Notes on Logics of Metric Spaces

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expressively complete over metric spaces for the (undecidable) two-variable fragment of first-order logic with binary pred-icates interpreting the metric. The frame conditions needed correspond rather directly with a Boolean modal logic that is, again, of the same expressivity as the two-variable fragment. We use this representation to derive an axiomatisation of the modal hybrid variant of the two-variable fragment, discuss the compactness property in distance logics, and derive some results on (the failure of) interpolation in distance logics of various expressive power. Presented by Melvin Fitting     

Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.     

Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality

This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.

Duality and Canonical Extensions of Bounded Distributive Lattices with Operators,and Applications to the Semantics of Non-Classical Logics II

The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models.     

Kripke's sole route to the necessary a posteriori

In ‘Kripke on epistemic and metaphysical possibility: two routes to the necessary a posteriori’, Scott Soames identifies two arguments for the existence of necessary a posteriori truths in Naming and Necessity (NN). He argues that Kripke's second argument relies on either of two principles, each of which leads to contradiction. He also claims that it has led to ‘two-dimensionalist’ approaches to the necessary a posteriori which are fundamentally at odds with the insights about meaning and modality expressed in NN. I argue that the alleged second argument is not in NN. I identify the mistakes that lead to Soames' misinterpretation.     

Completing the incomplete: a defense of positive obligations to distant others

Global justice is, at its core, about moral obligations to distant others. But which obligations ought to be included is a matter of considerable debate. In the discussion that follows I will explicate and challenge two objections to the inclusion of foundationally positive obligations in our account of global justice. The first objection is based on the proposition that negative obligations possess and positive obligations lack a property necessary for a moral demand to be a matter justice. The second objection is that even the most trivial positive obligation becomes overly burdensome when applied to the global arena. And, though I do not offer any particular substantive account of positive obligations to distant others; I assess some of the implications that would arise were positive obligations to distant others to be included in our account of global justice.     

ON THE DISTINCTION BETWEEN REDUCTIVE AND NONREDUCTIVE PHYSICALISM

Abtract: This article argues that the debate between reductive and nonreductive physicalists is best characterized as a disagreement about which properties are natural. Among other things, natural properties are those that characterize the world completely. All physicalists accept the “completeness of physics,” but this claim contains a subtle ambiguity, which results in two conceptions of natural properties. Reductive physicalists should assert, while nonreductive physicalists should deny, that a single set of low‐level physical properties is natural in both of these senses. This way of drawing the distinction succeeds where previous approaches have failed and illuminates why the debate about reductionism is important.     

潮汕话-普通话双言者的词汇习得年龄效应

采用潮汕话-普通话双言者为被试, 通过3个实验, 考察了词汇习得年龄效应。实验1采用汉字命名和图片命名范式, 证实了在双言者的两种语言中都存在词汇习得年龄效应。实验2和实验3分别采用语义范畴判断及声母监控任务, 在语义层面及语音层面检验了双言者的两种语言的词汇习得年龄效应的特点。结果表明, 在语义任务上发现了词汇习得年龄效应, 在语音任务上未发现。整个研究表明, 语义在汉语词汇习得年龄效应产生中具有重要作用, 支持了语义假设。     

Normal Modal Substructural Logics with Strong Negation

We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.