We give an axiomatic framework for the non-modular simple 0-categorical structures constructed by Hrushovski. This allows us to verify some of their properties in a uniform way, and to show that these properties are preserved by iterations of the construction.
An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.
Recently, several articles in the scholarly literature on medical ethics proclaim the need for “responsible scholarship” in the debate over the proper criteria for death, in which “responsible scholarship” is defined in terms of support for current neurological criteria for death. In a recent article, James M. DuBois is concerned that academic critiques of current death criteria create unnecessary doubt about the moral acceptability of organ donation, which may affect the public’s willingness to donate. Thus he calls for a closing (...) of the debate on current death criteria and for journal editors to publish only critiques that “substantially engage and advance the debate.” We argue that such positions as DuBois’ are a threat to responsible scholarship in medical ethics, especially scholarship that opposes popular stances, because it erodes academic freedom and the necessity of debate on an issue that is literally a matter of life and death, no matter what side a person defends. (shrink)
Using data on the ‘career’ paths of one thousand ‘leading scientists’ from 1450 to 1900, what is conventionally called the ‘rise of modern science’ is mapped as a changing geography of scientific practice in urban networks. Four distinctive networks of scientific practice are identified. A primate network centred on Padua and central and northern Italy in the sixteenth century expands across the Alps to become a polycentric network in the seventeenth century, which in turn dissipates into a weak polycentric network (...) in the eighteenth century. The nineteenth century marks a huge change of scale as a primate network centred on Berlin and dominated by German-speaking universities. These geographies are interpreted as core-producing processes in Wallerstein’s modern world-system; the rise of modern scientific practice is central to the development of structures of knowledge that relate to, but do not mirror, material changes in the system. (shrink)
An intermediate stage in Hrushovski’s construction of flat strongly minimal structures in a relational language L produces ω-stable structures of rank ω. We analyze the pregeometries given by forking on the regular type of rank ω in these structures. We show that varying L can affect the isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.
Kant's short essay is a reflection on the contemporary structure of academic studies; he examines this structure in terms of the functions of the State and of the Universities which form part of it. His analysis links the empirical facts with conceptual distinctions, in ways that are familiar from his more general and abstract philosophy. His main aim is to ground a distinction between legitimate and illegitimate ways in which different Faculties of the University may approach intellectual issues that are (...) of common interest to them. I then consider to what extent and how a Kantian analysis might be applied to our contemporary University situation. Despite the societal and intellectual differences between Kant's environment and ours, I argue that significant parallels exist between the two cases and that Kant's proposals and strictures for his own time have application for us today. (shrink)
We are concerned with identifying by how much a finite cover of an 0-categorical structure differs from a sequence of free covers. The main results show that this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover.These results (...) generalise results of the second author obtained in the case where the base of the cover is a grassmannian of a disintegrated set. They also give a complete proof of a statement of the second author extending this case to the case of a grassmannian of a modular set. To do this, we need to analyse the possible superlinked covers of such a set.We also give a combinatorial condition on the base of a cover which guarantees various chain conditions on finite covers over this base, and introduce a pregeometry which is useful in the analysis of finite covers with simple fibre groups. (shrink)
We are concerned with the following problem. Suppose Γ and Σ are closed permutation groups on infinite sets C and W and ρ: Γ → Σ is a non-split, continuous epimorphism with finite kernel. Describe the possibilities for ρ. Here, we consider the case where ρ arises from a finite cover π: C → W. We give reasonably general conditions on the permutation structure W;Σ which allow us to prove that these covers arise in two possible ways. The first way, (...) reminiscent of covers of topological spaces, is as a covering of some Σ-invariant digraph on W. The second construction is less easy to describe, but produces the most familiar of these types of covers: a vector space covering its projective space. (shrink)
We construct a stable one-based, trivial theory with a reduct which is not trivial. This answers a question of John B. Goode. Using this, we construct a stable theory which is n-ample for all natural numbers n, and does not interpret an infinite group.
Kant’s moral philosophy is celebrated for its doctrines of the primacy of the good will, the categorical imperative, and the significance of autonomy. These themes are pursued in the section of the Critique of Practical Reason which Kant called the Analytic, as well as in less formal works such as The Foundations of the Metaphysics of Morals. In his main work Kant added a Dialectic, which is less well studied but is still essential to understanding his whole project. The concept (...) of the Highest Good, summum bonum, the ultimate goal in life, incorporates both an objective and a subjective element. It pronounces on what we ought to want and how we ought to want it: it bears on our happiness and on our virtue. The aim in the Dialectic is to highlight the tension that can result from these twoelements, so that the need for a rapprochement between them becomes better appreciated. This tension remains in contemporary moral philosophy, with its diverse approaches of virtue ethics, deontology, and consequentialism. Kant’s stance regarding this dialectical tension needs to be understood, by Kant scholars and by moral philosophers. (shrink)
Plato wrote dialogues, and he praised dialectic, or conversation, as a suitable style for fruitful philosophical investigation. His works are great literature; and nodoubt this quality derives much from their form as dialogues. They also have definite philosophical content; and an important part of this content is their dialecticalepistemology. Dialectic is part of the content of Plato's philosophy. Can we reconcile this content with his literary style? I shall examine and sharpen the sense of this problem by referring to four (...) passages from different works of Plato: Parmenides 132b-c, Protagoras 351-2, Sophist 248-9, Republic 592. In these passages we can distinguish a main position, which represents what it is natural to label Platonism, from a line of thought which diverges from that position and yet also seems authentically Platonic. I argue that the solution to this tension lies in the notion of dialectic as a tentative and exploratory method of philosophy. This view of dialectic is in some conflict with Plato's official account of the method as guaranteed to deliver fundamental truth; but that conflict presents one more version of the phenomenon which I am exploring. The theory of dialectic provides philosophical support for the method of dialogue. That is how philosophy and literature are linked in Plato's pursuit of truth. (shrink)
Aristotle assigns positive value to artistry and its skills, placing them below science but nearby. Fuller content for this view of art can be garnered from his technical treatises, especially the accounts of rhetoric and dialectic, where the subjectivity imported by the role of audiences is explored with subtlety. These ideas have influence on later philosophy of aesthetics and of technology, and they need to be pondered by those engaged in current debate in these areas.
Philosophy is taught and studied throughout the world. In consequence the activity is suffused with the pluralism which cultural diversity imports; but still there are universals that need to be explored and stated. I set out a list of issues that should concern teachers of philosophy in any cultural context, and then proceed to try to resolve them. A number of these problems relate to the scope of philosophy teaching and its relation to other subjects at its boundaries. In this (...) paper, I discuss how we can sustain the integrity of philosophy while at the same time not restricting its scope of operation. (shrink)
We show that the N₀-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's $SOP_n $ hierarchy: if they are not simple, then they have SOP₃ and NSOP₄. We also show that structures produced without using a control function can be undecidable and have SOP.
In our post-modern cultural climate we are often told that reality is value-free. Indeed sometimes it is even said to be fact-free. Yet almost all philosophers have been deeply concerned with matters of value, in addition to their other main pre-occupation: that is the nature of truth and our knowledge of it. The question therefore arises: why should these two – good and truth – be so powerfully connected? And why should this business of value continue to exert the hold (...) on philosophers that it evidently does? (shrink)
Because complex organs taken from unequivocally dead people are not suitable for transplantation, human death has been redefined so that it can be certified at some earlier stage in the dying process and thereby make viable organs available without legal problems. Redefinitions based on concepts of.