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  1. Abduction and diagrams.Ahti-Veikko Pietarinen - forthcoming - Logic Journal of the IGPL.
    Abductive conclusions are drawn in a special, co-hortative mood. Abductive conclusions are representative interpretants that represent abduction as a form of reasoning that can convey a general conception of the truth. The truth is not asserted; abduction merely delivers the idea of a matter of course, rendering that idea comparatively simple and natural, hence assuring us of its justified assertibility. Hence abductive reasoning is at home in addressing ‘How Possible’-questions in science. Abductive reasoning concerns the question of how things might, (...)
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  • Peirce’s calculi for classical propositional logic.Minghui Ma & Ahti-Veikko Pietarinen - 2020 - Review of Symbolic Logic 13 (3):509-540.
    This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...)
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  • Peirce’s Dragon-Head Logic.Minghui Ma & Ahti-Veikko Pietarinen - 2022 - Archive for History of Exact Sciences 76 (3):261-317.
    Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...)
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  • On the Logical Philosophy of Assertive Graphs.Daniele Chiffi & Ahti-Veikko Pietarinen - 2020 - Journal of Logic, Language and Information 29 (4):375-397.
    The logic of assertive graphs is a modification of Peirce’s logic of existential graphs, which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions whose internal logic is classical. The characteristic feature is that both AGs and ClAG retain deep-inference rules of transformation. Unlike classical EGs, both AGs and ClAG can do so without explicitly introducing polarities of areas in their language. We then compare (...)
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  • Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):80-95.
    We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...)
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  • Introduction: History and Philosophy of Logical Notation.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):1-2.
    We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...)
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  • On Three Levels of Abstractness in Peirce’s Beta Graphs.Richard Kenneth Atkins - 2022 - History and Philosophy of Logic 44 (1):16-32.
    Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first to (...)
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