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  1.  43
    Grounding Megethology on Plural Reference.Massimiliano Carrara & Enrico Martino - 2015 - Studia Logica 103 (4):697-711.
    In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...)
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  2.  92
    To Be is to Be the Object of a Possible Act of Choice.Massimiliano Carrara & Enrico Martino - 2010 - Studia Logica 96 (2):289-313.
    Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...)
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  3. The Mereological Foundation of Megethology.Massimiliano Carrara & Enrico Martino - 2016 - Journal of Philosophical Logic 45 (2):227-235.
    In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed (...)
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  4.  80
    Arbitrary Reference in Mathematical Reasoning.Enrico Martino - 2001 - Topoi 20 (1):65-77.
  5. On the Infinite in Mereology with Plural Quantification.Massimiliano Carrara & Enrico Martino - 2011 - Review of Symbolic Logic 4 (1):54-62.
    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...)
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  6. On the Ontological Commitment of Mereology.Massimiliano Carrara & Enrico Martino - 2009 - Review of Symbolic Logic 2 (1):164-174.
    In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification . Instead, in the mereological case: (Lewis, 1991, p. 87). The aim of the paper is to (...)
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  7.  87
    Temporal and Atemporal Truth in Intuitionistic Mathematics.Enrico Martino & Gabriele Usberti - 1994 - Topoi 13 (2):83-92.
    In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability (...)
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  8.  95
    DLEAC: A Dialetheic Logic with Exclusive Assumptions and Conclusions.Massimiliano Carrara & Enrico Martino - 2019 - Topoi 38 (2):379-388.
    This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...)
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  9.  34
    On the Alleged Innocence of Mereology.Massimiliano Carrara & Enrico Martino - unknown
    In Parts of Classes [Lewis 1991] David Lewis attempts to draw a sharp contrast between mereology and set theory and to assimilate mereology to logic. He argues that, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – (...)
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  10.  12
    Four Theses on the Alleged Innocence of Mereology.Massimiliano Carrara & Enrico Martino - 2011 - Humana Mente 4 (19).
    In Parts of Classes David Lewis attempts to draw a sharp contrast between mereology and set theory and he tries to assimilate mereology to logic. For him, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – unlike (...)
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  11. Four Theses on the Alleged Innocence of Mereology.Massimiliano Carrara & Enrico Martino - 2011 - Humana. Mente. Journal of Philosophical Studies 19:57-77.
     
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  12.  41
    On the Brouwerian Concept of Negative Continuity.Enrico Martino - 1985 - Journal of Philosophical Logic 14 (4):379 - 398.
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  13.  61
    The Priority of Arithmetical Truth Over Arithmetical Provability.Enrico Martino - 2002 - Topoi 21 (1-2):55-63.
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  14.  50
    Negationless Intuitionism.Enrico Martino - 1998 - Journal of Philosophical Logic 27 (2):165-177.
    The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, (...)
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  15. On Dialetheic Entailment.Massimiliano Carrara, Enrico Martino & Vittorio Morato - 2011 - In The Logica Yearbook 2010. London:
    The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use (...)
     
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  16.  16
    Fictional Propositions and the Unprovability of Consistency.Enrico Martino - 2006 - Grazer Philosophische Studien 72 (1):201-210.
    We introduce an epistemic version of validity and completeness of first order logic, based on the notions of ideal agent and fictional model. We then show how the perspective here considered may help to solve an epistemic puzzle arising from Gödel's second incompleteness theorem.
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  17.  13
    Brouwer's Equivalence Between Virtual and Inextensible Order.Enrico Martino - 1988 - History and Philosophy of Logic 9 (1):57-66.
    Brouwer's theorem of 1927 on the equivalence between virtual and inextensible order is discussed. Several commentators considered the theorem at issue as problematic in various ways. Brouwer himself, at a certain time, believed to have found a very simple counter-example to his theorem. In some later publications, however, he stated the theorem in the original form again. It is argued that the source of all criticisms is Brouwer's overly elliptical formulation of the definition of inextensible order, as well as a (...)
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  18. Computability, Finiteness and the Standard Model of Arithmetic.Enrico Martino, Matteo Plebani & Massimiliano Carrara - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics. Springer Verlag.
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  19.  3
    Intuitionistic Proof Versus Classical Truth: The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics.Enrico Martino - 2018 - Springer Verlag.
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