{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/52706"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/52706","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The Utility of Mathematical Symbols","abstract":"Explanations of why mathematics is useful to empirical research focus on mathematics' role as a representation or model. On platonist accounts, the representational relation is one of structural correspondence between features of the real world and the abstract mathematical structures that represent them. Where real numbers are concerned, however, there is good reason to think the world's correspondence with systems of real number symbols, rather than the real numbers themselves, can be utilized for our representational purposes. One way this can be accomplished is through a paraphrase interpretation of real number symbols where the symbols are taken to refer directly to the things in the world real numbers are supposed to represent. A platonist account of structural correspondence between structures of real numbers and the world can be found in the foundations of measurement where a scale of real numbers is applied to quantities of physical properties like length, mass and velocity. This subject will be employed as a demonstration of how abstract real numbers, traditionally construed as modeling features of the world, are superfluous if their symbols are taken to refer directly to those features.","abstract_html":"Explanations of why mathematics is useful to empirical research focus on mathematics' role as a representation or model. On platonist accounts, the representational relation is one of structural correspondence between features of the real world and the abstract mathematical structures that represent them. Where real numbers are concerned, however, there is good reason to think the world's correspondence with systems of real number symbols, rather than the real numbers themselves, can be utilized for our representational purposes. One way this can be accomplished is through a paraphrase interpretation of real number symbols where the symbols are taken to refer directly to the things in the world real numbers are supposed to represent. A platonist account of structural correspondence between structures of real numbers and the world can be found in the foundations of measurement where a scale of real numbers is applied to quantities of physical properties like length, mass and velocity. This subject will be employed as a demonstration of how abstract real numbers, traditionally construed as modeling features of the world, are superfluous if their symbols are taken to refer directly to those features.","abstract_has_math":false,"creators":["Waters, John Michael"],"institution":"Virginia Tech","degree_name":"Master of Arts","degree_level":"masters","degree_discipline":"Philosophy","degree_department":"Philosophy","school":null,"contributors":[],"advisors":[],"committee_chairs":["Mayo, Deborah G."],"committee_members":["Trogdon, Kelly Griffith","Patton, Lydia K."],"year":2015,"date_issued":"2015-05-27","date_published":"2015-05-27","updated_at":"2026-07-22T22:19:06Z","subjects":["Measurement theory","number symbol","structural correspondence"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:5488"],"render_values":[{"text":"vt_gsexam:5488","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/52706","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Mayo, Deborah G."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Trogdon, Kelly Griffith","Patton, Lydia K."]},{"key":"dc:contributor.department","label":"Department","values":["Philosophy"]},{"key":"dc:creator","label":"Author","values":["Waters, John Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-05-28T08:00:31Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-28T08:00:31Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-05-27"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Philosophy"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Measurement theory","number symbol","structural correspondence"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:5488"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/52706"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Explanations of why mathematics is useful to empirical research focus on mathematics' role as a representation or model. On platonist accounts, the representational relation is one of structural correspondence between features of the real world and the abstract mathematical structures that represent them. Where real numbers are concerned, however, there is good reason to think the world's correspondence with systems of real number symbols, rather than the real numbers themselves, can be utilized for our representational purposes. One way this can be accomplished is through a paraphrase interpretation of real number symbols where the symbols are taken to refer directly to the things in the world real numbers are supposed to represent. A platonist account of structural correspondence between structures of real numbers and the world can be found in the foundations of measurement where a scale of real numbers is applied to quantities of physical properties like length, mass and velocity. This subject will be employed as a demonstration of how abstract real numbers, traditionally construed as modeling features of the world, are superfluous if their symbols are taken to refer directly to those features."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Arts"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["The Utility of Mathematical Symbols"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Mayo, Deborah G."],"dc:contributor.committeemember":["Trogdon, Kelly Griffith","Patton, Lydia K."],"dc:contributor.department":["Philosophy"],"dc:creator":["Waters, John Michael"],"dc:date.accessioned":["2015-05-28T08:00:31Z"],"dc:date.available":["2015-05-28T08:00:31Z"],"dc:date.issued":["2015-05-27"],"dc:description.abstract":["Explanations of why mathematics is useful to empirical research focus on mathematics' role as a representation or model. On platonist accounts, the representational relation is one of structural correspondence between features of the real world and the abstract mathematical structures that represent them. Where real numbers are concerned, however, there is good reason to think the world's correspondence with systems of real number symbols, rather than the real numbers themselves, can be utilized for our representational purposes. One way this can be accomplished is through a paraphrase interpretation of real number symbols where the symbols are taken to refer directly to the things in the world real numbers are supposed to represent. A platonist account of structural correspondence between structures of real numbers and the world can be found in the foundations of measurement where a scale of real numbers is applied to quantities of physical properties like length, mass and velocity. This subject will be employed as a demonstration of how abstract real numbers, traditionally construed as modeling features of the world, are superfluous if their symbols are taken to refer directly to those features."],"dc:description.degree":["Master of Arts"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:5488"],"dc:identifier.uri":["http://hdl.handle.net/10919/52706"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Measurement theory","number symbol","structural correspondence"],"dc:title":["The Utility of Mathematical Symbols"],"dc:type":["Thesis"],"thesis:degree_discipline":["Philosophy"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Arts"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:06Z"}