This article aims to classify those reducts of expansions of (Q, <) by unary predicates which eliminate quantifiers, and in particular to show that, up to interdefinability, there are only finitely many for a given language. Equivalently, we wish to classify the closed subgroups of Sym(Q) containing the group of all automorphisms of (Q, <) fixing setwise certain subsets. This goal is achieved for expansions by convex predicates, yielding expansions by constants as a special case, and for the expansion by (...) a dense, co-dense predicate. Partial results are obtained in the general setting of several dense predicates. (shrink)
As frequently pointed out in this discussion, one of the most characteristic features of Mayr's approach to the history of biology stems from the fact that he is dealing to a considerable degree with his own professional history. Furthermore, his main criterion for the selection of historical episodes is their relevance for modern biological theory. As W. F. Bynum and others have noted, the general impression of his reviewers is that “one of the towering figures of evolutionary biology has now (...) written a towering history of his discipline.”138 Bynum is here referring to The Growth of Biological Thought, but this observation holds equally true for Mayr's other historical writings: One must surely read this book [One Long Argument] not only for its content in itself, but for what it tells of its author. And certainly as one does so, one comes away full-handed. Many, if not all, of the disputes and controversies that have driven Mayr through his long intellectual life reappear, stated as forcefully and elegantly as ever.139Up to this point, most reviewers agree; the bone of contention is, rather, how to evaluate Mayr's historical work, considering this observation. The two related characteristics of his work-I will call them subjectivity and presentism-stand in opposition to a widespread approach in the history of science exemplified by Kuhn's suggestion that “insofar as possible..., the historian should set aside the science that he knows. His science should be learned from the textbooks and journals of the period he studies.”140 There are, however, historians who consider the close connection between Mayr and the subject matter of his historical studies to be an advantage.141On the other hand, it is assumed that the connection between past and present must result in a distortion of the historical truth and lead to a historiographical fallacy, commonly referred to as “Whig history”. Herbert Butterfield, who in 1931 gave the term its now generally accepted meaning, believed that “real historical understanding is not achieved by the subordination of the past to the present, but rather by our making the past our present and attempting to see life with the eyes of another century than our own”142. Unfortunately, Butterfield's definition of what he considers Whig history remains somewhat vague, and modern authors have emphasized what they consider most important. Butterfield's “subordination of the past to the present” is referred to in respect to the selection of subjects (there are more biographies of Charles Darwin than of, let's say, Louis Agassiz),143 to the evaluation of historical authors,144 or, more generally, to all kinds of histories “with one eye, so to speak, upon the present.”145 The underlying tendency of Whig historians is to produce a “historical account told from the viewpoint of those in power,”146 leading to a “glorification of the present.”147 It is obvious that Mayr's strongly presentist approach to the history of biology can be called Whiggish, if we apply the criteria of “selection” or “reference.” However, it might be worth mentioning that the program of writing a strictly historicist account of the history of science is challenged by various authors.148 For Mayr, it is not only legitimate but necessary to compare the present situation with the past. “Whiggish” is only the evaluation of an author in terms of our time.149I cannot discuss the Whit/anti-Whig controversy in any detail here, apart from saying that Mayr has defended himself rather extensively against the charges of being Whiggish.150 Nevertheless, it may be useful to touch on some of the criticisms that are predominant in reviews of his writings. First, we encounter the notion that historians can write a true and convincing historical account only if they have no personal interest or interpretation of their own; Mayr, on the other hand, because he “has such strong interpretations of his own, ... cannot possibly convince everyone that he is right about everything.”151 It makes one wonder, what historian has ever been able to convince everyone that he or she is right about everything? But apart from this peculiar idea, it unquestionably poses certain dangers if the subject matter of historical scrutiny and the author are identical. At the same time, this identity brings certain advantages with it, especially firsthand experiences of the period in discussion. Whether these personal memories ultimately result in a distorted picture of the past has to be decided in every particular instance. The notion that a scientific study can be conducted by a completely detached observer from a neutral standpoint has been shown to be impossible in physics, and it is also an illusion in historiography. The question is not whether, but which kind of interest are the underlying motivation for a historian. At this point, Mayr is ahead of his critics when he suggests that our understanding of the past always has a subjective component: The main reason, however, why histories are in constant need of revision is that at any given time they merely reflect the present state of understanding; they depend on how the author interpreted the current zeitgeist of biology and on his own conceptual framework and background. Thus, by necessity the writing of history is subjective and ephemeral.152Second, the temporal proximity between the event and the historical analysis makes difficulties inevitable and will finally result in certain false assessments. But this applies to all historians when they discuss recent problems, regardless of whether they are personally involved or not: As long as the battle between Darwinism and Lamarckism was raging, it was quite impossible to undertake an unbiased evaluation of Lamarck. ...[The] definite refutation of Lamarck's theory of evolutionary causation clears the air. We can now study him without bias and emotion and give him the attention that this major figure in the history of biology clearly deserves.153Third, Mayr is primarily interested in biological problems and not, for instance, historiographical, sociological, or psychological questions. Several authors have remarked that since the beginning of the professionalization of the history of science in the 1960s, a rift between two groups has developed, resulting from the heterogeneous professional backgrounds and interests of the people involved: the authors who were originally biologists and became interested in the history of their discipline only later on, and the authors who were trained as historians.154 Whereas the first group, the “biologists,” tend to be laymen in history proper, the “historians” are in most cases laymen in biology. Different professional backgrounds obviously shape the historical perspective in both groups, but neither approach is necessarily superior. The great number of important books in the history of biology written by “biologist” documents how valuable this point of view can be. On the other hand, it cannot be denied that the writings of biologists in the history of science tend to have a strong “internalist” tendency and often neglect the professional, cultural, and political context of science. Mayr's approach is that of a “biologist”; it is “internalist,” and typical for scientists who turn to the history of their discipline.I want to conclude my analysis with a quotation from a review by Douglas J. Futuyma, which gives a perceptive glimpse of Mayr's personality and style: One cannot help standing in awe of the germanic capacity for vast, allembracing synthesis: consider the lifelong devotion of Goethe to Faust, or Wagner's integration of the arts into a Gesamtkunstwerk in which all of human history and experience is wrought into epic myth. It is perhaps in this tradition that Ernst Mayr's The Growth of Biological Thought stands: a history of all of biology, a Ring des Nibelungen complete with leitmotivs such as the failures of reductionism, the struggle of biology for independence from physics, and the liberation of population thinking from the bounds of essentialism.155 Within this style of thinking Mayr has “to offer...nothing less than a vision of biology that places neodarwinian evolutionary theory firmly at the centre.”156 There may be other visions of biology, but few of them have as indefatigable and able representatives as Darwinism has in Ernst Mayr. (shrink)
Consider sentences like (1): 1. Null Complement Containing Sentences a. Aryn followed b. Marie-Odile promised c. Corinne left d. Samir found out at midnight e. I applied f. They already know g. He volunteered h. Abdiwahid insisted i. I suppose j. Paul gave to Amnesty International These illustrate the phenomenon of null complements -- also called ‘pragmatically controlled zero anaphora’, ‘understood arguments’, and ‘linguistically unrealized arguments’. In each case, a complement is (phonologically) omitted, yet (a) the sentence is well-formed and (...) (b) the meaning effect is as if a complement were present. This contrasts on the one hand with structures that lack complements, but are ill-formed as a result – e.g., (2a-c) – and, on the other hand, with structures that lack overt complements, are well-formed, but do not exhibit the meaning effect of a complement – e.g., sentences (3a-b). 2. Contrast with Ill-formed Structures.. (shrink)
In recent years, the question of national styles in science has received increasing attention. The different forms of Darwinism that emerged in the nineteenth century provide an impressive example of the role of non-scientific factors in the development of scientific ideas. Although the reception of Darwinian theory has been acknowledged to differ according to distinct national traditions even in Darwin's time, there have been few systematic efforts to understand the underlying causal factors. Usually these explanations have conceived of the relationship (...) of science to its social and political context as a distortion of science by ideology. In contrast to this picture, I attempt to demonstrate here how a scientific research program was situated in a concrete historical context. The German tradition of Darwinism in the nineteenth century will be described as a coalition of political liberalism, materialism, and morphology. Whereas the liberals used Darwinism to give their anti-religious and progressive program a naturalistic foundation, the morphologists appreciated that Darwinian theory allowed them to dispense with the idealistic origins of their research program, and the materialists were provided with a naturalistic explanation of the origin of organic form. (shrink)
The Synthetic Theory of Evolution (SyntheticDarwinism) was forged between 1925 and 1950.Several historians of science have pointed outthat this synthesis was a joint venture ofSoviet, German, American and Britishbiologists: A fascinating example of scientificcooperation, considering the fact that theevolutionary synthesis emerged during thedecades in which these countries were engagedin fierce political, military and ideologicalconflicts. The ideological background of itsAnglo-American representatives has beenanalyzed in the literature. We have examinedthe scientific work and ideological commitmentsof the German Darwinians during the ThirdReich. We based (...) our analysis on four criteria:1) General attitude towards the Third Reich. 2) Membership in the NSDAP and other nationalsocialist organizations. Endorsement anddisapproval of the state ideology in 3) scientific and 4) other publications. We willmainly discuss the various authors that havecontributed to Die Evolution derOrganismen (1943), a collection thatrepresented the evolutionary synthesis inGermany. Most of the authors promoted eugenicideas, but not all of them adopted the racistinterpretation of the Third Reich. Anotherfinding is that there existed no directconnection between party membership andpromotion of the state ideology. (shrink)
We study finitely generated free Heyting algebras from a topological and from a model theoretic point of view. We review Bellissima’s representation of the finitely generated free Heyting algebra; we prove that it yields an embedding in the profinite completion, which is also the completion with respect to a naturally defined metric. We give an algebraic interpretation of the Kripke model used by Bellissima as the principal ideal spectrum and show it to be first order interpretable in the Heyting algebra, (...) from which several model theoretic and algebraic properties are derived. In particular, we prove that a free finitely generated Heyting algebra has only one set of free generators, which is definable in it. As a consequence its automorphism group is the permutation group over its generators. (shrink)
We revisit via a path-integral approach the magnetic top proposed recently by Barut, Božić, and Marić. We point out that the magnetic top has the SU(2) symmetry and that it can be viewed as a free top seen from a rotating frame. We present an alternative path-integral quantization of the magnetic top on the basis of the symmetry, and show that the magnetic coupling does not participate in altering the spin quantum numbers.
p. 13: But if Mayr himself was an unconscious 'physicalist', why did he argue so forcefully against the machine theory of life? In part his dissatisfaction with this approach can be explained as a residue of earlier experiences. When he started to argue for the autonomy of biology in the early 1960s, the unique, emergent characteristics of organisms were ignored by the philosophy of science which was dominated by physics (Greene 1994; Hull 1994). In this situation Mayr not only criticised (...) this particular neglect as reductionism, but questioned the usefulness of the physicalist approach for biology in general. In recent decades this situation has clearly changed and this was also due to Mayr's relentless fight for the recognition of the unique aspects of biology. Nevertheless he stuck to his broad rejection and ignored developments toward a more sophisticated view (cf. Emmeche, Koppe and Stjernfelt 1997). But there is probably more to it. His second motivation is an emotional aversion against connotations and implications of the word 'machine'. The view that organisms-including humans!-are 'survival machines', 'robot vehicles' programmed to preserve their genes conveys a deterministic and mechanistic view that is perceived by many persons as a gross 'narcissistic insult' (Freud 1917, pp. 6, 7). It is a view that Mayr definitely did not appreciate. (shrink)
We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies. The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.
The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bohm problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. “Everything that is made beautiful and fair and lovely is made (...) for the eye of one who sees.” Jelaluddin Rumi,Mathnawi [I, 2383]. (shrink)
We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields and henselian valued fields of characteristic 0.