Mathematics and its logics: philosophical essays
In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refin...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2021
|
| Subjects: | |
| Links: | https://doi.org/10.1017/9781108657419 https://doi.org/10.1017/9781108657419 https://doi.org/10.1017/9781108657419 https://doi.org/10.1017/9781108657419 |
| Summary: | In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Feb 2021) |
| Physical Description: | 1 Online-Ressource (vii, 286 Seiten) |
| ISBN: | 9781108657419 |
| DOI: | 10.1017/9781108657419 |
Staff View
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV047177813 | ||
| 003 | DE-604 | ||
| 005 | 20231204 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 210305s2021 xx o|||| 00||| eng d | ||
| 020 | |a 9781108657419 |c Online |9 978-1-108-65741-9 | ||
| 024 | 7 | |a 10.1017/9781108657419 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781108657419 | ||
| 035 | |a (OCoLC)1241674550 | ||
| 035 | |a (DE-599)BVBBV047177813 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-473 | ||
| 082 | 0 | |a 511.3 | |
| 084 | |a SG 700 |0 (DE-625)143071: |2 rvk | ||
| 100 | 1 | |a Hellman, Geoffrey |d 1943- |0 (DE-588)1169845142 |4 aut | |
| 245 | 1 | 0 | |a Mathematics and its logics |b philosophical essays |c Geoffrey Hellman |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2021 | |
| 300 | |a 1 Online-Ressource (vii, 286 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Feb 2021) | ||
| 520 | |a In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic | ||
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-1-108-49418-2 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781108657419 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-032583164 | |
| 966 | e | |u https://doi.org/10.1017/9781108657419 |l DE-12 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781108657419 |l DE-92 |p ZDB-20-CBO |q FHN_PDA_CBO_Kauf |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781108657419 |l DE-473 |p ZDB-20-CBO |q UBG_PDA_CBO |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1818987768781471744 |
|---|---|
| any_adam_object | |
| author | Hellman, Geoffrey 1943- |
| author_GND | (DE-588)1169845142 |
| author_facet | Hellman, Geoffrey 1943- |
| author_role | aut |
| author_sort | Hellman, Geoffrey 1943- |
| author_variant | g h gh |
| building | Verbundindex |
| bvnumber | BV047177813 |
| classification_rvk | SG 700 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781108657419 (OCoLC)1241674550 (DE-599)BVBBV047177813 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781108657419 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02797nam a2200445zc 4500</leader><controlfield tag="001">BV047177813</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20231204 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">210305s2021 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781108657419</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-108-65741-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781108657419</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781108657419</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1241674550</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV047177813</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-473</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 700</subfield><subfield code="0">(DE-625)143071:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hellman, Geoffrey</subfield><subfield code="d">1943-</subfield><subfield code="0">(DE-588)1169845142</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematics and its logics</subfield><subfield code="b">philosophical essays</subfield><subfield code="c">Geoffrey Hellman</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (vii, 286 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Feb 2021)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-1-108-49418-2</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781108657419</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032583164</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108657419</subfield><subfield code="l">DE-12</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108657419</subfield><subfield code="l">DE-92</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO_Kauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108657419</subfield><subfield code="l">DE-473</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBG_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV047177813 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T19:11:56Z |
| institution | BVB |
| isbn | 9781108657419 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032583164 |
| oclc_num | 1241674550 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-473 DE-BY-UBG |
| owner_facet | DE-12 DE-92 DE-473 DE-BY-UBG |
| physical | 1 Online-Ressource (vii, 286 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO_Kauf ZDB-20-CBO UBG_PDA_CBO |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Hellman, Geoffrey 1943- (DE-588)1169845142 aut Mathematics and its logics philosophical essays Geoffrey Hellman Cambridge Cambridge University Press 2021 1 Online-Ressource (vii, 286 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Feb 2021) In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-108-49418-2 https://doi.org/10.1017/9781108657419 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hellman, Geoffrey 1943- Mathematics and its logics philosophical essays Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Mathematics and its logics philosophical essays |
| title_auth | Mathematics and its logics philosophical essays |
| title_exact_search | Mathematics and its logics philosophical essays |
| title_full | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_fullStr | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_full_unstemmed | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_short | Mathematics and its logics |
| title_sort | mathematics and its logics philosophical essays |
| title_sub | philosophical essays |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik |
| url | https://doi.org/10.1017/9781108657419 |
| work_keys_str_mv | AT hellmangeoffrey mathematicsanditslogicsphilosophicalessays |