15 found
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  1.  77
    Logic without contraction as based on inclusion and unrestricted abstraction.Uwe Petersen - 2000 - Studia Logica 64 (3):365-403.
    On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within (...)
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  2.  15
    Is cut-free logic fit for unrestricted abstraction?Uwe Petersen - 2022 - Annals of Pure and Applied Logic 173 (6):103101.
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  3.  14
    On Zardini’s Rules for Multiplicative Quantification as the Source of Contra(di)Ctions.Uwe Petersen - 2023 - Review of Symbolic Logic 16 (4):1110-1119.
    Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.
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  4.  43
    Is Cantor’s Theorem a Dialetheia? Variations on a Paraconsistent Approach to Cantor’s Theorem.Uwe Petersen - forthcoming - Review of Symbolic Logic:1-18.
    The present note was prompted by Weber’s approach to proving Cantor’s theorem, i.e., the claim that the cardinality of the power set of a set is always greater than that of the set itself. While I do not contest that his proof succeeds, my point is that he neglects the possibility that by similar methods it can be shown also that no non-empty set satisfies Cantor’s theorem. In this paper unrestricted abstraction based on a cut free Gentzen type sequential calculus (...)
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  5.  25
    L i D Z λ as a basis for PRA.Uwe Petersen - 2003 - Archive for Mathematical Logic 42 (7):665-694.
    This paper is a sequel to my [7]. It focuses on the notion of natural number as introduced in section 11 of that paper with regard to forms of induction and recursive definitions. One point is that this notion of natural number is somewhat weaker than the classical one in so far as it is defined in terms of a weak implication. The other point is the lack of even a weak form of extensionality. As a main result of the (...)
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  6.  17
    LiDZλ as a basis for PRA.Uwe Petersen - 2003 - Archive for Mathematical Logic 42 (7):665-694.
    Abstract.This paper is a sequel to my [7]. It focuses on the notion of natural number as introduced in section 11 of that paper with regard to forms of induction and recursive definitions. One point is that this notion of natural number is somewhat weaker than the classical one in so far as it is defined in terms of a weak implication. The other point is the lack of even a weak form of extensionality. As a main result of the (...)
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  7.  22
    Dialetheias and Numbers Distinct from Themselves.Uwe Petersen - 2023 - Notre Dame Journal of Formal Logic 64 (2):239-246.
    According to Priest, a proof can be distinct from itself in the same way that a number can. Priest does not specify any such number, so the present little note aims at filling this lacuna by providing a plain arithmetical code of a dialetheia similar to but simpler than the one presented in our recent work and thereby a natural number distinct from itself.
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  8. Dialetheism and Paradoxes of the Berry Family.Uwe Petersen - 1992 - Logique Et Analyse 35:273-89.
     
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  9.  3
    Anthropologie und Handlungsphilosophie.Uwe Petersen - 2011 - Hamburg: Verlag Dr. Kovač.
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  10.  33
    Diagonal method and dialectical logic: tools, materials, and groundworks for a logical foundation of dialectic and speculative philosophy.Uwe Petersen - 2002 - Osnabrück: Der Andere Verlag.
    bk. 1. Tools for dialectic -- bk. 2. Historical-philosophical background materials -- bk. 3. Groundworks for dialectical logic.
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  11.  6
    Das Verhältnis von Theorie und Praxis in der transzendentalen Phänomenologie Edmund Husserls.Uwe Petersen - 1964 - [Heidelberg]: Turnshare Ltd. - Publisher.
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  12.  7
    Enhancing induction in a contraction free logic with unrestricted abstraction: from $$\mathbf {Z}$$ Z to $$\mathbf {Z}_2$$ Z 2.Uwe Petersen - forthcoming - Archive for Mathematical Logic:1-45.
    \ is a new type of non-finitist inference, i.e., an inference that involves treating some infinite collection as completed, designed for contraction free logic with unrestricted abstraction. It has been introduced in Petersen and shown to be consistent within a system \ \ of contraction free logic with unrestricted abstraction. In Petersen :665–694, 2003) it was established that adding \ to \ \ is sufficient to prove the totality of primitive recursive functions but it was also indicated that this would (...)
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  13.  9
    Enhancing induction in a contraction free logic with unrestricted abstraction: from $$\mathbf {Z}$$ to $$\mathbf {Z}_2$$.Uwe Petersen - 2022 - Archive for Mathematical Logic 61 (7):1007-1051.
    $$\mathbf {Z}$$ is a new type of non-finitist inference, i.e., an inference that involves treating some infinite collection as completed, designed for contraction free logic with unrestricted abstraction. It has been introduced in Petersen (Studia Logica 64:365–403, 2000) and shown to be consistent within a system $$\mathbf {{}L^iD{}}{}$$ $$_{\uplambda }$$ of contraction free logic with unrestricted abstraction. In Petersen (Arch Math Log 42(7):665–694, 2003) it was established that adding $$ \mathbf {Z}$$ to $$\mathbf {{}L^iD{}}{}$$ $$_{\uplambda }$$ is sufficient to prove (...)
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  14.  4
    Philosophie der Psychologie, Psychogenealogie und Psychotherapie: ein Leitfaden für philosophische Praxis.Uwe Petersen - 2010 - Hamburg: Kovac̆.
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  15.  2
    Enhancing induction in a contraction free logic with unrestricted abstraction: from Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Z}$$\end{document} to Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Z}_2$$\end{document}. [REVIEW]Uwe Petersen - 2022 - Archive for Mathematical Logic 61 (7-8):1007-1051.
    Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Z}$$\end{document} is a new type of non-finitist inference, i.e., an inference that involves treating some infinite collection as completed, designed for contraction free logic with unrestricted abstraction. It has been introduced in Petersen and shown to be consistent within a system LiD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {{}L^iD{}}{}$$\end{document}λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\uplambda }$$\end{document} of contraction free logic with unrestricted abstraction. In Petersen (...)
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