Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...) the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions. (shrink)

Oxford Scholarly Classics brings together a number of great academic works from the archives of Oxford University Press. Reissued in a uniform series design, they will enable libraries, scholars, and students to gain fresh access to some of the finest scholarship of the last century.

Presumably it is common ground that this verb has in addition to the basic sense ‘recognize’ the derivative sense ‘oread’, and that one must judge from the context whether reading to one or more other people, or private reading, is meant. The reading of the text of a law to a jury at an orator's request is marked by the circumstances themselves as public reading; so is the reading of the Athenian decree to the Mitylenaeans in Thucydides. When Theaetetus answers (...) in the affirmative the question whether he has read the book of Protagoras which contains the statement that man is the measure of all things (); or when it is asked ‘Why is it that some people, if they begin to read, are overcome by sleep even against their will, whereas others wishing to be overcome by sleep are kept awake by taking up a book?’ Evidently what is intended is reading in the privacy of one's own room. When Socrates in the Phaedo says that he heard a person reading from Anaxagoras and eagerly took the book home to read, both senses are found within a few pages. (shrink)

Love's bitter fruits: Martha C. Nussbaum The Therapy of Desire: Theory and Practice in Hellenistic Ethics.Max Horkheimer, Between Philosophy and Social Science: Selected Early Writings.

A Distinction of four species of tragedy and epic poetry is laid down, though not explained at length, in two passages of the Poetics, and, as I hope to show, mentioned in another. At the end of the treatise, Aristotle positively says that he has given an explanation of both the species and the component parts of tragedy and epic poetry.

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.

This new translation of _De Caelo_ fits seamlessly with other volumes in the New Hackett Aristotle series, enabling Anglophone readers to study Aristotle’s work in a way previously not possible. The Introduction describes the book that lies ahead, explaining what it is about, what it is trying to do, how it goes about doing it, and what sort of audience it presupposes. Sequentially numbered endnotes provide the information most needed at each juncture, while a detailed Index indicates the places where (...) focused discussion of key notions occurs. (shrink)

Arguing from a sort of reasonable Protestant ethic, Henry offers a worthwhile and sometimes quite practical analysis of a Christian social ideal. In Henry's approach, no "prattling about love" can take the place of justice when the latter is what is needed.—D. J. B.