LanCog Logic Seminar Series<\/p>\n
<\/p>\n
Friday, March 10, 10:00\u201412:00 (UTC)<\/p>\n
The University of Lisbon<\/p>\n
Faculty of Letters, room\u00a0B112.G (Library wing)<\/p>\n
<\/p>\n
Francesca Boccuni<\/p>\n
University San Raffaele, Milan<\/p>\n
<\/p>\n
The Logical Ontology of Abstractionism<\/strong><\/p>\n Neologicism aims at founding arithmetic on full second-order logic and Hume\u2019s Principle, which states that the number of the\u00a0Fs is identical with the number of the\u00a0Gs if, and only if, there are as many\u00a0Fs as\u00a0Gs, and vice versa. Nevertheless, Neologicism faces the\u00a0problem of the logical ontology\u00a0([5]), according to which the underlying second-order logic is ontologically committal. In this paper, such a problem will be tackled by substituting second-order logic by Boolos\u2019\u00a0plural logic\u00a0([2, 3]), augmented by the\u00a0Plural Frege Quantifier\u00a0Fmodelled on [1]. The resulting theory (PHP) interprets second-order Peano arithmetic PA2. Its ontological innocence will be evaluated. In this respect, PHP provides an alternative that solves the problem of the logical ontology pervading Neologicism.<\/p>\n <\/p>\n References<\/p>\n [1] Antonelli, A. (2010), \u2018Numerical Abstraction via the Frege Quantifier\u2019,\u00a0Notre Dame Journal of Formal Logic\u00a051(2): 161\u2013179.<\/p>\n [2] Boolos, G. (1998a), \u2018To be is to be the Value of a Variable (or the Values of Some Variables)\u2019, in [4]: 54\u201372.<\/p>\n [3] Boolos, G. (1998b), \u2018Nominalist Platonism\u2019, in [4]: 73\u201387.<\/p>\n [4] Boolos, G. (1998c),\u00a0Logic, Logic, and Logic, J. Burgess & R. Jeffrey (eds.), Cambridge, MA: Harvard University Press.<\/p>\n [5] Hale, B. & Wright, C. (2001),\u00a0The Reason\u2019s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, Oxford University Press.<\/p>\n","protected":false},"excerpt":{"rendered":" LanCog Logic Seminar Series Friday, March 10, 10:00\u201412:00 (UTC) The University of Lisbon Faculty of Letters, room\u00a0B112.G (Library wing) Francesca Boccuni University San Raffaele, Milan The Logical Ontology of Abstractionism Neologicism aims at founding arithmetic on full second-order logic and Hume\u2019s Principle, which states that the number of the\u00a0Fs is identical with […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"","activitypub_status":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1540","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/posts\/1540","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/comments?post=1540"}],"version-history":[{"count":1,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/posts\/1540\/revisions"}],"predecessor-version":[{"id":1541,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/posts\/1540\/revisions\/1541"}],"wp:attachment":[{"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/media?parent=1540"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/categories?post=1540"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cful.letras.ulisboa.pt\/lancog\/wp-json\/wp\/v2\/tags?post=1540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}