Functions and generality of logic: reflections on Dedekind's and Frege's logicisms
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2015
|
| Schriftenreihe: | Logic, epistemology and the unity of science
37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxi, 125 S. graph. Darst. |
| ISBN: | 9783319171081 |
Internformat
MARC
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| 100 | 1 | |a Sinaceur, Hourya |d 1940- |e Verfasser |0 (DE-588)142488240 |4 aut | |
| 245 | 1 | 0 | |a Functions and generality of logic |b reflections on Dedekind's and Frege's logicisms |c Hourya Benis-Sinaceur ; Marco Panza ; Gabriel Sandu |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2015 | |
| 300 | |a xxi, 125 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Logic, epistemology and the unity of science |v 37 | |
| 600 | 1 | 7 | |a Lagrange, Joseph Louis de |d 1736-1813 |0 (DE-588)118568698 |2 gnd |9 rswk-swf |
| 600 | 1 | 7 | |a Dedekind, Richard |d 1831-1916 |0 (DE-588)118524259 |2 gnd |9 rswk-swf |
| 600 | 1 | 7 | |a Frege, Gottlob |d 1848-1925 |0 (DE-588)118535161 |2 gnd |9 rswk-swf |
| 600 | 1 | 7 | |a Russell, Bertrand |d 1872-1970 |0 (DE-588)118604287 |2 gnd |9 rswk-swf |
| 600 | 1 | 7 | |a Ramsey, Frank Plumpton |d 1903-1930 |0 (DE-588)118787829 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Logik |0 (DE-588)4036202-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Frege, Gottlob |d 1848-1925 |0 (DE-588)118535161 |D p |
| 689 | 1 | 1 | |a Dedekind, Richard |d 1831-1916 |0 (DE-588)118524259 |D p |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Frege, Gottlob |d 1848-1925 |0 (DE-588)118535161 |D p |
| 689 | 2 | 1 | |a Russell, Bertrand |d 1872-1970 |0 (DE-588)118604287 |D p |
| 689 | 2 | 2 | |a Ramsey, Frank Plumpton |d 1903-1930 |0 (DE-588)118787829 |D p |
| 689 | 2 | 3 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |D s |
| 689 | 2 | 4 | |a Logik |0 (DE-588)4036202-4 |D s |
| 689 | 2 | |8 1\p |5 DE-604 | |
| 689 | 3 | 0 | |a Lagrange, Joseph Louis de |d 1736-1813 |0 (DE-588)118568698 |D p |
| 689 | 3 | 1 | |a Frege, Gottlob |d 1848-1925 |0 (DE-588)118535161 |D p |
| 689 | 3 | 2 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |D s |
| 689 | 3 | 3 | |a Logik |0 (DE-588)4036202-4 |D s |
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| 689 | 4 | 0 | |a Dedekind, Richard |d 1831-1916 |0 (DE-588)118524259 |D p |
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| 689 | 4 | 2 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 4 | |8 3\p |5 DE-604 | |
| 700 | 1 | |a Panza, Marco |e Verfasser |4 aut | |
| 700 | 1 | |a Sandu, Gabriel |d 1954- |e Verfasser |0 (DE-588)138540985 |4 aut | |
| 830 | 0 | |a Logic, epistemology and the unity of science |v 37 |w (DE-604)BV019709027 |9 37 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-028721649 | ||
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| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804175834675675136 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION ..........................................
IX
1
ISDEDEKIND
ALOGICIST?
WHY
DOESSUCH
AQUESTION
ARISE?
.....
HOURYA
BENIS-SINACEUR
1.1
1NTRODUCTION
....................................
1
1.2
THELOGICIST
THESIS.
..............................
8
1.2.1
THE
NEW
LOGIC
..........................
8
1.2.2
LOGICIST
FOUNDATIONS
OFMATHEMATICS
............
10
1.3
SIMILAR
CLAIMS,
DIFFERENT
FUNDAMENTAL
CONCEPTIONS
........
14
1.3.1
REASON
VERSUS
INTUITION
AND
THEFOUNDATIONS
OFARITHMETIC
.............................
15
1.3.2
PURETHOUGHT,
OBJECTIVITY,
LOGIC,
PROOF.
..........
20
1.3.3
MORE
ONINFERENCE:
TMTHS
AND
LOGICAL
TMTHS
......
27
1.4
ONDEFINITIONS
..................................
28
1.4.1
DEDEKIND S
DEFINITION
BYAXIOMS.
..............
28
1.4.2
FREGE S
ONTO1OGICA1CONCEPTION
OFDEFINITIONS
OFOBJECTS
...............................
29
1.4.3
FREGE S
EPISTEMO1OGY
.......................
32
1.4.4
DEDEKIND S
TREPPEN-VERSTAND
AND
STUECKEWEISE
DEFINITIONS.
..............................
34
1.4.5
FREGE S
CRITICISM
OFDEDEKIND S
STUECKWEISE
ANDCREATIVE
DEFINITIONS
.....................
35
1.4.6
FREGE S
TECHNICA1
CONCEPTION
OFDEFINITIONS
.......
38
1.4.7
FREGE S
AND
DEDEKIND S
PHI1OSOPHICA1ASSUMPTIONS.
..
40
1.5
SYSTEM
AND
ABBILDUNG:
STMCTURA1ISM
AND/OR
LOGICISM
......
42
1.5.1
CONCEPT.
................................
42
1.5.2
SYSTEM
ANDABBILDUNG:
THESEARCH
OFGENERALITY
....
46
1.5.3
DEDEKIND S
CHAINS
AND
FREGE S
FOLLOWING
INAQJ-SEQUENCE.
..........................
53
1.6
CONCLUSIONS
....................................
55
VII
VIII
CONTENTS
2 FROM
LAGRANGE
TOFREGE:
FUNCTIONS
AND
EXPRESSIONS
..........
59
MARCO
PANZA
2.1
INTRODUCTION
....................................
59
2.2
LAGRANGE S
NOTION
OFAFUNCTION.
.....................
60
2.3
ARBITRARY
FUNCTIONS
AND
THEARITHMETISATION
OFANALYSIS
.....
64
2.4
FUNCTIONS
INFREGE S
GRUNDGESETZE.
...................
70
2.4.1
ELUCIDATING
THENOTION
OFAFUNCTION.
............
71
2.4.2
HOW
(FIRST-LEVEL)
FUNCTIONS
WORK
INTHEBEGRIFFSSCHRIFT.
.......................
75
2.4.3
(FIRST-LEVEL)
FUNCTIONS
AND
NAMES
OFFUNCTIONS
80
2.4.4
COMPOSITIONALITY
OFFUNCTIONS,
HIGHER-LEVEL
FUNCTIONS,
AND
THENOTION
OFANARBITRARY
FUNCTION
................................
88
2.5
CONCLUDING
REMARKS.
.............................
93
3
FREGE,
RUSSELI,
RAMSEY
AND
THENOTION
OFANARBITRARY
FUNCTION.
..........................................
97
GABRIEL
SANDU
3.1
THE
BACKGROUND.
................................
97
3.2
THE
STANDARD
VERSUS
NON-STANDARD
DISTINCTION
AND
DEDEKIND
THEOREM
............................
99
3.3
THE
ISOMORPHISM
THEOREM.
........................
100
3.4
RAMSEY S
NOTION
OFAPREDICATIVE
FUNCTION
IN FOUNDATIONS
OFMATHEMATICS
.....................
104
3.5
RAMSEY S
REDUCTION
OFTYPE
(2).
.....................
106
3.5.1
LOGICAL
NECESSITY
VERSUS
ANALYTICAL
NECESSITY
......
107
3.5.2
RAMSEY S
PROPOSITIONAL
FUNCTIONS
INEXTENSION
.....
108
3.5.3
SULLIVAN S
OBJECTION
TOTHENOTION
OFPROPOSITIONAL
FUNCTION
INEXTENSION:
CONTAINMENT
.............
110
3.5.4
SUBSTITUTION.
.............................
111
3.5.5
ARBITRARY
FUNCTIONS.
........................
112
3.6
CONCLUSION.....................................
114
BIBLIOGRAPHY
...........................................
117
|
| any_adam_object | 1 |
| author | Sinaceur, Hourya 1940- Panza, Marco Sandu, Gabriel 1954- |
| author_GND | (DE-588)142488240 (DE-588)138540985 |
| author_facet | Sinaceur, Hourya 1940- Panza, Marco Sandu, Gabriel 1954- |
| author_role | aut aut aut |
| author_sort | Sinaceur, Hourya 1940- |
| author_variant | h s hs m p mp g s gs |
| building | Verbundindex |
| bvnumber | BV043300766 |
| classification_rvk | CC 2600 CG 3397 |
| ctrlnum | (OCoLC)927127932 (DE-599)BVBBV043300766 |
| 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 Philosophie |
| format | Book |
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| id | DE-604.BV043300766 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:22:35Z |
| institution | BVB |
| isbn | 9783319171081 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028721649 |
| oclc_num | 927127932 |
| open_access_boolean | |
| owner | DE-29 |
| owner_facet | DE-29 |
| physical | xxi, 125 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series | Logic, epistemology and the unity of science |
| series2 | Logic, epistemology and the unity of science |
| spelling | Sinaceur, Hourya 1940- Verfasser (DE-588)142488240 aut Functions and generality of logic reflections on Dedekind's and Frege's logicisms Hourya Benis-Sinaceur ; Marco Panza ; Gabriel Sandu Cham [u.a.] Springer 2015 xxi, 125 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Logic, epistemology and the unity of science 37 Lagrange, Joseph Louis de 1736-1813 (DE-588)118568698 gnd rswk-swf Dedekind, Richard 1831-1916 (DE-588)118524259 gnd rswk-swf Frege, Gottlob 1848-1925 (DE-588)118535161 gnd rswk-swf Russell, Bertrand 1872-1970 (DE-588)118604287 gnd rswk-swf Ramsey, Frank Plumpton 1903-1930 (DE-588)118787829 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Frege, Gottlob 1848-1925 (DE-588)118535161 p Dedekind, Richard 1831-1916 (DE-588)118524259 p Russell, Bertrand 1872-1970 (DE-588)118604287 p Ramsey, Frank Plumpton 1903-1930 (DE-588)118787829 p Funktion Mathematik (DE-588)4071510-3 s Logik (DE-588)4036202-4 s 1\p DE-604 Lagrange, Joseph Louis de 1736-1813 (DE-588)118568698 p 2\p DE-604 Mathematik (DE-588)4037944-9 s 3\p DE-604 Panza, Marco Verfasser aut Sandu, Gabriel 1954- Verfasser (DE-588)138540985 aut Logic, epistemology and the unity of science 37 (DE-604)BV019709027 37 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028721649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sinaceur, Hourya 1940- Panza, Marco Sandu, Gabriel 1954- Functions and generality of logic reflections on Dedekind's and Frege's logicisms Logic, epistemology and the unity of science Lagrange, Joseph Louis de 1736-1813 (DE-588)118568698 gnd Dedekind, Richard 1831-1916 (DE-588)118524259 gnd Frege, Gottlob 1848-1925 (DE-588)118535161 gnd Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Ramsey, Frank Plumpton 1903-1930 (DE-588)118787829 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Logik (DE-588)4036202-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)118568698 (DE-588)118524259 (DE-588)118535161 (DE-588)118604287 (DE-588)118787829 (DE-588)4037944-9 (DE-588)4037951-6 (DE-588)4036202-4 (DE-588)4071510-3 |
| title | Functions and generality of logic reflections on Dedekind's and Frege's logicisms |
| title_auth | Functions and generality of logic reflections on Dedekind's and Frege's logicisms |
| title_exact_search | Functions and generality of logic reflections on Dedekind's and Frege's logicisms |
| title_full | Functions and generality of logic reflections on Dedekind's and Frege's logicisms Hourya Benis-Sinaceur ; Marco Panza ; Gabriel Sandu |
| title_fullStr | Functions and generality of logic reflections on Dedekind's and Frege's logicisms Hourya Benis-Sinaceur ; Marco Panza ; Gabriel Sandu |
| title_full_unstemmed | Functions and generality of logic reflections on Dedekind's and Frege's logicisms Hourya Benis-Sinaceur ; Marco Panza ; Gabriel Sandu |
| title_short | Functions and generality of logic |
| title_sort | functions and generality of logic reflections on dedekind s and frege s logicisms |
| title_sub | reflections on Dedekind's and Frege's logicisms |
| topic | Lagrange, Joseph Louis de 1736-1813 (DE-588)118568698 gnd Dedekind, Richard 1831-1916 (DE-588)118524259 gnd Frege, Gottlob 1848-1925 (DE-588)118535161 gnd Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Ramsey, Frank Plumpton 1903-1930 (DE-588)118787829 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Logik (DE-588)4036202-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Lagrange, Joseph Louis de 1736-1813 Dedekind, Richard 1831-1916 Frege, Gottlob 1848-1925 Russell, Bertrand 1872-1970 Ramsey, Frank Plumpton 1903-1930 Mathematik Mathematische Logik Logik Funktion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028721649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019709027 |
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