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Lemmon argues that dilemmas occur between classes of 'oughts;' duties, obligations, and moral principles. He claims that there are not conflicts within each class, presumably because he is a utilitarian, and thinks that moral principles will always be univocal.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

Combining logics has become a rapidly expanding enterprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages. By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. (...) Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...

In chapter one, I motivate the results to follow by discussing their impact on our conception of the nature of philosophy. ;In chapter two, I define, by way of a description of its rules of inference, a system of quantified modal logic. I then use this system in subsequent chapters to codify definitions of concepts and to construct formal derivations. ;Chapter three considers an essay by Nasser and Brown in which they attempt to answer our basic question: does an omniscient (...) being exist? I also evaluate their claim to be addressing an argument by Hartshorne . ;In chapter four I distinguish four traditional concepts of omniscience. Each is defined in terms of the formal system of chapter two, making use of only non-logical predicate, the dyadic relation 'x knows that p'. I then define adequacy conditions and prove that the definitions given meet them. ;In chapter five, I construct valid derivations of the existence of an omniscient being . ;In chapter six, I consider the premisses used in the Seven Epistemic Ways, and show that, with the exception of the premise that it is possible that there be an omniscient being, each of these premisses is a theorem when omniscience is construed as in the classical tradition . ;In chapter seven alternatives to the classical concepts of omniscience are defined formally . I then show which of the seven ways are sound when the premisses are interpreted in terms of these alternative concepts. (shrink)