In recent years, in the UK and elsewhere, scientists and science policymakers have grappled with the question of how to reap the benefits of nanotechnologies while minimising the risks. Having recognised the importance of public support for future innovations, they have placed increasing emphasis on ‘engaging’ ‘the public’ during the early phase of technology development. Meaningful engagement suggests some common ground between experts and lay publics in relation to the definition of nanotechnologies and of their benefits and risks. However, views (...) on nanotechnologies are likely to vary according to where actors stand in the technology production/consumption/assessment cycle. Drawing on data from a recent UK-based study, this article examines how scientists (‘upstream’ and ‘downstream’) and policymakers portray the benefits and risks of nanotechnologies, particularly as they relate to two major areas of predicted application, namely medicine/public health and environmental sustainability. The findings reveal that, in the main, scientists and science policymakers held a positive conception of nanotechnologies and see imminent applications, although they acknowledged particular risks, including adverse public reaction. While definitions of ‘benefit’ and ‘risk’ varied, most saw the benefits as outweighing the risks and believed that the risks could be adequately regulated once they were assessed. The difficulties of assessing risk, however, were acknowledged. The study raises a number of questions that will need to be addressed if regulations are to be developed that not only protect people’s heath and wellbeing and the environment but also engender public trust in nanotechnologies. (shrink)

Following a suggestion of Feys, we use “rigorous implication” as a translation of Ackermann's strenge Implikation ([1]). Interest in Ackermann's system stems in part from the fact that it formalizes the properties of a strong, natural sort of implication which provably avoids standard implicational paradoxes, and which is consequently a good candidate for a formalization of entailment (considered as a narrower relation than that of strict implication). Our present purpose will not be to defend this suggestion, but rather to present (...) some information about rigorous implication. In particular, we show first that the structure of modalities (in the sense of Parry [4]) in Ackermann's system is identical with the structure of modalities in Lewis's S4, and secondly that (Ackermann's apparent conjecture to the contrary notwithstanding) it is possible to define modalities with the help of rigorous implication. (shrink)

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. (shrink)

In this note we present an axiomatization of the classical two-valued propositional calculus, for which proofs of decidability, consistency, completeness, and independence, are almost trivial (given an understanding of truth tables).

Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. Fitch (...) on consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)

What is new here is the detailed discussion of several important results in the classical foundations of mathematics and of the relation of logic to mathematics. As regards logical questions, the central thesis of Wittgenstein's later philosophy is well known, both from the earlier posthumous volume and from the writings of his many disciples. In the Investigations the thesis is applied to the "logic of our expressions" in everyday contexts; here he discusses in the same spirit the more specialized language (...) used in talking about the foundations of mathematics. (shrink)

R-Dagger is the theory of relevant implication, Got from the calculus r (see belnap, Jsl, 32, 1-22), By adding machinery for propositional quantification. In r-Dagger define t as for some p, P, F as for all p, P. Then (t, F) is closed in r-Dagger under truth-Functions and relevant implication, Which, When confined to (t, F) acts just like material 'implication.' but r-Dagger admits of many propositions other than t, F. The article also contains polemics against extensionalism and nominalism. (edited).

One striking point of similarity is this: there is a sense in which we feel we do not know what we are talking about. By this we mean that our remarks to follow do not constitute a theory. And as evidence for this contention we cite the fact that we have no logically valid arguments to support what we say. To be sure, we believe ourselves to be in very good company in this respect, at least as far as the (...) behavioral sciences and systems of synthetic philosophy are concerned--we do not believe others know what they are talking about either. Whitehead, for example, gives us very few arguments in favor of his metaphysics--he just tells us how the world looks to him. In this paper we will be presumptuous enough to try to tell you how the world looks to us. At worst the picture we want to draw will be misleading; at best it may suggest some experimental or formal problems of interest. (shrink)

Of course it has always been recognized, in philosophical circles at least, that such deductions are at best plausible inferences, rather than a species of logically valid inferences, and we will not pretend otherwise. Still, it seems interesting to consider the question: why do people have puzzles, games of chance, games of strategy, and aesthetic objects, universally in human societies?

Brand Blanshard has been among the most stubborn of contemporary philosophers in rejecting that mathematical analysis of “logic” which has most enchanted his contemporary mathematical practitioners of the trade. He has said repeatedly that the mathematically orthodox have simply got hold of the whole topic by the wrong handle, and cited many complaints about material and strict “implication” as evidence that something has gone gravely wrong. Most of the objections he raises coincide with those of students newly introduced to the (...) topic. But in the case of our students, it seems that the vast majority can be either brainwashed or browbeaten into ignoring the initial objections we all felt, on introduction, to principles like ⊃q, or p ⊃, or ☐ p ⊰. Blanshard has, however, continued to champion the cause of the “common man” against the mathematically precise, but allegedly misguided dogmas of orthodoxy. (shrink)