Mathematics without numbers :: towards a modal-structural interpretation /
Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford : New York :
Clarendon Press ; Oxford Univ. Press,
©1989.
|
| Schriftenreihe: | Clarendon Paperbacks Ser.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. |
| Beschreibung: | 1 online resource (ix, 154 pages) |
| Bibliographie: | Includes bibliographical references (pages 145-150) and index. |
| ISBN: | 9780191520112 019152011X 1282052039 9781282052031 9786612052033 6612052031 |
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| 100 | 1 | |a Hellman, Geoffrey. |0 http://id.loc.gov/authorities/names/n88226801 | |
| 245 | 1 | 0 | |a Mathematics without numbers : |b towards a modal-structural interpretation / |c Geoffrey Hellman. |
| 260 | |a Oxford : |b Clarendon Press ; |a New York : |b Oxford Univ. Press, |c ©1989. | ||
| 300 | |a 1 online resource (ix, 154 pages) | ||
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| 490 | 1 | |a Clarendon Paperbacks Ser. | |
| 504 | |a Includes bibliographical references (pages 145-150) and index. | ||
| 520 | 8 | |a Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Introduction -- 1. The Natural Numbers and Analysis -- 0. Introduction -- 1. The Modal-Structuralist Framework: The Hypothetical Component -- 2. The Categorical Component: An Axiom of Infinity and a Derivation (inspired by Dedekind, with help from Frege) -- 3. Justifying the Translation Scheme -- 4. Justification from within -- 5. Extensions -- 6. The Question of Nominalism -- 2. Set Theory -- 0. Introduction -- 1. Informal Principles: Many vs. One -- 2. The Relevant Structures -- 3. Unbounded Sentences: Putnam Semantics -- 4. Axioms of Infinity: Looking back. | |
| 505 | 8 | |a 5. Axioms of Infinity: Climbing up -- Appendix -- 3. Mathematics and Physical Reality -- 0. Introduction -- 1. The Leading Ideas -- 2. Carrying the Mathematics of Modern Physics: RA(2) as a Framework -- 3. Global Solutions -- 4. "Metaphysical Realist" Commitments? "Synthetic Determination" Relations -- 5. A Role for Representation Theorems? -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z. | |
| 546 | |a English. | ||
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| 776 | 0 | 8 | |i Print version: |a Hellman, Geoffrey. |t Mathematics without numbers. |d Oxford : Clarendon Press ; New York : Oxford Univ. Press, ©1989 |z 0198249349 |z 9780198249344 |w (DLC) 89030517 |w (OCoLC)19266575 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn340869607 |
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| _version_ | 1816881692522053632 |
| adam_text | |
| any_adam_object | |
| author | Hellman, Geoffrey |
| author_GND | http://id.loc.gov/authorities/names/n88226801 |
| author_facet | Hellman, Geoffrey |
| author_role | |
| author_sort | Hellman, Geoffrey |
| author_variant | g h gh |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| callnumber-raw | QA37.2 .H42 1989eb |
| callnumber-search | QA37.2 .H42 1989eb |
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| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Introduction -- 1. The Natural Numbers and Analysis -- 0. Introduction -- 1. The Modal-Structuralist Framework: The Hypothetical Component -- 2. The Categorical Component: An Axiom of Infinity and a Derivation (inspired by Dedekind, with help from Frege) -- 3. Justifying the Translation Scheme -- 4. Justification from within -- 5. Extensions -- 6. The Question of Nominalism -- 2. Set Theory -- 0. Introduction -- 1. Informal Principles: Many vs. One -- 2. The Relevant Structures -- 3. Unbounded Sentences: Putnam Semantics -- 4. Axioms of Infinity: Looking back. 5. Axioms of Infinity: Climbing up -- Appendix -- 3. Mathematics and Physical Reality -- 0. Introduction -- 1. The Leading Ideas -- 2. Carrying the Mathematics of Modern Physics: RA(2) as a Framework -- 3. Global Solutions -- 4. "Metaphysical Realist" Commitments? "Synthetic Determination" Relations -- 5. A Role for Representation Theorems? -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z. |
| ctrlnum | (OCoLC)340869607 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn340869607 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:46Z |
| institution | BVB |
| isbn | 9780191520112 019152011X 1282052039 9781282052031 9786612052033 6612052031 |
| language | English |
| oclc_num | 340869607 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 154 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Clarendon Press ; Oxford Univ. Press, |
| record_format | marc |
| series | Clarendon Paperbacks Ser. |
| series2 | Clarendon Paperbacks Ser. |
| spelling | Hellman, Geoffrey. http://id.loc.gov/authorities/names/n88226801 Mathematics without numbers : towards a modal-structural interpretation / Geoffrey Hellman. Oxford : Clarendon Press ; New York : Oxford Univ. Press, ©1989. 1 online resource (ix, 154 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Clarendon Paperbacks Ser. Includes bibliographical references (pages 145-150) and index. Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. Print version record. Introduction -- 1. The Natural Numbers and Analysis -- 0. Introduction -- 1. The Modal-Structuralist Framework: The Hypothetical Component -- 2. The Categorical Component: An Axiom of Infinity and a Derivation (inspired by Dedekind, with help from Frege) -- 3. Justifying the Translation Scheme -- 4. Justification from within -- 5. Extensions -- 6. The Question of Nominalism -- 2. Set Theory -- 0. Introduction -- 1. Informal Principles: Many vs. One -- 2. The Relevant Structures -- 3. Unbounded Sentences: Putnam Semantics -- 4. Axioms of Infinity: Looking back. 5. Axioms of Infinity: Climbing up -- Appendix -- 3. Mathematics and Physical Reality -- 0. Introduction -- 1. The Leading Ideas -- 2. Carrying the Mathematics of Modern Physics: RA(2) as a Framework -- 3. Global Solutions -- 4. "Metaphysical Realist" Commitments? "Synthetic Determination" Relations -- 5. A Role for Representation Theorems? -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z. English. Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Mathematics https://id.nlm.nih.gov/mesh/D008433 Mathématiques. MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh MATHEMATICS Essays. bisacsh Mathematics fast Wiskunde. gtt Logica. gtt Mathematics Philosophy Mathematics Theories has work: Mathematics without numbers (Text) https://id.oclc.org/worldcat/entity/E39PCGq6v64WGm8fPPt8kXPcMX https://id.oclc.org/worldcat/ontology/hasWork Print version: Hellman, Geoffrey. Mathematics without numbers. Oxford : Clarendon Press ; New York : Oxford Univ. Press, ©1989 0198249349 9780198249344 (DLC) 89030517 (OCoLC)19266575 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=273485 Volltext |
| spellingShingle | Hellman, Geoffrey Mathematics without numbers : towards a modal-structural interpretation / Clarendon Paperbacks Ser. Introduction -- 1. The Natural Numbers and Analysis -- 0. Introduction -- 1. The Modal-Structuralist Framework: The Hypothetical Component -- 2. The Categorical Component: An Axiom of Infinity and a Derivation (inspired by Dedekind, with help from Frege) -- 3. Justifying the Translation Scheme -- 4. Justification from within -- 5. Extensions -- 6. The Question of Nominalism -- 2. Set Theory -- 0. Introduction -- 1. Informal Principles: Many vs. One -- 2. The Relevant Structures -- 3. Unbounded Sentences: Putnam Semantics -- 4. Axioms of Infinity: Looking back. 5. Axioms of Infinity: Climbing up -- Appendix -- 3. Mathematics and Physical Reality -- 0. Introduction -- 1. The Leading Ideas -- 2. Carrying the Mathematics of Modern Physics: RA(2) as a Framework -- 3. Global Solutions -- 4. "Metaphysical Realist" Commitments? "Synthetic Determination" Relations -- 5. A Role for Representation Theorems? -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z. Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Mathematics https://id.nlm.nih.gov/mesh/D008433 Mathématiques. MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh MATHEMATICS Essays. bisacsh Mathematics fast Wiskunde. gtt Logica. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082139 https://id.nlm.nih.gov/mesh/D008433 |
| title | Mathematics without numbers : towards a modal-structural interpretation / |
| title_auth | Mathematics without numbers : towards a modal-structural interpretation / |
| title_exact_search | Mathematics without numbers : towards a modal-structural interpretation / |
| title_full | Mathematics without numbers : towards a modal-structural interpretation / Geoffrey Hellman. |
| title_fullStr | Mathematics without numbers : towards a modal-structural interpretation / Geoffrey Hellman. |
| title_full_unstemmed | Mathematics without numbers : towards a modal-structural interpretation / Geoffrey Hellman. |
| title_short | Mathematics without numbers : |
| title_sort | mathematics without numbers towards a modal structural interpretation |
| title_sub | towards a modal-structural interpretation / |
| topic | Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Mathematics https://id.nlm.nih.gov/mesh/D008433 Mathématiques. MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh MATHEMATICS Essays. bisacsh Mathematics fast Wiskunde. gtt Logica. gtt |
| topic_facet | Mathematics. Mathematics Mathématiques. MATHEMATICS Pre-Calculus. MATHEMATICS Reference. MATHEMATICS Essays. Wiskunde. Logica. |
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