{"id":4105,"date":"2018-07-10T16:20:05","date_gmt":"2018-07-10T15:20:05","guid":{"rendered":"https:\/\/www.st-andrews.ac.uk\/arche\/?post_type=tribe_events&#038;eventDate=2019-06-06#038;p=4095"},"modified":"2019-05-30T08:14:17","modified_gmt":"2019-05-30T07:14:17","slug":"semantics-arche-logic-group-2019-06-06","status":"publish","type":"tribe_events","link":"https:\/\/www.st-andrews.ac.uk\/arche\/event\/semantics-arche-logic-group-2019-06-06\/","title":{"rendered":"Semantics\/Arche Logic Group: Thomas Schindler Talk"},"content":{"rendered":"<div><b>Thomas Schindler: A G\u00f6delian solution of the class-theoretic paradoxes<\/b><\/div>\n<div><\/div>\n<div>Abstract: A class is the extension of some predicate. Classes are not to be confused with sets: many sets cannot be defined by a predicate, and some predicates have extensions which are \u201ctoo big\u201d to be set. Classes are useful because they allow us to generalise predicate places in our language (I\u2019ll elaborate on this in my talk). Unfortunately, due to Russell\u2019s paradox, the naive notion of class is inconsistent, and the standard solution to the paradoxes &#8211; the theory of types &#8211; is insufficient for many purposes in logic and philosophy (I\u2019ll elaborate this point as well). In this talk I will present a type-free theory of classes (i.e. a theory that admits self-membered classes) that is loosely based on some ideas of G\u00f6del. In particular, I\u2019ll present an axiom which essentially states that all paradoxes are due to some form of circularity, and show that this axiom gives you full second-order logic. I\u2019ll also present a strengthening of the circularity axiom from which one can derive axioms of infinity, separation, sums, pairs, and instances of replacement. If time permits, I\u2019ll argue that G\u00f6del\u2019s idea allows one to formulate a (positive) solution to the problem of unrestricted quantification &#8211; the question whether we can quantify over absolutely everything.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Thomas Schindler: A G\u00f6delian solution of the class-theoretic paradoxes Abstract: A class is the extension of some predicate. Classes are not to be confused with&#8230;<\/p>\n","protected":false},"author":2,"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":"","_members_access_role":[],"_members_access_error":"","_links_to":"","_links_to_target":""},"tags":[],"tribe_events_cat":[44,28],"class_list":["post-4105","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-arche-logic-group","tribe_events_cat-asg-semantics-seminar","cat_arche-logic-group","cat_asg-semantics-seminar"],"_links":{"self":[{"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tribe_events\/4105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/users\/2"}],"version-history":[{"count":2,"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tribe_events\/4105\/revisions"}],"predecessor-version":[{"id":4874,"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tribe_events\/4105\/revisions\/4874"}],"wp:attachment":[{"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/media?parent=4105"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tags?post=4105"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/wp\/v2\/tribe_events_cat?post=4105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}