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By adding the concepts of necessary and possible, their system has laid the foundation of modern modal logic (ML).
By contrast, in order to investigate the possible worlds of modal logic we have to employ essentially logical devices, consistent and systemic.
Appropriately, this paper uses symbols from temporal modal logic as well as a "doxastic" modal (pertaining to belief).
Chapter 2 covers many-valued and modal logics, with algebraic semantics; Chapter 3 is about properties of connectives such as truth-functionality and extensionality.
Of course, today, such a route through modal logic to an ultimate explanation cannot be taken for granted, depending, as it does, upon a robust modal realism, which is precisely what many twentieth century logicians have called into question--a modal realism, to put it loosely, of the Platonic variety, which sees modal logic as reflecting a kind of eternal logic (ultimately proper to an eternal Logos), and thus as affording a kind of ladder to the real par excellence.
Those with a basic background in classical logic but not already familiar with modal logic would probably find it difficult to use this chapter for independent study.
These errors are the result of his misconceptions concerning the nature of necessity and his failure to properly understand the semantics of modal logic.
Apart from the two introductory papers the papers are technical and require a background in modal logic and model theory.
In Brandom's story, the overthrow of Quineanism waits on the work of David Lewis whose possible world semantics yields the modal logic that Quine would not sanction.
In the final paper, Greg Restall defends an interesting result for proponents of KP: Although FR engenders paradox, a suitably weakened modal logic can sustained a Conjunctive Knowability Principle, according to which, for any truth, there is a collection of truths such that each is knowable and their conjunction is logically equivalent to the initial truth in question.
Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions, VOLKER HALBACK and PHILIP WELCH
Given normal modal logic it is a theorem: (p [contains] Kp) [contains](p [contains] [?