{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/107892"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/107892","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Investigations linking the philosophy and psychology of mathematics","abstract":"Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of mathematics and philosophy of mathematics. This dissertation seeks to add to recent examples of such interdisciplinary work. I discuss three somewhat self-contained topics. In chapter two, I discuss some recent work in cognitive science on the topic of mental representation and show how we can shed light on a puzzle in the philosophy of mathematics by applying it to the issue of the mental representation of mathematics. In chapter three, I discuss a couple theories of the cognitive psychology of deduction and why some recent work in the philosophy of mathematics on diagrammatic reasoning in Euclidian proofs shows those theories have some shortcomings. Finally, in chapter four, I discuss how we can get at the question of what makes a system of representation, e.g. numeral systems or formal languages, good for doing mathematics, by considering how the cognitive system uses such things in the course of doing mathematics.","abstract_html":"Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of mathematics and philosophy of mathematics. This dissertation seeks to add to recent examples of such interdisciplinary work. I discuss three somewhat self-contained topics. In chapter two, I discuss some recent work in cognitive science on the topic of mental representation and show how we can shed light on a puzzle in the philosophy of mathematics by applying it to the issue of the mental representation of mathematics. In chapter three, I discuss a couple theories of the cognitive psychology of deduction and why some recent work in the philosophy of mathematics on diagrammatic reasoning in Euclidian proofs shows those theories have some shortcomings. Finally, in chapter four, I discuss how we can get at the question of what makes a system of representation, e.g. numeral systems or formal languages, good for doing mathematics, by considering how the cognitive system uses such things in the course of doing mathematics.","abstract_has_math":false,"creators":["Keller, James"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Philosophy","degree_department":null,"school":null,"contributors":["Arana, Andrew","Saenz, Noel","Livengood, Jonathan","Levinstein, Benjamin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T21:54:21Z","date_published":"2020-08-26T21:54:21Z","updated_at":"2026-07-22T22:24:47Z","subjects":["Philosophy","Mathematics","Psychology","Deduction","Understanding","Representation","Cognitive","Practice","Mental","Proof"],"languages":["en"],"rights":["Copyright 2020 James Keller"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/107892","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Arana, Andrew","Saenz, Noel","Livengood, Jonathan","Levinstein, Benjamin"]},{"key":"dc:creator","label":"Author","values":["Keller, James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T21:54:21Z","2020-04-20","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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","Psychology","Deduction","Understanding","Representation","Cognitive","Practice","Mental","Proof"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 James Keller"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/107892"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of mathematics and philosophy of mathematics. This dissertation seeks to add to recent examples of such interdisciplinary work. I discuss three somewhat self-contained topics. In chapter two, I discuss some recent work in cognitive science on the topic of mental representation and show how we can shed light on a puzzle in the philosophy of mathematics by applying it to the issue of the mental representation of mathematics. In chapter three, I discuss a couple theories of the cognitive psychology of deduction and why some recent work in the philosophy of mathematics on diagrammatic reasoning in Euclidian proofs shows those theories have some shortcomings. Finally, in chapter four, I discuss how we can get at the question of what makes a system of representation, e.g. numeral systems or formal languages, good for doing mathematics, by considering how the cognitive system uses such things in the course of doing mathematics.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, James Keller, accepted the attached license on 2020-04-17 at 10:36.","The student, James Keller, submitted this Dissertation for approval on 2020-04-17 at 10:50.","This Dissertation was approved for publication on 2020-04-20 at 09:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14992 on 2020-08-25 at 17:07:12","Made available in DSpace on 2020-08-26T21:54:21Z (GMT). No. of bitstreams: 3 KELLER-DISSERTATION-2020.pdf: 801413 bytes, checksum: a6864f5dfe53f7236639e66db7fbe0d8 (MD5) Thesis-Doctoral-JAMES-KELLER.docx: 480982 bytes, checksum: c9eee2cab582b2409b6a4e9ad8f21cc3 (MD5) LICENSE.txt: 4209 bytes, checksum: 47bb97399a7711a10044c1c8e1ccd55b (MD5) Previous issue date: 2020-04-20"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Investigations linking the philosophy and psychology of mathematics"]}]}],"canonical_facts":{"dc:contributor":["Arana, Andrew","Saenz, Noel","Livengood, Jonathan","Levinstein, Benjamin"],"dc:creator":["Keller, James"],"dc:date":["2020-08-26T21:54:21Z","2020-04-20","2020-05"],"dc:description":["Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of mathematics and philosophy of mathematics. This dissertation seeks to add to recent examples of such interdisciplinary work. I discuss three somewhat self-contained topics. In chapter two, I discuss some recent work in cognitive science on the topic of mental representation and show how we can shed light on a puzzle in the philosophy of mathematics by applying it to the issue of the mental representation of mathematics. In chapter three, I discuss a couple theories of the cognitive psychology of deduction and why some recent work in the philosophy of mathematics on diagrammatic reasoning in Euclidian proofs shows those theories have some shortcomings. Finally, in chapter four, I discuss how we can get at the question of what makes a system of representation, e.g. numeral systems or formal languages, good for doing mathematics, by considering how the cognitive system uses such things in the course of doing mathematics.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, James Keller, accepted the attached license on 2020-04-17 at 10:36.","The student, James Keller, submitted this Dissertation for approval on 2020-04-17 at 10:50.","This Dissertation was approved for publication on 2020-04-20 at 09:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14992 on 2020-08-25 at 17:07:12","Made available in DSpace on 2020-08-26T21:54:21Z (GMT). No. of bitstreams: 3 KELLER-DISSERTATION-2020.pdf: 801413 bytes, checksum: a6864f5dfe53f7236639e66db7fbe0d8 (MD5) Thesis-Doctoral-JAMES-KELLER.docx: 480982 bytes, checksum: c9eee2cab582b2409b6a4e9ad8f21cc3 (MD5) LICENSE.txt: 4209 bytes, checksum: 47bb97399a7711a10044c1c8e1ccd55b (MD5) Previous issue date: 2020-04-20"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/107892"],"dc:language":["en"],"dc:rights":["Copyright 2020 James Keller"],"dc:subject":["Philosophy","Mathematics","Psychology","Deduction","Understanding","Representation","Cognitive","Practice","Mental","Proof"],"dc:title":["Investigations linking the philosophy and psychology of mathematics"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Philosophy"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}