Inconsistent Mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
312 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories |
| Beschreibung: | 1 Online-Ressource (X, 158 p) |
| ISBN: | 9789401584531 9789048144808 |
| DOI: | 10.1007/978-94-015-8453-1 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424059 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1995 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401584531 |c Online |9 978-94-015-8453-1 | ||
| 020 | |a 9789048144808 |c Print |9 978-90-481-4480-8 | ||
| 024 | 7 | |a 10.1007/978-94-015-8453-1 |2 doi | |
| 035 | |a (OCoLC)1184497664 | ||
| 035 | |a (DE-599)BVBBV042424059 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 511.3 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Mortensen, Chris |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Inconsistent Mathematics |c by Chris Mortensen |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1995 | |
| 300 | |a 1 Online-Ressource (X, 158 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 312 | |
| 500 | |a without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Logic | |
| 650 | 4 | |a Algebra / Data processing | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Mathematical Logic and Foundations | |
| 650 | 4 | |a Symbolic and Algebraic Manipulation | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Parakonsistente Logik |0 (DE-588)4226190-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Parakonsistente Logik |0 (DE-588)4226190-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-015-8453-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859476 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100548702208 |
|---|---|
| any_adam_object | |
| author | Mortensen, Chris |
| author_facet | Mortensen, Chris |
| author_role | aut |
| author_sort | Mortensen, Chris |
| author_variant | c m cm |
| building | Verbundindex |
| bvnumber | BV042424059 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184497664 (DE-599)BVBBV042424059 |
| 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 | 10.1007/978-94-015-8453-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03195nmm a2200505zcb4500</leader><controlfield tag="001">BV042424059</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1995 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401584531</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-015-8453-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048144808</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-4480-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-015-8453-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184497664</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424059</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mortensen, Chris</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Inconsistent Mathematics</subfield><subfield code="c">by Chris Mortensen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 158 p)</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="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">312</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra / Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical Logic and Foundations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symbolic and Algebraic Manipulation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Parakonsistente Logik</subfield><subfield code="0">(DE-588)4226190-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Parakonsistente Logik</subfield><subfield code="0">(DE-588)4226190-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-015-8453-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859476</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042424059 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401584531 9789048144808 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859476 |
| oclc_num | 1184497664 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 158 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Mortensen, Chris Verfasser aut Inconsistent Mathematics by Chris Mortensen Dordrecht Springer Netherlands 1995 1 Online-Ressource (X, 158 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 312 without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories Mathematics Logic Algebra / Data processing Logic, Symbolic and mathematical Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Datenverarbeitung Mathematik Parakonsistente Logik (DE-588)4226190-9 gnd rswk-swf Parakonsistente Logik (DE-588)4226190-9 s 1\p DE-604 https://doi.org/10.1007/978-94-015-8453-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mortensen, Chris Inconsistent Mathematics Mathematics Logic Algebra / Data processing Logic, Symbolic and mathematical Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Datenverarbeitung Mathematik Parakonsistente Logik (DE-588)4226190-9 gnd |
| subject_GND | (DE-588)4226190-9 |
| title | Inconsistent Mathematics |
| title_auth | Inconsistent Mathematics |
| title_exact_search | Inconsistent Mathematics |
| title_full | Inconsistent Mathematics by Chris Mortensen |
| title_fullStr | Inconsistent Mathematics by Chris Mortensen |
| title_full_unstemmed | Inconsistent Mathematics by Chris Mortensen |
| title_short | Inconsistent Mathematics |
| title_sort | inconsistent mathematics |
| topic | Mathematics Logic Algebra / Data processing Logic, Symbolic and mathematical Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Datenverarbeitung Mathematik Parakonsistente Logik (DE-588)4226190-9 gnd |
| topic_facet | Mathematics Logic Algebra / Data processing Logic, Symbolic and mathematical Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Datenverarbeitung Mathematik Parakonsistente Logik |
| url | https://doi.org/10.1007/978-94-015-8453-1 |
| work_keys_str_mv | AT mortensenchris inconsistentmathematics |