The aim of this paper is to develop the theory of groups definable in the p-adic field ${{\mathbb {Q}}_p}$, with “definable f-generics” in the sense of an ambient saturated elementary extension of ${{\mathbb {Q}}_p}$. We call such groups definable f-generic groups.So, by a “definable f-generic” or $dfg$ group we mean a definable group in a saturated model with a global f-generic type which is definable over a small model. In the present context the group is definable over ${{\mathbb {Q}}_p}$, and (...) the small model will be ${{\mathbb {Q}}_p}$ itself. The notion of a $\mathrm {dfg}$ group is dual, or rather opposite to that of an $\operatorname {\mathrm {fsg}}$ group (group with “finitely satisfiable generics”) and is a useful tool to describe the analogue of torsion-free o-minimal groups in the p-adic context.In the current paper our group will be definable over ${{\mathbb {Q}}_p}$ in an ambient saturated elementary extension $\mathbb {K}$ of ${{\mathbb {Q}}_p}$, so as to make sense of the notions of f-generic type, etc. In this paper we will show that every definable f-generic group definable in ${{\mathbb {Q}}_p}$ is virtually isomorphic to a finite index subgroup of a trigonalizable algebraic group over ${{\mathbb {Q}}_p}$. This is analogous to the o-minimal context, where every connected torsion-free group definable in $\mathbb {R}$ is isomorphic to a trigonalizable algebraic group [5, Lemma 3.4]. We will also show that every open definable f-generic subgroup of a definable f-generic group has finite index, and every f-generic type of a definable f-generic group is almost periodic, which gives a positive answer to the problem raised in [28] of whether f-generic types coincide with almost periodic types in the p-adic case. (shrink)

Gadamer's attempt to 'rehabilitate tradition' in general clarifies that which theology and the human sciences have in common since he claims that the rehabilitation of tradition is crucial for all human science enquiry. His systematic unfolding of the hermeneutical process described in Truth and Method is discussed under three headings: The meaning of tradition and how the idea of tradition may be rehabilitated; how do we know in the human sciences? and, the nature of theological reflection as part of the (...) human sciences. Gadamer's hermeneutics helps to transcend the antithesis between reason and tradition. It offers a more appropriate way to under stand cultural and historical texts and broadens the purview of the human sciences. It is within this broader understanding of the human sciences that theological reflection comes to itself. S. Afr. J. Philos. Vol.21(4) 2002: 345-358. (shrink)

Bio-heteronormative conceptions of the family have long reinforced a nuclear ideal of the family as a heterosexual marriage, with children who are the genetic progeny of that union. This ideal, however, has also long been resisted in light of recent social developments, exhibited through the increased incidence and acceptance of step-families, donor-conceived families, and so forth. Although to this end some might claim that the bio-heteronormative ideal is not necessary for a social unit to count as a family, a more (...) systematic conceptualization of the family—the kind of family that matters morally—is relatively underexplored in the philosophical literature. This paper makes a start at developing and defending an account of the family that is normatively attractive and in line with the growing prevalence of non-conventional families and methods of family-formation. Our account, which we call a constitutive-affirmative model of the family, takes the family to be constituted by an ongoing process of relevant affective and affirmative relations between the putative family members. (shrink)

The common liberal understanding of reproductive autonomy – characterized by free choice and a principle of non-interference – serves as a useful way to analyse the normative appeal of having certain choices open to people in the reproductive realm, especially for issues like abortion rights. However, this liberal reading of reproductive autonomy only offers us a limited ethical understanding of what is at stake in many kinds of reproductive choices, particularly when it comes to different uses of reproductive technologies and (...) third-party reproduction. This is because the liberal framework does not fully capture who benefits from which reproductive options, the extent of the risks and harms involved in various reproductive interventions, and the reasons for why people are driven to make certain reproductive choices. (shrink)

We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of (...) K. (shrink)

Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.

Let T be a complete O-minimal theory in a language L. We first give an elementary proof of the result (due to Marker and Steinhorn) that all types over Dedekind complete models of T are definable. Let L * be L together with a unary predicate P. Let T * be the L * -theory of all pairs (N, M), where M is a Dedekind complete model of T and N is an |M| + -saturated elementary extension of N (and (...) M is the interpretation of P). Using the definability of types result, we show that T * is complete and we give a simple set of axioms for T * . We also show that for every L * -formula φ(x) there is an L-formula ψ(x) such that $T^\ast \models (\forall \mathbf{x})(P(\mathbf{x}) \rightarrow (\phi(\mathbf{x}) \mapsto \psi (\mathbf{x}))$ . This yields the following result: Let M be a Dedekind complete model of T. Let φ(x, y) be an L-formula where l(y) = k. Let $\mathbf{X} = \{X \subset M^k$ : for some a in an elementary extension N of M, X = φ (a,y N ∩ M k }. Then there is a formula ψ(y, z) of L such that X = {ψ (y, b) M : b in M}. (shrink)

Edward Said's book Orientalism stands in a long lineage of critique of European scholarship responsible for shaping European understandings of foreign cultures. His book contributed significantly to the debate about the epistemological presuppositions informing European scholars of other cultures. However, while Said exposed in considerable detail the ways in which the Orient was distorted by the theories of the European academy, he left unexamined the possibility of genuine cross-cultural understanding. This article considers the significance of hermeneutics for cross-cultural rather than (...) historical understanding. It explores the implicit claim Gadamer makes for the universal validity of hermeneutics not only for understanding in history, but for a genuine intellectual rapprochement across geographical and cultural lines as well. S. Afr. J. Philos. Vol.21(4) 2002: 330-344. (shrink)

Literature on testimonial injustice and ways that perpetrators might combat it have flourished since Miranda Fricker’s ground-breaking work on testimonial injustice. Less attention has been given, however, to the role of bystanders. In this paper, I examine the accountability that bystanders may have for their omissions to redress testimonial injustice. I argue that bystander accountability applies in cases where it is opportune for bystanders to intervene, and if they are also sufficiently equipped and able to redress the testimonial injustice. Moreover, (...) I recommend that we move beyond virtue responsibilism for ameliorative thinking about testimonial injustice. (shrink)

This classic edition presents the correspondence of one of the great thinkers of the 18th century, and offers a rich picture of the man and his age. This first volume contains David Hume's letters from 1727 to 1765. Hume's correspondents include such famous public figures as Jean-Jacques Rousseau, Adam Smith, James Boswell, and Benjamin Franklin.

This classic edition presents the correspondence of one of the great thinkers of the 18th century, and offers a rich picture of the man and his age. This second volume contains David Hume's letters from 1766 to 1776. Hume's correspondents include such famous public figures as Jean-Jacques Rousseau, Adam Smith, James Boswell, and Benjamin Franklin.

Abortion is the deliberate termination of a pregnancy. In current practice, this involves the death of the foetus. Consequently, the debate on whether those experiencing an unwanted pregnancy have the right to abortion is usually dichotomized as a matter of pro-choice versus pro-life. Pro-choice advocates maintain that abortion is acceptable under various circumstances. The idea that we ought to respect pregnant people’s rights to choose what to do with their bodies – respect for bodily autonomy – is cited as a (...) major reason for granting them abortion rights. Pro-life advocates, on the other hand, claim that abortion is not acceptable under most circumstances. They argue, typically, that the foetus has a right to life. Recent events, such as Poland’s High Court decision in October 2020 to ban most abortions, and the huge protests and outcries this generated around the world, indicate that the abortion debate is far from resolved. (shrink)

It was natural and inevitable that his two Aethiopias, in the eastern and western extremities of the world, should be identified with the countries of the two dark-skinned peoples in the Far East and the Far West of the Ancient World: India and Mauretania.There was the difficulty that the real Aethiopia was in Africa, neither in the Far East nor in the Far West. Serious writers on geography tried to reconcile Homer and the geographical facts.I wish to excerpt from Strabo (...) three theories concerning Aethiopia and the Aethiopians which will then be used to elucidate passages in Latin literature. (shrink)

Originally published: Oxford: Clarendon Press, 1932.

The "space" of Lascar strong types, on some sort and relative to a given complete theory T, is in general not a compact Hausdorff topological space. We have at least three aims in this paper. The first is to show that spaces of Lascar strong types, as well as other related spaces and objects such as the Lascar group Gal L of T, have well-defined Borel cardinalities. The second is to compute the Borel cardinalities of the known examples as well (...) as of some new examples that we give. The third is to explore notions of definable map, embedding, and isomorphism, between these and related quotient objects. We also make some conjectures, the main one being roughly "smooth if and only if trivial". The possibility of a descriptive set-theoretic account of the complexity of spaces of Lascar strong types was touched on in the paper [E. Casanovas, D. Lascar, A. Pillay and M. Ziegler, Galois groups of first order theories, J. Math. Logic1 305–319], where the first example of a "non-G-compact theory" was given. The motivation for writing this paper is partly the discovery of new examples via definable groups, in [A. Conversano and A. Pillay, Connected components of definable groups and o-minimality I, Adv. Math.231 605–623; Connected components of definable groups and o-minimality II, to appear in Ann. Pure Appl. Logic] and the generalizations in [J. Gismatullin and K. Krupiński, On model-theoretic connected components in some group extensions, preprint, arXiv:1201.5221v1]. (shrink)