The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern. Indeed, nothing quite like it exists in biology or physics, or any other branch of science, for that matter. One sees periodic tables everywhere: in industrial labs, workshops, academic labs, and of course, lecture halls. -/- It is sometimes said that chemistry has no deep ideas, unlike physics, which can boast quantum mechanics (...) and relativity, and biology, which has produced the theory of evolution. This view is mistaken, however, since there are in fact two big ideas in chemistry. They are chemical periodicity and chemical bonding, and they are deeply interconnected. The observation that certain elements prefer to combine with speciﬁc kinds of elements prompted early chemists to classify the elements in tables of chemical afﬁnity. Later these tables would lead, somewhat indirectly, to the discovery of the periodic system, perhaps the biggest idea in the whole of chemistry. Indeed, periodic tables arose partly through the attempts by Dimitri Mendeleev and numerous others to make sense of the way in which particular elements enter into chemical bonding. (shrink)
The periodic table may be seen as the most successful example of inquiry in the history of science, both in terms of practical application and theoretic understanding. As such, it serves as a model for truth as it emerges from inquiry. This paper offers a sketch of a central moment in the history of chemistry that illustrates an intuitive metamathematical construction, a model of emerging truth. The MET, reflecting the structure the surrounds the periodic table, attempts to capture the salient (...) epistemological elements that warrant truth claims based on sets of models that are progressive in light of both empirical and theoretical advance seen over time. (shrink)
In this essay I intend to flesh out and discuss what I consider to be the groundbreaking contribution by the German historian and theorist of history Reinhart Koselleck to postwar historiography: his theory of historical times. I begin by discussing the view, so prominent in the Anglophone context, that Koselleck's idea of the plurality of historical times can be grasped only in terms of a plurality of historical periods in chronological succession, and hence, that Koselleck's theory of historical times is (...) in reality a theory of periodization. Against this interpretation, to be found in works by Kathleen Davis, Peter Osborne, and Lynn Hunt, among others, I will argue that not only is Koselleck's theory of historical times, or, with a more phenomenlogical turn of phrase, his theory of multiple temporalities, not a theory of periodization, it is, furthermore, a theory developed to defy periodization. Hence, at the core of Koselleck's work is the attempt to replace the idea of linear, homogeneous time with a more complex, heterogeneous, and multilayered notion of temporality. In this essay I will demonstrate how this shift is achieved by means of three dichotomies: between natural and historical, extralinguistic and intralinguistic, and diachronic and synchronic time. (shrink)
The basis of the Periodic Table is discussed. Electronic configuration recurs in only 21 out of the 32 groups. A better basis is derived by considering the highest classical valency (v) exhibited by an element and a new measure, the highest valency in carbonyl compounds (v*). This leads to a table based on the number of outer electrons possessed by an atom (N) and the number of electrons required for it to achieve an inert (noble) gas configuration (N*). Periodicity (...) of these is nearly complete. The new basis helps to settle the question of the best form of table and related issues. (shrink)
The early Periodic Tables displayed an 8-Group system. Though we now use an 18-Group array, the old versions were based on evidence of similarities between what we now label as Group (n) and the corresponding Group (n + 10). As part of a series on patterns in the Periodic Table, in this contribution, these similarities are explored for the first time in a systematic manner. Pourbaix (Eh–pH) diagrams have been found particularly useful in this context.
Analyzing and modeling interconnections between crucial factors of human development, rates of growth thereof and elasticity of the growth rates, the authors have defined specific periods of the development and have made a forecast for the dynamics of the human resources development. Those periods have been defined more exactly and arranged as follows: the first one – «Before Christ»; the second one – «Early Medieval» (1–1100 a.d.); the third one – «Advanced Medieval» (1101–1625); the forth one – «Pioneer’s Modernization» (1626–1970); (...) the fifth one – «Industrialization» (1871–2030) and the sixth one – «Informational society» – after 2030. The results received enable to make forecasts of the global factors dynamics, to find out unified solutions in socio-economic sphere, to define tendencies in social development and to build up unified strategic approaches for modeling global influence on human resources. (shrink)
In this paper, with the aid of symbolic computation, several kinds of exact solutions including periodic waves, cross-kink waves, and breather are proposed by using a trilinear form for the -dimensional Sharmo–Tasso–Olver equation. Then, by combing the different forms, the interactions between a lump and one-kink soliton and between a lump and periodic waves are generated. Moreover, the dynamic characteristics of interaction solutions are analyzed graphically by selecting suitable parameters with the help of Maple.
Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase of regression the entire knowledge (...) about the systematic application and the history of euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with lange. The third period of expansion started around 1760 with the works of Ploucquet, euler and lambert. Finally, it is shown that euler-type diagrams became popular in the debate about intuition which took place in the 1790s between leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800. (shrink)
According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for any finitely many numbers greater than 1, (...) if any of them is not divisible by any other, we can construct a Boolean paradox whose primary revision periods are just these numbers. Consequently, the degrees of Boolean paradoxes form an unbounded dense lattice. The area of Boolean paradoxes is proved to be rich in mathematical structures and properties. (shrink)
The modern history of verisimilitude can be divided into three periods. The first began in 1960, when Karl Popper proposed his qualitative definition of what it is for one theory to be more truthlike than another theory, and lasted until 1974, when David Miller and Pavel Trich published their refutation of Popper's definition. The second period started immediately with the attempt to explicate truthlikeness by means of relations of similarity or resemblance between states of affairs (or their linguistic representations); the (...) work within this similarity approach was summarized in the books of Graham Oddie  and Ilkka Niiniluoto . During the subsequent third period, studies in verisimilitude have been actively continued, and interesting results and applications have been achieved, but not many dramatic novelties. While it is now obsolete to claim that truthlikeness with reasonable properties cannot be defined at all, there is still a lot of controversy about the best and least arbitrary approach to doing this. (shrink)
Revision sequences were introduced in 1982 by Herzberger and Gupta as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the (...) way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. (shrink)
The psychoanalytical case history was in many ways the pivot point of John Forrester’s reflections on case-based reasoning. Yet the Freudian case is not without its own textual forebears. This article closely analyses texts from two earlier case-writing traditions in order to elucidate some of the negotiations by which the case history as a textual form came to articulate the mode of reasoning that we now call ‘thinking in cases’. It reads Eugène Azam’s 1876 observation of Félida X and her (...) ‘double personality’—the case that brought both Azam and Félida to prominence in late 19th-century French science—against a medico-surgical case penned by the Bordeaux physician in the same decade. While the stylistics of Azam’s medical case mirror its epistemic underpinnings in the ‘vertical’ logics of positivist science, the multiple narratives interwoven in Félida’s case grant both Azam and his patient the role of knowledge-making actors in the text. This narrative transformation chimes with the way Azam reasons ‘horizontally’ from particulars to Félida’s singular condition, but sits in tension with his choice to structure the observation along a ‘vertical’ axis. Between the two, we glimpse the emergence of the psychological observation as a mode of writing and thus of thinking in cases. (shrink)
This paper puts forward a class of ratio-dependent Leslie predator-prey models. Firstly, a neutral delay predator-prey model with ratio dependence and impulse control is established and the existence of positive periodic solutions is proved by the coincidence degree theory. Secondly, a stochastic disturbance Leslie model of Smith growth is obtained when the interference of white noise is taken into consideration and the impact of delay is ignored. Applying Ito^’s formula, we get the conditions of system persistence and extinction. Finally we (...) verify the correctness of theoretical analysis with numerical simulations. (shrink)
The debate about the relative epistemic weights carried in favour of a theory by predictions of new phenomena as opposed to accommodations of already known phenomena has a long history. We readdress the issue through a detailed re-examination of a particular historical case that has often been discussed in connection with it—that of Mendeleev and the prediction by his periodic law of the three ‘new’ elements, gallium, scandium and germanium. We find little support for the standard story that these predictive (...) successes were outstandingly important in the success of Mendeleev's scheme. Accommodations played an equal role—notably that of argon, the first of the ‘noble gases’ to be discovered; and the methodological situation in this chemical example turns out to be in interesting ways different from that in other cases—invariably from physics—that have been discussed in this connection. The historical episode when accurately analysed provides support for a different account of the relative weight of prediction and accommodation—one that is further articulated here. (shrink)
We study the formalization within sybsystems of second-order arithmetic of theorems concerning periodic points in dynamical systems on the real line. We show that Sharkovsky's theorem is provable in WKL0. We show that, with an additional assumption, Sharkovsky's theorem is provable in RCA0. We show that the existence for all n of n-fold iterates of continuous mappings of the closed unit interval into itself is equivalent to the disjunction of Σ02 induction and weak König's lemma.
The periodic table represents and organizes all known chemical elements on the basis of their properties. While the importance of this table in chemistry is uncontroversial, the role that it plays in scientific reasoning remains heavily disputed. Many philosophers deny the explanatory role of the table and insist that it is “merely” classificatory The structure of scientific theories, University of Illinois Press, Illinois, 1977; Scerri in Erkenntnis 47:229–243, 1997). In particular, it has been claimed that the table does not figure (...) in causal explanation because it “does not reveal causal structure”. This paper provides an analysis of what it means to say that a scientific figure reveals causal structure and it argues that the modern periodic table does just this. It also clarifies why these “merely” classificatory claims have seemed so compelling–this is because these claims often focus on the earliest periodic tables, which lack the causal structure present in modern versions. (shrink)
Periodization is rooted in historical theory. It reflects our priorities, our values, and our understanding of the forces of continuity and change. Yet periodization is also subject to practical constraints. For pedagogical reasons, world historians must seek reasonable symmetry between major historical eras despite huge discrepancies in the availability of historical data for separate time periods and for different areas of the world.Political issues arise in periodization. Should world history provide integrated treatment of the evolution of civilization, focusing upon the (...) most developed societies ? Or should it provide equal time to cultures outside the evolutionary mainstream ? If integration is to be preferred--as this article advocates--it is incumbent upon integrationists to provide some overarching theory of change to demonstrate how the destinies of the world's peoples have been linked through the millennia.Although the article attempts to demonstrate how comprehensive theories of change can facilitate the formulation of world history periodization, it does not minimize the difficulty of developing a universally operative organic theory of change. It examines several theoretical orientations, but principal attention is given to world-systems analysis, the most fully refined and well articulated body of theory currently commended as a vehicle for structuring world history.Acknowledging that no body of theory currently achieves a satisfactory universal integration of world history and that this situation may prevail in the future, the author recommends, for the present, an eclectic periodization of four epochs divided at roughly 1000 B.C.E., 400-600 C.E., and circa. 1492. (shrink)
Although the periodic system of elements is central to the study of chemistry and has been influential in the development of quantum theory and quantum mechanics, its study has been largely neglected in philosophy of science. The present article is a detailed criticism of one notable exception, an attempt by Hettema and Kuipers to axiomatize the periodic table and to discuss the reduction of chemistry in this context.
There is no doubt that periodization is a rather effective method of data ordering and analysis, but it deals with exceptionally complex types of processual and temporal phenomena and thus it simplifies historical reality. Many scholars emphasize the great importance of periodization for the study of history. In fact, any periodization suffers from one-sidedness and certain deviations from reality. However, the number and significance of such deviations can be radically diminished as the effectiveness of periodization is directly connected with its (...) author's understanding of the rules and peculiarities of this methodological procedure. In this paper we would like to suggest a model of periodization of history based on our theory of historical process. We shall also demonstrate some possibilities of mathematical modeling for the problems concerning the macroperiodization of the world historical process. This analysis identifies a number of cycles within this process and suggests its generally hyperexponential shape, which makes it possible to propose a number of forecasts concerning the forthcoming decades. (shrink)
In the same way that it is possible - by a loosely specified class of more or less well accepted statements - to know the referent of an ordinary proper name, we can understand a name like "the Renaissance." But names of events and periods have an indeterminacy not shared by names of men; with holistic names, the criteria of identity for the kind of thing are fluid, while the analogous criteria for being a man are not. Despite this indeterminacy, (...) the conceptualization of events and periods is useful in historical inquiry, where general statements about events, periods, and institutions can be reconciled with statements about particular facts, and with the evidence. Holistic terms cannot reasonably be prohibited on philosophical grounds; their legitimate use is a problem historians must judge case by case. (shrink)
The aim of this paper is to indicate the systematic place of arguments based on the concept of analogy within the theoretical framework of the Periodic Table of Arguments, a new method for describing and classifying arguments that integrates traditional dialectical accounts of arguments and fallacies and rhetorical accounts of the means of persuasion into a comprehensive framework. The paper begins with an inventory of existing approaches to arguments based on analogy, similarity and adjacent concepts. Then, the theoretical framework of (...) the table will be expounded and several concrete examples of arguments based on these concepts will be analyzed in terms of the framework. Finally, the results of these analyses will be summarized and it will be indicated how they can be refined in further research related to the Periodic Table of Arguments. (shrink)
It is proposed here that there is a sensitive period in the first two to three years of life during which humans acquire a basic knowledge of what foods are safe to eat. In support of this, it is shown that willingness to eat a wide variety of foods is greatest between the ages of one and two years, and then declines to low levels by age four. These data also show that children who are introduced to solids unusually late (...) have a narrower diet breadth throughout childhood, perhaps because the duration of the sensitive period has been shortened. By reducing the costs associated with learning, a sensitive period for food learning should be adaptive for any omnivore (including early humans) that remains in the same environment throughout its life. (shrink)
A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek (...) et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)
In a lengthy article E. Scerri and J. Worrall put forward the case for a novel ‘accommodationist’ version of the events surrounding the development of Mendeleef's Periodic Table 1869–1899. However these authors lay undue stress on the fact that President of the Royal Society of London Spottiswoode made absolutely no mention of Mendeleef's famous predictions in the Davy Medal eulogy in 1883 and undue stress on the fact that Cleve's classic 1879 Scandium paper contained an acknowledgement of Mendeleef's prior prediction (...) of eka-boron.They also fail to analyse in any detail the so-called ‘rare earth problem’ which, in the opinion of this author, causes problems for their account but not for a predictivist account. (shrink)
Diagonal relationships in the periodic table were recognized by both Mendeléev and Newlands. More appropriately called isodiagonal relationships, the same three examples of lithium with magnesium, beryllium with aluminum, and boron with silicon, are commonly cited. Here, these three pairs of elements are discussed in detail, together with evidence of isodiagonal linkages elsewhere in the periodic table. General criteria for defining isodiagonality are proposed.
Whether man is predisposed to lethal violence, ranging from homicide to warfare, and how that may have impacted human evolution, are among the most controversial topics of debate on human evolution. Although recent studies on the evolution of warfare have been based on various archaeological and ethnographic data, they have reported mixed results: it is unclear whether or not warfare among prehistoric hunter – gatherers was common enough to be a component of human nature and a selective pressure for the (...) evolution of human behaviour. This paper reports the mortality attributable to violence, and the spatio-temporal pattern of violence thus shown among ancient hunter–gatherers using skeletal evidence in prehistoric Japan (the Jomon period: 13000 cal BC–800 cal BC). Our results suggest that the mortality due to violence was low and spatio-temporally highly restricted in the Jomon period, which implies that violence including warfare in prehistoric Japan was not common. (shrink)
In recent years, philosophical ideas developed during the Wei-Jin period, broadly referred to as xuanxue in Chinese and ‘Neo-Daoism’ or ‘Dark Learning’ in English, have been accorded increasing attention in academia. This article provides an introduction to some major thinkers of the Wei-Jin period, addressing both their original writings and recent scholarly interpretations. The article aims to demonstrate that many Wei-Jin period intellectuals formed their theories through reinterpreting the relationship between texts associated with Daoism and Confucianism. Thinkers of this period (...) often attempted to show how these defining ‘schools’ of pre-Qin Chinese thought did not propose theories that were fundamentally inconsistent, and that their ideas could be woven together as elements of a coherent view. This intellectual movement can thus be, and often has been, viewed as an attempt to integrate Daoism and Confucianism. However, a more nuanced reading demonstrates that these thinkers were reworking the relationship between what were seen as predominately Daoist or Confucian themes from their very foundation. Accordingly, the common description of Wei-Jin thinkers as ‘Daoist’ is decidedly incongruous. (shrink)
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