I present an annotated development of the basic ideas of the Geneva School approach to the foundations of physics and the structures which emerge as mathematical representations of the physically dual notions of state and property.

Full text of erratum: "In the article by D.J. Buller, on p. 278, the y-axis label to Fig. IIb was incorrect. Instead of 'Percentage choosing "Eats cassava root" and "Tattoo," it should have read: 'Percentage choosing "Eats cassava root" and "No tattoo."' We apologise to readers for this error.".

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)

The ordinary concept of death is analysed and compared with revisionary medical definitions, especially those based on irreversible loss of brain function. Prior critics of revisionary definitions have focused on the locus, the brain; I am concerned with the irreversibility condition. I argue that 1) the irreversibility condition is ambiguous, 2) it has unacceptable epistemic and other consequences on any plausible construal, and 3) irreversibility is not part of the ordinary concept of death. I conclude that recent medical definitions seek (...) illegitimately to obtain the certainty of a weak construal of 'irreversible' along with the freedom from moral obligation of the strong construal. (shrink)

Recent studies using functional magnetic resonance imaging of patients in a vegetative state have raised the possibility that such patients retain some degree of consciousness. In this paper, the ethical implications of such findings are outlined, in particular in relation to decisions about withdrawing life-sustaining treatment. It is sometimes assumed that if there is evidence of consciousness, treatment should not be withdrawn. But, paradoxically, the discovery of consciousness in very severely brain-damaged patients may provide more reason to let them die. (...) Although functional neuroimaging is likely to play an increasing role in the assessment of patients in a vegetative state, caution is needed in the interpretation of neuroimaging findings. (shrink)

We review the fact that an MV-algebra is the same thing as a lattice-ordered effect algebra in which disjoint elements are orthogonal. An HMV-algebra is an MV-effect algebra that is also a Heyting algebra and in which the Heyting center and the effect-algebra center coincide. We show that every effect algebra with the generalized comparability property is an HMV-algebra. We prove that, for an MV-effect algebra E, the following conditions are mutually equivalent: (i) E is HMV, (ii) E has a (...) center valued pseudocomplementation, (iii) E admits a central cover mapping γ such that, for all p, q∈E, p∧q=0⇒γ(p)∧q=0. (shrink)

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)

The letter sent by the Royal Society to the London optician, John Marshall, in 1694, commending his new method of grinding, has been reprinted, and referred to, in recent years. However, there has been no comprehensive analysis of the method itself, the letter and the circumstances in which it was written, nor the consequences for trade practices. The significance of the approval by the Royal Society of this innovation and the use of that approbation by John Marshall and other practitioners (...) are examined. Gaps in existing accounts of Marshall's method are partly remedied by supplementing surviving written materials with accounts of contemporary, and present-day, trade practices based on his method. The reasons why Marshall and his contemporaries failed to record his method and specify his improvements are discussed. The reactions of the Spectacle Makers' Company and its more prominent members, both to the innovation itself and to the Royal Society's letter, are analysed. The impact of the new technique on contemporary and later opticians is described. (shrink)