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

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Bibliographische Detailangaben
Beteiligte Personen:	Sinaceur, Hourya 1940- (VerfasserIn), Panza, Marco (VerfasserIn), Sandu, Gabriel 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cham [u.a.] Springer 2015
Schriftenreihe:	Logic, epistemology and the unity of science 37
Schlagwörter:	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
Links:	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
Umfang:	xxi, 125 S. graph. Darst.
ISBN:	9783319171081

Internformat

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Datensatz im Suchindex

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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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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
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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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