15:33:28","date_gmt":"2020-01-29T15:33:28","guid":{"rendered":"https:\/\/www.st-andrews.ac.uk\/philevents\/event\/super-special-seminar-walter-dean-warwick-on-consistency-and-existence-in-mathematics\/"},"modified":"2020-02-11T15:34:14","modified_gmt":"2020-02-11T15:34:14","slug":"super-special-seminar-walter-dean-warwick-on-consistency-and-existence-in-mathematics","status":"publish","type":"tribe_events","link":"https:\/\/www.st-andrews.ac.uk\/philevents\/event\/super-special-seminar-walter-dean-warwick-on-consistency-and-existence-in-mathematics\/","title":{"rendered":"Super Special Seminar Walter Dean (Warwick) On consistency and existence in mathematics"},"content":{"rendered":"

Abstract:\u00a0<\/strong> Following the publication of his Foundations of Geometry<\/i>\u00a0in 1899, David Hilbert engaged in a well-known debate with Frege which concerned (amongst other things) the question of whether the consistency of a set of axioms entails the existence of a model in which they are satisfied.\u00a0 \u00a0I will consider this dimension of the so-called Frege-Hilbert controversy in light of the subsequent work in logic and philosophy which it inspired.\u00a0 I will argue for the following claims: i) the controversy both anticipated G\u00f6del’s completeness theorem and shaped its reception (in which Bernays played a central role); ii) Frege was right to maintain that consistency checking is as difficult as it can be; ii) Hilbert was also right to maintain that given consistency,\u00a0<\/i>\u00a0demonstrating the existence of a model is as easy as it can be.<\/p>\n","protected":false},"excerpt":{"rendered":"

Abstract:\u00a0 Following the publication of his Foundations of Geometry\u00a0in 1899, David Hilbert engaged in a well-known debate with Frege which concerned (amongst other things) the question of whether the consistency…<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","meta":{"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":""},"tags":[],"tribe_events_cat":[7],"class_list":["post-30","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-super-special-seminar-series","cat_super-special-seminar-series"],"_links":{"self":[{"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tribe_events\/30","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":1,"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tribe_events\/30\/revisions"}],"predecessor-version":[{"id":196,"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tribe_events\/30\/revisions\/196"}],"wp:attachment":[{"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/media?parent=30"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tags?post=30"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/philevents\/wp-json\/wp\/v2\/tribe_events_cat?post=30"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}