{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97532"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97532","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Mathematics, cognition, and you!","abstract":"In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics (and back again) without losing anything that is characteristic of either methodological class. Mathematics is a collection of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including (though not limited to) logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the characteristic of being convincing to a sound mathematical mind. Even though what in particular makes each of these methods of proof convincing differs, that they are convincing is enough to usher forth mathematical understanding. The chapters of this dissertation explore (i) a new naturalistic metaphysics for under- standing “where mathematics comes from”, (ii) recent psychological findings in the the nature of mathematical reasoning, (iii) the concatenation of two historical forms of reasoning (real and ideal), (iv) the possibility of an epistemic bridge between real and ideal methods, and (v) the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.","abstract_html":"In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics (and back again) without losing anything that is characteristic of either methodological class. Mathematics is a collection of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including (though not limited to) logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the characteristic of being convincing to a sound mathematical mind. Even though what in particular makes each of these methods of proof convincing differs, that they are convincing is enough to usher forth mathematical understanding. The chapters of this dissertation explore (i) a new naturalistic metaphysics for under- standing “where mathematics comes from”, (ii) recent psychological findings in the the nature of mathematical reasoning, (iii) the concatenation of two historical forms of reasoning (real and ideal), (iv) the possibility of an epistemic bridge between real and ideal methods, and (v) the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.","abstract_has_math":false,"creators":["Bohall, Jordan Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Philosophy","degree_department":null,"school":null,"contributors":["Carr, Jennifer","Sanders, Kirk","Waskan, Jon","Hummel, John"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:51:35Z","date_published":"2017-08-10T19:51:35Z","updated_at":"2026-07-22T22:24:34Z","subjects":["Philosophy","Mathematics"],"languages":["en"],"rights":["Copyright 2017 Jordan Bohall"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97532","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carr, Jennifer","Sanders, Kirk","Waskan, Jon","Hummel, John"]},{"key":"dc:creator","label":"Author","values":["Bohall, Jordan Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:51:35Z","2019-08-11T09:15:24Z","2017-01-25","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Philosophy"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Philosophy","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Jordan Bohall"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97532"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In what follows I argue for an epistemic bridge principle that allows us to move from real mathematics to ideal mathematics (and back again) without losing anything that is characteristic of either methodological class. 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The chapters of this dissertation explore (i) a new naturalistic metaphysics for under- standing “where mathematics comes from”, (ii) recent psychological findings in the the nature of mathematical reasoning, (iii) the concatenation of two historical forms of reasoning (real and ideal), (iv) the possibility of an epistemic bridge between real and ideal methods, and (v) the implication of this new bridge principle for the long-standing concern that Go ̈del’s Incompleteness Theorems shake the foundation of modern mathematics.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-05-01","The student, Jordan Bohall, accepted the attached license on 2017-01-18 at 16:44.","The student, Jordan Bohall, submitted this Dissertation for approval on 2017-01-18 at 16:48.","This Dissertation was approved for publication on 2017-01-25 at 16:02.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10543 on 2017-08-10 at 14:29:27","Made available in DSpace on 2017-08-10T19:51:35Z (GMT). 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Mathematics is a collection of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including (though not limited to) logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the characteristic of being convincing to a sound mathematical mind. Even though what in particular makes each of these methods of proof convincing differs, that they are convincing is enough to usher forth mathematical understanding. 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