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Intuitionism vs. Classicism

Nick Haverkamp

Reihe: Studies in Theoretical Philosophy

Band 2 2015

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Chapter 3: Counterexamples to Classical Logic S. 81-120

„… classical logic to be understood? On the one hand, intuitionists accept mathematical sentences which …” „… mathematical arguments whose conclusions are strong counterexamples to classical logic, if they are true. The …” „… classical logic hinges on the non-existence of certain finite ‘quasi-mathematical’ objects: rules which …”

Introduction S. XIII-XVI

„… accept a mathematical argument that is logically valid according to standard logical principles, the …” „… introduce meta-mathematical arguments against classical logic. With those arguments, intuitionists try to …” „… community. The exceptional nature of logic and mathematics suggests that logical reasoning with purely …”

Chapter 6: Conclusion S. 240-243

„… . Rather, I plead for logical/mathematical fundamentalism. The dispute between classicists and …” „… , whichever of these two judgements is correct, it is based on logical/mathematical insight that conflicts …” „… there are arguments against either view that do not involve a logical or mathematical assumption that …”

Titelei/Inhaltsverzeichnis S. I-X

„… refutation of widely accepted mathematical assumptions including fundamental principles of classical logic …” „… Mathematical attack on classical logic Vittorio KloSterMann Bibliographische information der deutschen …” „… Non-Standard Classical Logic . . . . . . . 31 2 A Purely Verbal Dispute? 35 2.1 Mathematical Languages …”

Chapter 2: A Purely Verbal Dispute? S. 35-80

„… mathematics and classical logic deserves philosophical attention. Mathematical intuitionism is a kind of …” „… call this view logical/mathematical dualism. Others adopt an exclusive attitude which involves the …” „… this view exclusive logical/mathematical monism.5 I think theories of dualism and exclusive monism are …”

Chapter 1: Arguing about Classical Logic S. 1-34

„… logic. In particular, in many ordinary mathematical proofs a sentence S2 is inferred from two sentences …” „… Mares 2004: 3. Mares here criticises classical logic for declaring certain mathematical arguments with …” „… descriptive criticism of classical logic. In particular with respect to mathematical argumentations, it is not …”

Chapter 5: Proof-Theoretic Arguments S. 174-239

„… classical logic). Proof-theoretic arguments are usually based on certain mathematical results on calculi …” „… . This might be taken to suggest that the prospects of classical logic depend on future mathematical …” „… proof-theoretic arguments against classical logic do not claim that no mathematical structure determines exactly …”

Bibliography S. 257-267

„… , Willard van Orman 1940: Mathematical Logic, Harvard: Harvard University Press. Quine, Willard van Orman …” „… . Mathias and H. Rogers (eds.) 1973: Cambridge Summer School in Mathematical Logic, Berlin: Springer …” „… (ed.) 1977: Handbook of Mathematical Logic, Amsterdam: North- Holland, 973-1052. Troelstra, Anna Sjerp …”

Chapter 4: The Manifestation Argument S. 121-173

„… guaranteed to be truth-preserving. P2 If every argument which is logically valid according to classical logic …” „… argument which is logically valid according to classical logic is semantically guaranteed to be …” „… guaranteed to be truth-preserving. P2 If every argument which is logically valid according to classical logic …”

Preface S. XI-XII

„… Preface This book is based on my dissertation Intuitionistic Arguments Against Classical Logic …” „… to write about arguments against classical logic. Since I had (more or less) made up my mind about …” „… relevant logic already, I first turned to anti-classical arguments based on considerations about paradoxes …”

doi.org/10.5771/9783465139065

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Geschichte der Germanistik

Christoph König (Hrsg.), Anna Kinder (Hrsg.)

2019

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Andrea Bréard (Philo-)Logica-Mathematica –Giovanni Vacca’s (1872-1953) attempts of translation between mathematical formulas and Chinese text via simplified Latin S. 16-33

„… (Philo-) Logica-Mathematica – Giovanni Vacca’s (1872-1953) attempts of translation between mathematical …” „… . 278-298. For the continuity between Leibniz’ language project and Peano’s mathematical logic, see Andrea …” „… – decoding mathematical logic into Chinese – will be described in the follow ing in order to shed light on …”

Titelei/Inhaltsverzeichnis S. 1-4

„… -) Logica-Mathematica – Giovanni Vacca’s (1872-1953) attempts of translation between mathematical formulas and Chinese …”

doi.org/10.5771/9783835343740

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Intuition und Wissenschaft

Christian Bachhiesl (Hrsg.), Sonja Bachhiesl (Hrsg.), Stefan Köchel (Hrsg.)

2018

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Wolfgang Brumetz The Uses of Truth S. 61-86

„… settheoretic, also called: semantic terms«: Georg Kreisel, Jean-Louis Krivine, Elements of Mathematical Logic …” „… analysis of meaning, using some elementary concepts of mathematical logic.6 Consider sentences of the form …” „… Mathematical Logic (Amsterdam 1977), part C), but they lack the capability of interpreting all the other …”

doi.org/10.5771/9783845291079

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Braucht die Mathematik eine Grundlegung?

Felix Mühlhölzer

2014

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Literaturverzeichnis S. 577-592

„… Church, Alonzo: 1956, Introduction to Mathematical Logic, Princeton University Press. Coffa, J. Alberto …” „… : 1944, "Russell's mathematical logic", in The Philosophy of Bertrand Russell, Library of Living …” „… Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, vierte Auflage, Harvard University Press …”

II. Kommentar S. 103-572

„… Übersetzung des ersten Satzes von III.1 ("'A mathematical proof must be perspicuous'"), jedoch seltsamerweise …” „… . In Dummett 1994, heißt es auf S. 49: "The effect of a mathematical proof, on [W.'s] account, is to …” „… new criterion for the application of some mathematical concept." Und auf S. 56: "what a mathematical …”

I. Einleitung S. 1-102

„… bei einem Vortrag, den W. im Mai 1930 vor der Trinity Mathematical Society hielt und der unter dem …” „… . natürlich vertraut. In Kap. 1 seines Buches Mathematical Knowledge unterstellt Mark Steiner, W. hätte in …” „… "Tractatus logico-philosophicus" ist eine Erfindung George Edward Moores. W. selbst nannte sein erstes Buch …”

doi.org/10.5771/9783465136675

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Einführung in die moderne Logik

Franz von Kutschera, Alfred Breitkopf

2016

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Bibliographie S. 209-212

„… .: Einführung in die symbolische Logik, Wien, New York31968.Church, A.: Introduction to Mathematical Logic I …” „… Logic, New York u. a. 1968.Kreisel, G., und J. L. Krivine: Elements of Mathematical Logic (Mo-del Theory …” „… .Schütte, K.: Beweistheorie, Berlin u. a. 1960.Shoenfield, J. R.: Mathematical Logic, Reading u. a. 1967 …”

doi.org/10.5771/9783495860885

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