bluuebunny/crossref_metadata_2025 huggingface dataset:
Realism in the philosophy of mathematics
Authors: Blanchette Patricia A.
Published: September 2018

Mathematical realism is the view that the truths of mathematics are objective, which is to say that they are true independently of any human activities, beliefs or capacities. As the realist sees it, mathematics is the study of a body of necessary and unchanging facts, which it is the mathematician’s task to discover, not to create. These form the subject matter of mathematical discourse: a mathematical statement is true just in case it accurately describes the mathematical facts.

An important form of mathematical realism is mathematical Platonism, the view that mathematics is about a collection of independently existing mathematical objects. Platonism is to be distinguished from the more general thesis of realism, since the objectivity of mathematical truth does not, at least not obviously, require the existence of distinctively mathematical objects.

Realism is in a fairly clear sense the ‘natural’ position in the philosophy of mathematics, since ordinary mathematical statements make no explicit reference to human activities, beliefs or capacities. Because of the naturalness of mathematical realism, reasons for embracing antirealism typically stem from perceived problems with realism. These potential problems concern our knowledge of mathematical truth, and the connection between mathematical truth and practice. The antirealist argues that the kinds of objective facts posited by the realist would be inaccessible to us, and would bear no clear relation to the procedures we have for determining the truth of mathematical statements. If this is right, then realism implies that mathematical knowledge is inexplicable. The challenge to the realist is to show that the objectivity of mathematical facts does not conflict with our knowledge of them, and to show in particular how our ordinary proof-procedures can inform us about these facts.
Geometry, philosophical issues in
Authors: Ryckman T.A.
Published: September 2018

The least abstract form of mathematics, geometry has, from the earliest Hellenic times, been accorded a curious position straddling empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of land surveying and measuring, from the prominence of visual aids (figures and constructions) in geometric proofs and, in the twentieth century, from Einstein’s General Theory of Relativity, which holds that the geometry of spacetime is dependent upon physical quantities. On the other hand, very early on, the symmetry and perfect regularity of certain geometric figures were taken as representative of a higher knowledge than that afforded by sense experience. And its concern with figures and constructions, rather than with number and calculation, rendered geometry amenable to axiomatic formulation and syllogistic deduction, establishing a paradigm of demonstrative knowledge which endured for two millennia. While the progress of mathematics has surmounted traditional distinctions between geometry and the mathematics of number, leaving only a heuristic role for geometric intuition, geometric thinking remains a vital component of mathematical cognition.
Analysis, nonstandard
Authors: Machover Moshe
Published: September 2018

Nonstandard analysis is an important application of mathematical logic to the rest of mathematics. Invented in 1960, it provided a long-sought-for rigorous justification for the use of infinitely large and infinitely small (infinitesimal) quantities in the differential and integral calculus, and the first sound canon for manipulating such quantities.

Consider the structure ℜ of real numbers, that is, the set of real numbers together with operations and relations on them. We specify a formal language L, which has names for all individual real numbers as well as for the operations and relations of ℜ. We can then obtain an enlargement (a special kind of extension) *ℜ (‘pseudo-ℜ‘) of ℜ such that *ℜ and ℜ have exactly the same formal properties: that is, properties expressible in L. But, far from being merely a copy of ℜ, *ℜ has convenient properties not expressible in L, which are not shared by ℜ. In particular, *ℜ has additional ‘nonstandard’ objects (which have no names in L), some of which behave as infinite or infinitesimal quantities. If, using these novel objects and properties of *ℜ, we prove a proposition about *ℜ that can be expressed in L, then this proposition holds automatically also for ℜ. Such ‘nonstandard’ proofs of results about ℜ are often easier and more intuitive than conventional proofs, which operate wholly within ℜ.

More generally, this method is applied to other structures, in virtually every branch of mathematics – including algebraic number theory, various branches of classical and modern analysis, probability theory and mathematical physics, to yield highly intuitive characterizations of various infinitary concepts, to simplify proofs and to provide new, efficient ways of generating mathematical constructs.
Dedekind, Julius Wilhelm Richard (1831–1916)
Authors: Stein Howard
Published: September 2018

Dedekind is known chiefly, among philosophers, for contributions to the foundations of the arithmetic of the real and the natural numbers. These made available for the first time a systematic and explicit way, starting from very general notions (which Dedekind himself regarded as belonging to logic), to ground the differential and integral calculus without appeal to geometric ‘intuition’. This work also forms a pioneering contribution to set theory (further advanced in Dedekind’s correspondence with Georg Cantor) and to the general notion of a ‘mathematical structure’.

Dedekind’s foundational work had a close connection with his advancement of substantive mathematical knowledge, particularly in the theories of algebraic numbers and algebraic functions. His achievements in these fields make him one of the greatest mathematicians of the nineteenth century.
Category theory, introduction to
Authors: McLarty Colin
Published: September 2018

A ‘category’, in the mathematical sense, is a universe of structures and transformations. Category theory treats such a universe simply in terms of the network of transformations. For example, categorical set theory deals with the universe of sets and functions without saying what is in any set, or what any function ‘does to’ anything in its domain; it only talks about the patterns of functions that occur between sets.

This stress on patterns of functions originally served to clarify certain working techniques in topology. Grothendieck extended those techniques to number theory, in part by defining a kind of category which could itself represent a space. He called such a category a ‘topos’. It turned out that a topos could also be seen as a category rich enough to do all the usual constructions of set-theoretic mathematics, but that may get very different results from standard set theory.
Polish logic
Authors: Zygmunt Jan
Published: September 2018

The term ‘Polish logic’ was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent.

Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski’s systems, Łukasiewicz’s many-valued logics, Tarski’s theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.
Forcing
Authors: Burgess John P.
Published: September 2018

The method of forcing was introduced by Paul J. Cohen in order to prove the independence of the axiom of choice (AC) from the basic (ZF) axioms of set theory, and of the continuum hypothesis (CH) from the accepted axioms (ZFC = ZF + AC) of set theory (see set theory, axiom of choice, continuum hypothesis). Given a model M of ZF and a certain P∈M, it produces a ‘generic’ G⊆P and a model N of ZF with M⊆N and G∈N. By suitably choosing P, N can be ‘forced’ to be or not be a model of various hypotheses, which are thus shown to be consistent with or independent of the axioms. This method of proving undecidability has been very widely applied. The method has also motivated the proposal of new so-called forcing axioms to decide what is otherwise undecidable, the most important being that called Martin’s axiom (MA).
Fuzzy logic
Authors: Morgan Charles G.
Published: September 2018

The term ‘fuzzy’ refers to concepts without precise borders. Membership in a ‘fuzzy’ set – the set of things to which a ‘fuzzy’ concept (fuzzily) applies – is to be thought of as being a matter of degree. Hence, in order to specify a fuzzy set, one must specify for every item in the universe the extent to which the item is a member of the set. The engineer Lotfi Zadeh developed a theory of fuzzy sets and advocated their use in many areas of engineering and science. Zadeh and his zealous followers have attempted to develop fuzzy systems theory, fuzzy algorithms and even fuzzy arithmetic. The phrase ‘fuzzy logic’ has come to be applied rather imprecisely to any analysis that is not strictly binary. It does not refer to any particular formal logic, in the sense in which the term ‘logic’ is used by philosophers and mathematicians. (‘Fuzzy logic’ is sometimes used anachronistically to refer to any many-valued logic.)
Church, Alonzo (1903–95)
Authors: Dolnik Peter
Published: September 2018

Alonzo Church was one of the twentieth century’s leading logicians. His work covers an extensive range of topics in logic and in other areas of mathematics. His most influential work relates to three areas: the general properties of functions, as presented in his ‘calculus of lambda conversion’; the theory of computability and the decision problem, to which he made fundamental contributions, known as Church’s thesis and Church’s theorem; and intensional logic, developing Frege’s theory of sense and denotation. In the last four decades of his life Church continued working mostly in this last area.
Zermelo, Ernst (1871–1953)
Authors: Peckhaus Volker
Published: September 2018

The German mathematician Ernst Zermelo is today best known for his axiomatization of set theory (1908b), presented in the spirit of Hilbert’s early axiomatic programme. Originally working in the calculus of variations and mathematical physics, Zermelo concentrated on set theory after proving that every set can be well-ordered (1904). His proof, based on the axiom of choice, provoked a lively controversy. In the 1930s Zermelo worked on infinitary logic, trying to overcome Gödel’s incompleteness results.
Fictionalism in the philosophy of mathematics
Authors: Colyvan Mark
Published: September 2018

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘∏ is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or antirealist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and moreover are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities; and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics).

Although fictionalism holds that mathematical statements implying the existence of mathematical entities are strictly speaking false, there is a sense in which these statements are true - they are true in the story of mathematics. The idea here is borrowed from literary fiction, where statements like ‘Bilbo Baggins is a hobbit’ is strictly speaking false (because there are no hobbits), but true in Tolkien’s fiction The Hobbit. Fictionalism about mathematics shares the virtue of ontological parsimony with other nominalist accounts of mathematics. It also lends itself to a very straightforward epistemology: there is nothing to know beyond the human-authored story of mathematics. And coming to know the various fictional claims requires nothing more than knowledge of the story in question. The most serious problem fictionalism faces is accounting for the applicability of mathematics. Mathematics, unlike Tolkien’s stories, is apparently indispensable to our best scientific theories and this, according to some, suggests that we ought to be realists about mathematical entities.

It is fair to say that there are serious difficulties facing all extant philosophies of mathematics, and fictionalism is no exception. Despite its problems fictionalism remains a popular option in virtue of a number of attractive features. In particular, it endorses a uniform semantics across mathematical and nonmathematical discourse and it provides a neat answer to questions about attaining mathematical knowledge. The major challenge for fictionalism is to provide an adequate account of mathematics in applications.
Naturalized philosophy of mathematics
Authors: Paseau Alexander
Published: September 2018

There are three types of naturalism in the philosophy of mathematics: metaphysical, epistemological and methodological. Metaphysical naturalists maintain that all entities are natural. One reading of this claim is that mathematical ontology is the ontology of natural science - which of course leads immediately to the question as to just what ontology is indispensably needed by the natural sciences. Another reading is that all mathematical entities are spatiotemporal. This view faces considerable difficulties, as it seems to go against the claims and methods of mathematics. Epistemological naturalists maintain that we can only know about entities spatiotemporally or causally connected to us. Though prima facie plausible, epistemological naturalism has encountered resistance on many fronts.

Methodological naturalism sees scientific standards, suitably understood, as authoritative. In its canonical version, science is construed as natural science, and thus the acceptability of mathematics is linked to its role in natural science. The most obvious argument for this form of methodological naturalism is the success argument: natural science is the most successful sphere of human inquiry and should consequently trump other disciplines. However, it turns out that the success argument is difficult to develop convincingly. Some philosophers also believe, controversially, that there is room for a naturalism that takes the authoritative standards in the philosophy of mathematics to be those of mathematics itself.
Amo, Anton Wilhelm (c.1703–56)
Authors: Wright John S.
Published: September 2018

The first European-trained African philosopher, Amo pursued a scholarly career in jurisprudence and then in rationalist psychology, logic, and metaphysics. He trained at Halle, Wittenberg and Jena universities, and was influenced by the systems of Gottfried Wilhelm Leibniz and Christian von Wolff. While at Halle university, he wrote a pioneering legal dissertation on the application of Roman laws of slavery to Africans in Europe. Subsequently drawn to classical, biblical, and hermetic traditions that apotheosized a cultural continuity with ancient Africa, Amo focused his theoretical and practical concerns on the exterior world of international law and the interior world of deliberative intellectual acts.
Aesthetics, African
Authors: Hallen Barry
Published: September 2018

The study and analysis of African art and aesthetics have been dominated by Western culture. Initially the aesthetic sensitivities of African cultures were characterized as ‘primitive’ and of low intellectual calibre. Africans reacted to such negative stereotyping by articulating their own, deliberately non-Western aesthetic theories. The best known of these is négritude.

With its emphasis on learning about a culture by living in it for a period of time, anthropology encouraged scholars to relate African art directly to the aesthetic values of the cultures that produced it. This kind of contextual approach has also become the special concern of African art historians.

One can exemplify the exploration of the aesthetic conceptions of a particular culture in this way by considering the case of the Yoruba peoples of southwestern Nigeria. The Yoruba have a detailed and refined aesthetic vocabulary that has been subjected to extended description and analysis. Where human beings are concerned the highest form of beauty is attributed to a person’s good moral character. Where objects are concerned beauty is influenced by their utility or, in the case of figurative carvings, by the intelligence and ability of the artist.
Ethnophilosophy, African
Authors: Karp Ivan , Masolo D.A.
Published: September 2018

Ethnophilosophy refers to bodies of belief and knowledge that have philosophical relevance and which can be redescribed in terms drawn from academic philosophy, but which have not been consciously formulated as philosophy by philosophers. These bodies of belief and knowledge are manifested in the thoughts and actions of people who share a common culture.

Most of the literature on ethnophilosophy is written about African cultures. Ethnophilosophy’s most immediate African antecedents include Leopold Senghor’s philosophy of négritude and the writings of the Belgian missionary to the Congo (later Zaire), Placide Tempels. Ethnophilosophy examines the systems of thought of existing and precolonial African communities in order to determine what can be the ideal forms of ‘authentic’ African philosophy and praxis in the emerging postcolonial situation. In addition to the pioneering work of Senghor and Tempels, this school is represented in the writings of philosopher Alexis Kagamé (1956) and theologian John Mbiti (1969) among others, many of whom were regarded as Tempels’s disciples.

The central themes of the work of these disciples include assertions that there is a unified ‘Bantu philosophy’ and that its fundamental categories are manifested in features of language such as grammar, or features of culture such as cosmology and ritual. According to many of these authors writing about Bantu philosophy, the boundaries between self and other are not as rigid as in Western philosophy. Also, interdependence rather than competition is a primary social value and the human and nonhuman world is animated by a ‘vital force’, which underlies the perception of reality.
Egyptian philosophy: influence on ancient Greek thought
Authors: Lefkowitz Mary R.
Published: September 2018

Before the decipherment of hieroglyphics (a process only completed in the 1830s), it was widely believed that many famous Greek philosophers had studied in Egypt and that Greek philosophy was ultimately derived from a lost ’Egyptian mystery system’. This belief was derived in part from ancient sources, which described how certain Greek philosophers had studied with Egyptian priests. The notion that these individual sessions were part of an extensive formal programme of education derives from an historical novel, Séthos (1731), by the Abbé Jean Terrasson. This book, which pretended to be based on lost original sources, offered a detailed portrait of a complex Egyptian university system. It was translated into several European languages and widely popularized in the rituals and mythology of Freemasonry.

The existence of such a formal Egyptian mystery system of education was not confirmed by actual Egyptian sources once they could be read and translated. The myth has been given a new lease of life in revisionist histories of the ancient world composed by writers whose ancestors had been brought to the New World as slaves. These writers sought to show that Greek philosophy was derived from Egyptian philosophy and that what has been recognized as Western civilization stems from Africa. This entry reviews the evidence for these claims and concludes that although the Greeks had great respect for Egyptian wisdom and piety, what has always been known as Greek philosophy derives from the original work of Greeks. It finds moreover that if the Greek philosophers who lived in Ionia were influenced by any outside ideas, these came to them through the monotheistic religions of other peoples living in the Near East.
Black nationalism
Authors: Shelby Tommie
Published: September 2018

The philosophical underpinnings of black nationalism date back to the mid-nineteenth century, prior to the abolition of chattel slavery in the United States. Its key ideas are that black people should possess their own nation-state; that the flourishing of African peoples (including those of African descent in the Western hemisphere) requires racial solidarity and group self-help; that geographical racial separation is necessary for racial harmony; that blacks should cultivate pride in the historic achievements of those of African descent; that the survival of the race depends on militant collective resistance to anti-black racism and white supremacy; that psychic health requires the development and preservation of a distinctive black ethno-cultural identity; and that Africa is the authentic and rightful homeland of those who are racially black, regardless of where they were born or currently reside.

In its broadest sense, black nationalism is the view that blacks constitute a distinct people or nation with their own collective aims, and that their wellbeing depends upon their ability to sustain political, economic and cultural solidarity. Central to all versions of black nationalism are the beliefs that the primary source of black oppression is racism, and that overcoming racial domination will require some form of group autonomy and self-reliance, perhaps even a separate black republic.
South Africa, philosophy in
Authors: Duvenage Pieter
Published: September 2018

Although it is incorrect to refer to an independent South African philosophical tradition, South Africa is nevertheless the location of an interesting history of philosophical institutionalization. This institutionalization is closely intertwined with the colonial and postcolonial history of Western expansion (Dutch and English) and the reactions it unleashed within the South African context. It is especially interesting to trace the influence and the application of Anglo-American and continental origins in South Africa. Even in contemporary South Africa, philosophers who are working in fields such as postmodernism, postcolonialism, feminism and analytical philosophy do so mostly under the influence of contexts beyond South Africa’s borders.

After the early Dutch influence in South Africa (1652–1806) a British colonial educational system emerged during the nineteenth century. From the first institutions of higher education (the South African College in Cape Town, and the University of the Cape of Good Hope) the first tertiary institutions emerged in the early part of the twentieth century at Cape Town, Stellenbosch, Witwatersrand (Johannesburg) and Pretoria. Although other universities were subsequently instituted, these four can be considered the four founding residential universities in South Africa. It is also at these universities (and at Colleges in Grahamstown, Bloemfontein, Durban and Pietermaritzburg) that British idealism had a major influence on the early stages of South African philosophy (1873–1940). Against this background figures such as Fremantle (Cape Town), Walker (Stellenbosch), Hoernlé (Johannesburg), Lord (Grahamstown) and Macfadyen (Pretoria) were instrumental.

From the 1930s the hegemony of British idealism was challenged by analytical philosophy (mainly at English-speaking South African universities) and continental traditions (mainly at Afrikaans-speaking universities). Since the political transformation of South Africa (1994) African philosophy has also emerged as a major philosophical tradition.

The challenge for philosophy in contemporary South Africa is to explore those intellectual traditions that have shaped philosophy in South Africa, to know where they are coming from and to understand how they were transformed under (post)colonial conditions. Such a (genealogical) perspective provides a historical and material corrective to arguments that might otherwise strive to reconcile cultural values and ideas in an apolitical and ahistorical manner.
Argentina, philosophy in
Authors: Estrada Juan Carlos Torchia
Published: September 2018

Philosophy has been present throughout Argentine cultural life since the beginning of Spanish colonization. Despite institutional ups and downs, the teaching of philosophy was a practically constant component of higher and even secondary education. The principal currents that shaped that teaching for more than three centuries were Scholasticism, French ideology, eclectic spiritualism, positivism and in the twentieth century, all of the contemporary manifestations, such as, Husserlian phenomenology, existentialism, analytical philosophy and structuralism. A permanent characteristic, nevertheless, has been that the political vicissitudes of the country affected educational institutions.

In the nineteenth century, during the period of national independence and organization, public figures used philosophical ideas to analyse the problems of society and to make the political and institutional contributions that a country in formation required. Juan Bautista Alberdi and Domingo Sarmiento are, in this respect, two representative examples.

In the twentieth century, the figure of the professional philosopher, one who is interested in philosophical research for itself, emerged and expanded. However, thought that reflected direct interest in the problems of the community and in the ethical demands of praxis did not disappear during this era. This can be seen in such thinkers as José Ingenieros and Alejandro Korn and more recently in what has been called liberation philosophy.

Academic philosophy has made considerable progress. In the second half of the twentieth century, it has attained a high level of professional quality. In some cases, even original contributions have been made which go beyond assimilation or commentary about external philosophical influences.

In Argentina, as in the rest of Latin America, philosophy began as a pure transplant brought by those who conquered the continent. Upon creating centres of higher education (either as part of the religious orders or with the character of universities), the philosophical teaching being practised in the Spanish universities of Salamanca and Alcalá was reproduced in the Spanish colonies.

Argentine philosophy shares the same general characteristics and historical periods with the philosophies developed in other Latin American countries. In general terms, philosophy can be divided into three periods: the colonial period, the nineteenth century, or national period and the twentieth century.
Brazil, philosophy in
Authors: Sturm Fred Gillette
Published: September 2018

It is possible to distinguish between European philosophy in Brazil and Brazilian philosophy. The former refers to Brazilians who participate in discussions of issues occurring in the European philosophic tradition without any reference to Brazilian reality and its problems; the latter to those Brazilian intellectuals who respond to the problems growing out of situations which have confronted the nation historically whether their philosophical orientations have originated in Europe or elsewhere. This entry focuses on the latter and generally follows a historical progression. This progression spans from the precabralian Tupi-Guarani speaking societies of eastern South America to the healthy development of Brazilian philosophy since 1950 after the founding of the Institute of Brazilian Philosophy.
Marxist thought in Latin America
Authors: Schutte Ofelia
Published: September 2018

Marxism is a theory offering a critique of capitalist political economy. Marxism also views itself as an instrument or means of changing the world from a capitalist to a socialist (and/or communist), economic and political order. Given its interest in economic and political change, Marxism involves a philosophy of history which depicts the possibility of and conditions for change from a capitalist to a socialist order. Marxist intellectuals perform the dual task of analysing the failures or limitations of capitalist economic and political structures. The theory also proposes and evaluates socialist alternatives.

Latin American Marxism developed out of its own historical, economic, political and cultural conditions. Influenced by Lenin’s analysis of imperialism as the highest stage of capitalism, it directed the critique of capitalist political economy towards the capitalist world market and its disadvantageous effects for the countries, particularly the impoverished classes and social sectors, of the Latin American and Caribbean regions. Latin American Marxism-Leninism argues, on political and economic grounds, that national liberation cannot be achieved without liberation from imperialism.

Marxists believe that although the protagonists of history’s political projects are the workers (or if Leninist, the workers together with the peasants), in the end the interests of these groups represent the universal interests of humankind. Marxist political discourse often uses broader categories than those of ’workers’ or ’peasants’ to designate the agents of political emancipation, employing terms such as ’the people’, ’the popular sectors’ or ’the revolutionary masses’. In this way Marxism attempts to broaden its political base so as to make its goals more effective. The political discourse of the Cuban Revolution of 1959 and the Nicaraguan Sandinista Revolution of 1979 exemplify this practice.

There are and have been many differences among Marxists because of the different approaches to criticizing capitalism as well as the different conceptions held by those who profess a commitment to the ultimate Marxist goal of creating a nonexploitative socialist society. Representative issues in Latin American Marxism may be illustrated by focusing on three questions: the problem of orthodoxy, the socialist construction of a national identity and socialism’s relation to ethics, religion and culture. In addressing these issues, this entry draws significantly from the work of Peruvian Marxist José Carlos Mariátegui, a prominent founder of Latin American Marxism.
Mexico, philosophy in
Authors: Cerutti-Guldberg Horacio
Published: September 2018

Philosophy has been practised in Mexico for centuries, beginning with Nahuatl thought. Such thinking was rediscovered through laborious translation of surviving fragments of a document of exceptional value known as ‘Coloquio de los Doce’ (Debate of the Twelve) (1524). Since then, philosophy has come to enjoy a high degree of professionalization and a high quality of academic production. Generally, Mexican philosophical activity has evolved in accordance with world standards of rigour, information and quality of argumentation. In the twentieth century various philosophical groups have been created, namely the Ateneo de la Juventud, the contemporáneos and the Hyperion group.

Leopoldo Zea understood the essence of the Mexican and the Latin American as a historical being with a historically situated consciousness. Zea’s history of ideas involved a philosophy of Latin American history which placed the being, destiny and meaning of the history of Mexico and Latin America in the context of the history of the world. The 1940s and 1950s were unusually productive to this end. In the 1970s small groupings of philosophers gathered to focus on problems, traditions, teaching figures, leaders and spheres of influence.

There has been considerable interest in political philosophy, philosophy of history, philosophy of science and ethics. Since the 1980s, works about the history of ideas in Mexico and the history of science and technology have proliferated.
Modelización de los modos propios de un recinto paralelepipédico con superficies rígidas mediante el método de elementos finitos
Authors: Tarrazó-Serrano Daniel , Castiñeira-Ibáñez Sergio , Uris Antonio , Rubio Michavila Constanza
Published: September 2018

El análisis del campo sonoro en un recinto está incluido en los contenidos que forman parte del temario de las asignaturas relacionadas con la acústica de recintos. Sin embargo, los alumnos a menudo encuentran dificultades con la comprensión y visualización espacial de los modos propios de vibración que tienen lugar en el interior del recinto. Por este motivo, el encontrar procedimientos que permitan mejorar la visualización ahondará en la comprensión y por tanto mejorará el aprendizaje de esta parte de la acústica. En este trabajo se propone el uso de la simulación mediante el Método de los Elementos Finitos para facilita el aprendizaje y comprensión del fenómeno de los modos de vibración y la distribución de presiones acústicas en el recinto. Para ello se simula un recinto paralelepipédico recto rectangular con superficies rígidas y se obtienen las distribuciones de presiones acústicas de los distintos modos de vibración tanto axiales como tangenciales y oblicuos.
Jugando con la Teoría de Grupos: rompecabezas, puzzles y otros entretenimientos matemáticos
Authors: Felipe María José , Ortiz Sotomayor Víctor Manuel
Published: September 2018

En el presente trabajo mostramos cómo modelizar y analizar la resolubilidad de
algunos puzzles, rompecabezas y juegos matemáticos, haciendo uso de conceptos básicos de la teoría de grupos y del sistema algebraico computacional GAP (Groups, Algorithms and Programming). Se trata de motivar al alumnado que se inicia en esta teoría algebraica y al mismo tiempo mostrar su aplicabilidad de una forma lúdica para aquellos estudiantes ya iniciados en este campo.
GlSch: Planificación de Observaciones en la red de Telescopios GLORIA
Authors: López Casado Carmen , Pérez del Pulgar Mancebo Carlos Jesús , Muñoz Martínez Víctor Fernando , Castro Tirado Alberto
Published: September 2018

Este artículo propone el diseño y desarrollo de un planificador para la red de telescopios GLORIA. Esta red, cuyo principal objetivo es acercar los ciudadanos a la astronomía, está formada por 18 telescopios ubicados en cuatro continentes. Parte de la gestión de esta red se lleva a cabo por el planificador, que se encarga de recibir peticiones de observación de usuarios de usuarios y enviárselas a uno de los telescopios de la red. Para esto, necesita un algoritmo que decida el mejor telescopio, evitando ofrecer una petición a un telescopio que finalmente no pueda ejecutarla. Este artículo presenta dos algoritmos de decisión: el primero se basa únicamente en la predicción meteorológica, y el segundo emplea lógica difusa e información de cada telescopio. Ambos algoritmos fueron implantados en la red GLORIA. Los resultados obtenidos, así como una comparativa del rendimiento de ambos se presenta en este artículo. Así mismo, se detalla la arquitectura del planificador basada en una estructura híbrida distribuida-centralizada.
Control del Convertidor CD/CD Reductor–Paralelo Implementado en FPGA
Authors: Guerrero Ramírez Esteban Osvaldo , Martínez Barbosa Alberto , Guzmán Ramírez Enrique , Linares Flores Jesús , Sira Ramírez Hebertt
Published: September 2018

El presente artículo documenta el diseño e implementación de un controlador robusto para el convertidor CD/CD Reductor–Paralelo, bajo la perspectiva de la planitud diferencial y la técnica del control por rechazo activo de perturbaciones basado en un observador GPI. Los objetivos principales del controlador propuesto son: regular la tensión de salida y equilibrar las corrientes de los convertidores en paralelo. Para el modelado de la arquitectura hardware de este controlador se utiliza una herramienta con alto nivel de abstracción de hardware y se implementa en un FPGA Artix–7 de la compañía Xilinx. Finalmente, se muestran resultados experimentales del desempeño del controlador, cuando se somete al convertidor a diversas perturbaciones externas, desconocidas y variantes con el tiempo, y a cambios en los parámetros del mismo.
The importance of comprehensive parameter sampling and multiple observations for robust constraint of aerosol radiative forcing
Authors: Johnson Jill S. , Regayre Leighton A. , Yoshioka Masaru , Pringle Kirsty J. , Lee Lindsay A. , Sexton David M. H. , Rostron John W. , Booth Ben B. B. , Carslaw Kenneth S.
Published: September 2018

Abstract. Observational constraint of simulated aerosol and cloud
properties is an essential part of building trustworthy climate models for
calculating aerosol radiative forcing. Models are usually tuned to achieve
good agreement with observations, but tuning produces just one of many
potential variants of a model, so the model uncertainty cannot be determined.
Here we estimate the uncertainty in aerosol effective radiative forcing (ERF)
in a tuned climate model by constraining 4 million variants of the
HadGEM3-UKCA aerosol–climate model to match nine common observations
(top-of-atmosphere shortwave flux, aerosol optical depth, PM2.5, cloud
condensation nuclei at 0.2 % supersaturation (CCN0.2), and
concentrations of sulfate, black carbon and organic carbon, as well as
decadal trends in aerosol optical depth and surface shortwave radiation.) The
model uncertainty is calculated by using a perturbed parameter ensemble that
samples 27 uncertainties in both the aerosol model and the physical climate
model, and we use synthetic observations generated from the model itself to
determine the potential of each observational type to constrain this
uncertainty. Focusing over Europe in July,
we show that the aerosol ERF uncertainty can be reduced by about 30 % by
constraining it to the nine observations, demonstrating that producing
climate models with an observationally plausible “base state” can
contribute to narrowing the uncertainty in aerosol ERF. However, the
uncertainty in the aerosol ERF after observational constraint is large
compared to the typical spread of a multi-model ensemble. Our results
therefore raise questions about whether the underlying multi-model
uncertainty would be larger if similar approaches as adopted here were
applied more widely. The approach presented in this study could be used to
identify the most effective observations for model constraint. It is hoped
that aerosol ERF uncertainty can be further reduced by introducing
process-related constraints; however, any such results will be robust only if
the enormous number of potential model variants is explored.
Beyond Craig and Gordon: A model of water vapor isotopologues in
the marine boundary layer
Authors: Feng Xiahong , Posmentier Eric S. , Sonder Leslie J. , Fan Naixin
Published: September 2018

Abstract. We develop a one-dimensional (1D) steady state isotope marine boundary layer (MBL) model that includes meteorologically important features missing in Craig and Gordon type models, namely height-dependent diffusion/mixing, lifting to deliver air to the free troposphere, and convergence of subsiding air. Kinetic isotopic fractionation results from this height-dependent diffusion that starts as pure molecular diffusion at the air-water interface and increases with height due to turbulent eddies. Convergence causes mixing of dry, isotopically depleted air with ambient air. Model results fill a quadrilateral in δD-δ18O space, of which three boundaries are respectively defined by 1) vapor in equilibrium with various sea surface temperatures (SSTs); 2) mixing of vapor in equilibrium with seawater and vapor in subsiding air; and 3) vapor that has experienced maximum possible kinetic fractionation. Model processes also cause variations in d-excess of MBL vapor. In particular, mixing of relatively high d-excess descending/converging air into the MBL increases d-excess, even without kinetic isotope fractionation. The model is tested by comparison with seven datasets of marine vapor isotopic ratios, with excellent correspondence. About 95 % of observational data fall within the quadrilateral predicted by the model. The distribution of observations also highlights the significant influence of vapor from nearby converging descending air on isotopic variations within the MBL. At least three factors may explain the ~ 5 % of observations that fall slightly outside of the predicted regions in δD-δ18O and d-excess-δ18O space: 1) variations in seawater isotopic ratios, 2) variations in isotopic composition of subsiding air, and 3) influence of sea spray.
Wintertime secondary organic aerosol formation in
Beijing-Tianjin-Hebei (BTH):
Contributions of HONO sources and heterogeneous reactions
Authors: Xing Li , Wu Jiarui , Elser Miriam , Tong Shengrui , Liu Suixin , Li Xia , Liu Lang , Cao Junji , Zhou Jiamao , El-Haddad Imad , Huang Rujin , Ge Maofa , Tie Xuexi , Prévôt André S. H. , Li Guohui
Published: September 2018

Abstract. Organic aerosol (OA) concentrations are simulated over the Beijing-Tianjin-Hebei (BTH) region from 9 to 26 January, 2014 using the Weather Research and Forecasting model coupled with chemistry (WRF-CHEM), with the goal of examining the impact of heterogeneous HONO sources on SOA formation and the SOA formation from different pathways during wintertime haze days. The model generally performs well in simulating air pollutants and organic aerosols against measurements in BTH. Model results show that heterogeneous HONO sources substantially enhance the near-surface SOA formation, increasing regional average near-surface SOA concentration by about 46.3 % during the episode. Oxidation and partitioning of primary organic aerosols treated as semi-volatile dominate the SOA formation, contributing 58.9 % of the near-surface SOA mass in BTH. Irreversible uptake of glyoxal and methylglyoxal on aerosol surfaces constitutes the second most important SOA formation pathway during the episode, with SOA contribution increasing from 8.5 % in non-haze conditions to 30.2 % in haze conditions. Additionally, direct emissions of glyoxal and methylglyoxal from residential living sources contribute about 25.5 % to the total SOA mass on average in BTH. Our study highlights the importance of heterogeneous HONO sources and primary residential emissions of glyoxal and methylglyoxal to SOA formation in winter over BTH.
The effect of hydrophobic glassy organic material on the cloud
condensation nuclei activity of internally mixed particles with
different particle morphologies
Authors: Tandon Ankit , Rothfuss Nicholas El , Petters Markus D.
Published: September 2018

Abstract. Particles composed of organic and inorganic components can assume core-shell morphologies. The kinetic limitation of water uptake due to the presence of a hydrophobic viscous outer shell may increase the critical supersaturation required to activate such particles into cloud droplets. Here we test this hypothesis through laboratory experiments. Results show that the viscosity of polyethylene particles is 5×106 Pa s at 60 °C. Extrapolation of temperature dependent viscosity measurements suggests that the particles are glassy at room temperature. Cloud condensation nuclei (CCN) activity measurements demonstrate that pure polyethylene particles are CCN inactive at diameters less than 741 nm and 2.5 % water supersaturation. Thus, polyethylene is used as proxy for hydrophobic glassy organic material. Ammonium sulfate is used as proxy for hygroscopic CCN active inorganic material. Mixed particles were generated using coagulation of oppositely charged particles; charge-neutral polyethylene-ammonium sulfate dimers were then isolated for online observation. Morphology of these dimers was varied by heating, such that liquefied polyethylene partially or completely engulfed the ammonium sulfate. Critical supersaturation was measured as a function of dry particle volume, particle morphology, and organic volume fraction. The data show that kinetic limitations do not change the critical supersaturation of 50 nm ammonium sulfate cores coated with polyethylene and polyethylene volume fractions up to 97 %. Based on these results, and a synthesis of literature data, it is concluded that mass transfer limitations by glassy organic shells are unlikely to affect cloud droplet activation near laboratory temperatures.
Combined effects of altered N:P stoichometry and trees on Mediterranean savanna root dynamics
Authors: Nair Richard , Hertel Martin , Luo Yunpeng , Moreno Gerardo , Reichstein Markus , Schrumpf Marion , Migliavacca Mirco
Published: September 2018

Abstract. Mediterranean grasslands are highly seasonal and co-limited by water and nutrients. In such systems little is known about root dynamics which may depend on plant habit and environment as well seasonal water shortages and site fertility. This latter factor is affected by the presence of scattered trees and site management including grazing, as well as chronic nitrogen deposition, which may lead to N:P imbalance. In this study we combined observations from minirhizotrons collected in a Mediterranean tree-grass ecosystem (Spanish Dehesa), with root measurements from direct soil cores and ingrowth cores, and above-ground biomass to investigate seasonal root dynamics and root:shoot ratios. We investigated responses to soil fertility, using a nutrient manipulation (N / NP additions) and microhabitats effects between open pasture and under tree canopy locations. Root dynamics over time were compared with indices of above-ground growth drawn from proximal remote sensing (Normalised Difference Vegetation Index and Green Chromatic Coordinate derived from near-infrared enabled digital repeat photography). Results show distinct differences in root dynamics and biomass between treatments and microhabitats. Root biomass was higher with N additions, but not with NP additions in early spring, but by the end of the growing season root biomass had increased with NP in open pastures but not higher than N alone. In contrast, root length density (RLD) in pastures responded stronger to the NP than N only treatment, while beneath trees RLD tended to be higher with only N. Even though root biomass increased, root:shoot ratio decreased under nutrient treatments.We interpret these differences as a shift in community structure and/or root traits under changing stoichiometry and altered nutrient limitations. The timing of maximum root cover, as assessed by the minirhizotrons, did not match with above-ground phenology indicators at the site as root growth was low during autumn despite the greening up of the ecosystem. In other periods, roots responded quickly to rain events on the scale of days, matching changes in above-ground indices. Our results highlight the need for high resolution sampling to increase understanding of root dynamics in such systems, linkage with shifts in community structure and traits, and targeting of appropriate periods of the year for in-depth campaigns.