Holdings: Functions and generality of logic

Functions and generality of logic: reflections on Dedekind's and Frege's logicisms

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Bibliographic Details
Main Authors:	Sinaceur, Hourya 1940- (Author), Panza, Marco (Author), Sandu, Gabriel 1954- (Author)
Format:	Book
Language:	English
Published:	Cham [u.a.] Springer 2015
Series:	Logic, epistemology and the unity of science 37
Subjects:	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
Online Access:	Inhaltsverzeichnis
Physical Description:	xxi, 125 S. graph. Darst.
ISBN:	9783319171081

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Record in the Search Index

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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
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author	Sinaceur, Hourya 1940- Panza, Marco Sandu, Gabriel 1954-
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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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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
work_keys_str_mv	AT sinaceurhourya functionsandgeneralityoflogicreflectionsondedekindsandfregeslogicisms AT panzamarco functionsandgeneralityoflogicreflectionsondedekindsandfregeslogicisms AT sandugabriel functionsandgeneralityoflogicreflectionsondedekindsandfregeslogicisms

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