Guide Multi-Dimensional Modal Logic

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The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations in particular, multiple open problems.

On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. Enter your Postcode or Suburb to view availability and delivery times. See Terms for more information. Contact 07 online qbd.

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The RRP set by overseas publishers may vary to those set by local publishers due to exchange rates and shipping costs. I make some suggestions of what shape a suitable semantic treatment should take, and dwell on some unresolved issues to which this treatment gives rise, and whose proper resolution bears on the larger project of characterising justification in the ways proposed.

Post-Kripkean theorising concerning modal epistemology accepts a misalignment between apriority and necessity. Two-dimensional semantics provides a framework in which to analyse the Kripkean phenomena of the contingent a priori and the necessary a posteriori. But there is a problem concerning how these two levels compose and interact.

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Multi-Dimensional Modal Logic, Maarten Marx and Yde Venema. | BibSonomy

In particular the problem concerns nested environments: environments where sentences are nested under both modal and epistemic operators see Soames , Dever , and Forbes There is a general problem here for a multi-modal logic with operators for metaphysical necessity and epistemic necessity. In light of the contingent priori we face a dilemma: Either i what is a priori is a contingent matter or ii it is possible that something is a priori but false.

I conclude by exploring a solution which adds a truth predicate to the two-dimensional system. Its acceptance as the correct logic for vagueness has been hampered by two factors.

Second, switching from classical to intuitionistic logic does not appear to help with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. Our explanation assumes nothing about the form of a semantic theory for a language with vague terms. Let intensionalism be the view that necessarily equivalent propositions are identical.

Many-Dimensional Modal Logics: Theory and Applications, Volume 148

Assuming intensionalism, there is a promising account of possible worlds according to which they are special propositions, namely those which are possible although maximally strong. For such propositions to behave as worlds are widely expected to behave, it is necessary that each possible proposition can be strengthened to a maximally strong one; call this claim "atomicity".

Using higher-order logic as a framework in which to regiment our talk of propositions, properties and relations, this talk will explain why atomicity does not follow straightforwardly from intensionalism, but also show that it follows with plausible additional assumptions once the framework is expanded to include higher-order analogues of plural quantifiers. These considerations will presuppose necessitism, the claim that it is necessary what there is.

The talk will conclude by sketching some of the ways in which the situation becomes much more complicated when necessitism is rejected. Imposing the atomicity requirement would render possibility semantics for these languages no more general than possible world semantics, though there would still be advantages for extended modal languages.

In this talk, I will briefly outline the mathematical and logical interest of possibility semantics, but my main goal is to discuss whether possibility semantics—with the rejection of the atomicity requirement—is of philosophical interest.

Some philosophers, including Bob Hale and Ian Rumfitt, have explicitly rejected the atomicity requirement for possibilities. Other philosophers, including Kit Fine, have argued that every proposition is entailed by a world proposition, which in the context of possibility semantics implies the atomicity requirement.

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I will aim to refute these arguments, as formalized in modal logic with propositional quantifiers and an actuality operator. In the course of my response, I will discuss a distinctive kind of propositional contingentism that can be incorporated in possibility semantics.


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We develop some predicativist approaches within the modal framework for potentiality that was developed in Linnebo and Linnebo and Shapiro The result is illuminating, as it puts predicativism into a more general framework and helps to sharpen some of the key theses. All standard epistemic and doxastic logics legitimate something akin to the principle of closure.

And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. In this paper we describe a family of weak logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled.