We review some of the essential novel ideas introduced by Bohm through the implicate order and indicate how they can be given mathematical expression in terms of an algebra. We also show how some of the features that are needed in the implicate order were anticipated in the work of Grassmann, Hamilton, and Clifford. By developing these ideas further we are able to show how the spinor itself, when viewed as a geometric object within a geometric algebra, can be (...) given a meaning which transcends the notion of the usual metric geometry in the sense that it must be regarded as an element of a broader and more general pregeometry. (shrink)

Available from UMI in association with The British Library. Requires signed TDF. ;It is the aim of this thesis to consider two accounts of 1st-person utterances that are often mistakenly conflated--viz. that involving the 'no-reference' view of 'I', and that of the non-assertoric thesis of avowals. The first account says that in a large range of 'psychological' uses, 'I' is not a referring expression; the second, that avowals of 1st-personal 'immediate' experience are primarily 'expressive' and not genuine assertions. ;The two (...) views are expressions of what I term 'Trojanism'. This viewpoint constitutes one side of a 'Homeric Opposition in the Metaphysics of Experience', and has been endorsed by Wittgenstein throughout his writings; it has received recent expression in Professor Anscombe's article 'The First Person'. I explore the ideas of these writers in some depth, and consider to what extent they stand up to criticism by such notable 'Greek' contenders as P. F. Strawson and Gareth Evans. ;I first give neutral accounts of the key-concepts on which subsequent arguments are based. These are the immunity to error through misidentification of certain 1st-person utterances, the guaranteed reference of 'I', avowal, and the Generality Constraint. I consider the close relation of Trojanism to solipsism and behaviourism, and then assess the effectiveness of two arguments for that viewpoint--Anscombe's Tank Argument and the argument from IEM. Though each is appealing, neither is decisive; to assess Trojanism properly we need to look at the non-assertoric thesis of avowals, which alone affords the prospect of a resolution of the really intractable problems of the self generated by Cartesianism. ;In the course of the latter assessment I consider the different varieties of avowal, broadening the discussion beyond the over-used example 'I am in pain'. I explore Wittgenstein's notion of 'expression', and discuss how this notion may help to explain the authority a subject possesses on his mental states as expressed in avowals. My conclusion is that an expressive account of avowals can provide a satisfactory counter to the Cartesian account of authority without our needing recourse to a non-assertoric or even to a non-cognitive thesis. ;Discussion of self-consciousness is implicit in discussion of the Homeric Opposition, but there is in addition a short chapter on the concept itself. (shrink)

Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the (...) first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown nineteenth century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on ‘implication as inference’ where we explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas related to the subjects of this paper. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability (...) and preservation under ultrafilter extensions are introduced and studied as well. (shrink)

Avez-vous remarqué que dans le monde tout ce qui compte va par quatre? La musique : timbre, harmonie, rythme et mélodie. Le repérage : altitude, latitude, longitude et datation. Les quatre aspects de la cause: pour quoi, avec quoi, par quoi et selon quoi? Les forces de la nature : interactions faible, forte, électromagnétique et gravitationnelle... Les vingt-quatre particules élémentaires qui constituent la matière une famille de six leptons associée à trois familles de quarks. Et aussi la logique d'un discours (...) nuancé : oui, non, oui et non, ni oui ni non. Pourquoi quatre est-il partout? La notion de quaternité apporte une réponse à la fois simple et surprenante à cette question. A partir d'exemples tirés de l'expérience humaine, les auteurs en dégagent les aspects structurels et s'en servent pour approfondir le sens des mathématiques et de divers autres domaines liés à la genèse de la connaissance. Il s'agit d'une nouvelle épistémologie, fondée sur un modèle logique qui complète celui d'Aristote. (shrink)

Roman Catholic moral theology follows a centuries-old tradition of moral reflection. Contemporary Roman Catholic moral theory applies these traditional arguments to the realm of medical ethics, including the issues of active euthanasia and physician-assisted suicide. Unavoidable moral limits on licit medical intervention sometimes require that the moral duty to treat, cede to the duty to cease treatment when measures become more harmful than beneficial to the patient. This does not reduce the need for the compassionate use of palliative care in (...) response to suffering. However, it does mean that rather than being excessively committed to maintaining mere biological human life, or actively seeking death, that we learn a sober realism about the limits of human life. Catholic moral analysis examines an act objectively, both in its relation to the agent and as a material event in the world. This allows both the virtuous or vicious intentions of the agent and the effects of the action to be included in its moral evaluation. Thus, Catholic moral analysis is both quasi-deontological and quasi-consequentialist. Objectively, active euthanasia and physician-assisted suicide, as acts of deliberate killing, are seen as repugnant, in that they fail to incarnate a benign inner intention or to form an agent in virtue. Catholic moral theology is extremely skeptical that an act of intending death directly can be consonant with a sincere compassion for the dying, suffering person and views it as a direct negation of the precious gift of human life. (shrink)

Much ink has been spilt in consideration of the once pervasive reliance on military metaphors to depict the relationships between science and religion in the nineteenth century. This has resulted in historically sensitive treatments of secularization; and the realization that the relationship between science and religion was not a bloody war between intellectual nation states, but a protracted divorce of former partners. Moreover, historians of science have been encouraged to throw off the yoke of the internalism–externalism debate, and to explore (...) the cultural boundaries that impinged upon practitioners of a natural knowledge of the world. Within the historiography of nineteenth-century science, this has resulted in many new perspectives on science and natural knowledge in relation to cultural control and authority. (shrink)

The most important events of the immediately preceding period--1945-1954--were attempts at general readings of Descartes' thought by Jean Laporte, Fernand Alquié, and Martial Guéroult. In Le Rationalisme de Descartes Laporte struck sharply at stereotype by insisting that Descartes was not a rationalist. Deftly exploiting such issues as the soul-body union, the knowledge of the infinite and the faith-reason relationship, he draws the conclusion that "... if it were necessary to characterize Descartes' philosophy by one name, the name which would fit (...) it best, all paradox aside, would be empiricism, radical and integral empiricism." The readings of both Alquié and Gueroult are carefully attuned to the development in Descartes' thought. In La Découverte Métaphysique de l'Homme chez Descartes, the former maintains that this development is dominated by the progressive discovery of the meaning of man. Guéroult takes a remark from the Discourse on Method as key to the unfolding of Descartes' thought. The "long chains of reasons, so simple and easy, which geome- tricians use to arrive at their most difficult demonstrations..." are the central inspiration of Descartes selon l'Ordre des Raisons. Cartesianism, it is maintained, developed primarily by deductive movement along these chains. (shrink)