4,444 research outputs found

    Changing a semantics: opportunism or courage?

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    The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

    Reply to Rosanna Keefe’s ‘Modelling higher-order vagueness: columns, borderlines and boundaries’

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    This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in response to Keefe’s paper. In addition, the audio of the session, which is available online, becomes inaudible at the beginning of my reply to Keefe’s comments due to a technical defect. The following is a full version of my remarks

    Relations as Plural-Predications in Plato

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    <p>Plato was the first philosopher to discover the metaphysical phenomenon of plural-subjects and plural-predication; e.g. you and I are two, but neither you, nor I are two. I argue that Plato devised an ontology for plural-predication through his Theory of Forms, namely, plural-partaking in a Form. Furthermore, I argue that Plato used plural-partaking to offer an ontology of related individuals without reifying relations. My contention is that Plato’s theory of plural-relatives has evaded detection in the exegetical literature because his account of plural-subjects through the Theory of Forms had not been recognised for what it is. I further submit that Plato’s handling of related individuals through plural-predication is not only a ‘first’ in philosophy, but also an ‘only’, having remained a unique account in the metaphysics of relations. I hope that Plato’s account will introduce a fresh approach to contemporary debates on</p> <p>the subject.</p

    A Passage Theory of Time

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    This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage

    On What Counts as a Translation

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    In this article, instead of taking a particular method as translation, we ask: what does one expect to do with a translation? The answer to this question will reveal, though, that none of the first order methods are capable of fully represent the required transference of ontological commitments. Lastly, we will show that this view on translation enlarge considerably the scope of translatable, and, therefore, ontologically comparable theories
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