Pub Date : 2021-03-18DOI: 10.1017/9781139600293.004
John Hester
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main topics will be the independent existence of mathematics and controversies over the nature of the mathematical infinite. After describing these ideas, I will demonstrate some of the similarities that are common to these philosophies, showing that despite reaching different conclusions many are guided by the same driving idea.
{"title":"Metaphysics of Mathematics","authors":"John Hester","doi":"10.1017/9781139600293.004","DOIUrl":"https://doi.org/10.1017/9781139600293.004","url":null,"abstract":"The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main topics will be the independent existence of mathematics and controversies over the nature of the mathematical infinite. After describing these ideas, I will demonstrate some of the similarities that are common to these philosophies, showing that despite reaching different conclusions many are guided by the same driving idea.","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123748856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.010
{"title":"Generic Systems and Mathematical Structuralism","authors":"","doi":"10.1017/9781139600293.010","DOIUrl":"https://doi.org/10.1017/9781139600293.010","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"383 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116370914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.011
{"title":"Reasoning about Generic ω-Sequences","authors":"","doi":"10.1017/9781139600293.011","DOIUrl":"https://doi.org/10.1017/9781139600293.011","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130525029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.015
{"title":"Index","authors":"","doi":"10.1017/9781139600293.015","DOIUrl":"https://doi.org/10.1017/9781139600293.015","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127324715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.006
{"title":"Mathematical Objects as Arbitrary Objects","authors":"","doi":"10.1017/9781139600293.006","DOIUrl":"https://doi.org/10.1017/9781139600293.006","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125761820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.005
{"title":"Arbitrary Objects","authors":"","doi":"10.1017/9781139600293.005","DOIUrl":"https://doi.org/10.1017/9781139600293.005","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130092030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.013
{"title":"Directions for Future Research","authors":"","doi":"10.1017/9781139600293.013","DOIUrl":"https://doi.org/10.1017/9781139600293.013","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131691076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-30DOI: 10.1017/9781139600293.009
{"title":"Kit Fine","authors":"","doi":"10.1017/9781139600293.009","DOIUrl":"https://doi.org/10.1017/9781139600293.009","url":null,"abstract":"","PeriodicalId":259362,"journal":{"name":"The Metaphysics and Mathematics of Arbitrary Objects","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127119140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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