bluuebunny/crossref_metadata_2025 huggingface dataset:
Plural logic
Authors: Oliver Alex , Smiley Timothy
Published: September 2018

Plural phenomena are significant and inescapable. Granted, the plural idiom is sometimes reducible to the singular, e.g. ‘2 and 3 are prime is equivalent to ‘2 is prime and 3 is prime’. ‘Are prime’, however, belongs to the special class of predicates known as distributives. No such reductions are possible for the general case of collective (nondistributive) predicates, and they are to be found everywhere, from the everyday (‘Whitehead and Russell wrote Principia Mathematica’) to the heart of logic itself (‘The axioms are consistent’, ‘Those premises imply this conclusion’). It is no good dismissing grammatical number as a logically irrelevant complication like person or gender, since plural expressions are crucially involved in valid patterns of argument. To take an elementary example, ‘The Brontë sisters supported one another; the Brontë sisters were Anne, Charlotte and Emily; so Anne, Charlotte and Emily supported one another’. There can be no warrant for ignoring such patterns while attending to their singular counterparts. And some arguments do not even have a singular counterpart. For example, ‘Some numbers are prime. So some numbers are such that they are prime and a number is prime only if it is one of them.’ Logicians wedded to the singular logic of the predicate calculus typically try to dodge the issue of plurals by invoking sets, but we shall see that this is untenable.

Socrates exploited the difference between distributive and collective predicates in Hippias Major, but little of interest happened subsequently until Russell put plurals at the centre of his project for providing a foundation for mathematics, through his idea of the ‘class as many’ in The Principles of Mathematics. After another fallow period, the subject revived in the 1970s and 80s with the work of Black, Morton, Sharvy, Simons and Boolos. It would be premature to attempt a comprehensive survey. This entry offers a nontechnical outline of plural predicate logic, including the major differences between it and singular logic and some matters still to be resolved.
Church’s thesis
Authors: Shapiro Stewart
Published: September 2018

An algorithm or mechanical procedure A is said to ‘compute’ a function f if, for any n in the domain of f, when given n as input, A eventually produces fn as output. A function is ‘computable’ if there is an algorithm that computes it. A set S is ‘decidable’ if there is an algorithm that decides membership in S: if, given any appropriate n as input, the algorithm would output ‘yes’ if n∈S, and ‘no’ if n∉S. The notions of ‘algorithm’, ‘computable’ and ‘decidable’ are informal (or pre-formal) in that they have meaning independently of, and prior to, attempts at rigorous formulation.

Church’s thesis, first proposed by Alonzo Church in a paper published in 1936, is the assertion that a function is computable if and only if it is recursive: ‘We now define the notion…of an effectively calculable function…by identifying it with the notion of a recursive function….’ Independently, Alan Turing argued that a function is computable if and only if there is a Turing machine that computes it; and he showed that a function is Turing-computable if and only if it is recursive.

Church’s thesis is widely accepted today. Since an algorithm can be ‘read off’ a recursive derivation, every recursive function is computable. Three types of ‘evidence’ have been cited for the converse. First, every algorithm that has been examined has been shown to compute a recursive function. Second, Turing, Church and others provided analyses of the moves available to a person following a mechanical procedure, arguing that everything can be simulated by a Turing machine, a recursive derivation, and so on. The third consideration is ‘confluence’. Several different characterizations, developed more or less independently, have been shown to be coextensive, suggesting that all of them are on target. The list includes recursiveness, Turing computability, Herbrand–Gödel derivability, λ-definability and Markov algorithm computability.
Lambda calculus
Authors: McCarty David Charles
Published: September 2018

The lambda calculus presents a delimited formal setting for expressing and studying properties of mathematical operations and computer programs. Its syntactical unit is the term. Application terms tu represent supplying argument u to routine t. Abstraction terms λx. t (in which λx binds x in t) represent the explicit definition of an operation from a routine t. Term computation is by reduction: (λx. t) (u) reduces to t[x/u], the result of substituting u for x in t; this corresponds to operating with t on u. Terms are equal either when they differ only in bound variables or when one converts to the other via a finite chain of reductions and counter-reductions. There are two main varieties of lambda calculi: typed and untyped (or type-free). Any untyped term is applicable to any other and equality between such terms is undecidable. In the typed case, terms are indexed by types and application is permitted only when types conform. Here, equality is decidable. A. Church proposed formalisms for both varieties during the 1930s. He and his students S. Kleene and J. Rosser proved the early syntactical metatheorems linking the untyped calculus with computability theory. In 1969, D. Scott gave the first set-theoretic construction of a functional model of the untyped calculus; since then, many other models have been devised. As for the typed calculus, Gödel’s Dialectica interpretation inspired many of its applications to proof theory. Also, the idea, due to H. Curry and W. Howard, of using logical formulas as types reveals a close correspondence between typed terms and derivations in intuitionistic formal systems. In the last decades of the twentieth century, the lambda calculus and its models have been put to many uses in computer science, with functional programming and denotational semantics deserving special mention.
Formal languages and systems
Authors: Herre Heinrich , Schroeder-Heister Peter
Published: September 2018

Formal languages and systems are concerned with symbolic structures considered under the aspect of generation by formal (syntactic) rules, that is, irrespective of their or their components’ meaning(s). In the most general sense, a formal language is a set of expressions. The most important way of describing this set is by means of grammars. Formal systems are formal languages equipped with a consequence operation yielding a deductive system. If one further specifies the means by which expressions are built up (connectives, quantifiers) and the rules from which inferences are generated, one obtains logical calculi of various sorts, especially Frege–Hilbert-style and Gentzen-style systems.
Ordinal logics
Authors: Feferman Solomon
Published: September 2018

By an ordinal logic is meant any uniform effective means of associating a logic (that is, an effectively generated formal system) with each effective ordinal representation. This notion was first introduced and studied by Alan Turing in 1939 as a means to overcome the incompleteness of sufficiently strong consistent formal systems, established by Kurt Gödel in 1931.

The first ordinal logic to consider, in view of Gödel’s results, would be that obtained by iterating into the constructive transfinite the process of adjoining to each system the formal statement expressing its consistency. For that ordinal logic, Turing obtained a completeness result for the class of true statements of the form that all natural numbers have a given effectively decidable property. However, he also showed that any ordinal logic (such as this) which is strictly increasing with increasing ordinal representation cannot have the property of invariance: in general, different representations of the same ordinal will have different sets of theorems attached to them. This makes the choice of representation a crucial one, and without a clear rationale as to how that is to be made, the notion of ordinal logic becomes problematic for its intended use.

Research on ordinal logics lapsed until the late 1950s, when it was taken up again for more systematic development. Besides leading to improvements of Turing’s results in various respects (both positive and negative), the newer research turned to restrictions of ordinal logics by an autonomy (or ‘boot-strap’) condition which limits the choice of ordinal representations admitted, by requiring their recognition as such in advance.
Combinatory logic
Authors: McCarty David Charles
Published: September 2018

Combinatory logic comprises a battery of formalisms for expressing and studying properties of operations constitutive to contemporary logic and its applications. The sole syntactic category in combinatory logic is that of the applicative term. Closed terms are called ‘combinators’; there is no binding of variables. Systems containing the basic combinators S and K exhibit the crucial property of combinatorial completeness: every routine expressible in the system can be captured by a term composed of these two combinators alone. Combinatory logic is a close relative of Church’s lambda calculus. M. Schönfinkel first introduced and defined basic combinators in 1920 in assaying foundations for mathematics that avoid bound variables and take operations, rather than sets, as fundamental. H. Curry later rediscovered the combinators (and coined the term ‘combinatory logic’) independently of Schönfinkel. Curry constructed various formal systems for combinatory logic and, throughout most of the subject’s history, was the central figure in the research. In 1969, D. Scott succeeded in constructing set-theoretic, functional models for the lambda calculus and combinatory logic. Since then semantic studies of combinatory systems, together with research on their applications to computer science and further development as foundational systems, have dominated the field.
Löwenheim–Skolem theorems and nonstandard models
Authors: Hart W.D.
Published: September 2018

Sometimes we specify a structure by giving a description and counting anything that satisfies the description as just another model of it. But at other times we start from a conception we try to articulate, and then our articulation may fail to pin down what we had in mind. Sets seem to have had such a fate. For millennia sets lay fallow in logic, but when cultivated by mathematics in the nineteenth century, they seemed to bear both a foundation and a theory of the infinite. The paradoxes of set theory seemed to threaten this promise. With an eye to proving freedom from paradox, versions of set theory were articulated rigorously. But around 1920, Löwenheim and Skolem proved that no such formalized set theory can come out true only in the hugely infinite world it seemed to reveal, for if it is true in such a world, it will also be true in a world of the smallest infinite size. (Versions of this remain true even if we augment the standard expressive devices used to formalize set theory.) But then, Skolem inferred, we cannot articulate sets determinately enough for them to constitute a firm foundation for mathematics.
Consequence, conceptions of
Authors: Smiley Timothy
Published: September 2018

The idea of one proposition’s following from others – of their implying it – is central to argument. It is, however, an idea that comes with a history attached to it, and those who blithely appeal to an ‘intuitive’ or ‘pre-theoretic’ idea of consequence are likely to have got hold of just one strand in a string of diverse theories. This entry introduces the main alternatives – to call them rivals would be too strong, since it suggests that they are necessarily in competition with one another. Simply put, consequence may be conceived as a relation that is or is not modal in character, and is or is not formal. Thus for Aristotle, consequence is both necessary and formal; for Chrysippus it is necessary but not formal; for Bolzano and Tarski it is formal but not necessary; and for Philo and Russell it is neither necessary nor formal. Conceptions of consequence that are neither necessary nor formal are also needed if justice is to be done to deduction in science, the law and daily life. Cutting across all these other differences there is a perennial controversy about relevance. Does implication always require a full-blooded connection between premises and conclusion, or may it hold simply because of some property of either separately, for example, because the premises are impossible?
The constructible universe
Authors: Burgess John P.
Published: September 2018

the ‘universe’ of constructible sets was introduced by Kurt Gödel in order to prove the consistency of the axiom of choice (AC) and the continuum hypothesis (CH) with the basic (ZF) axioms of set theory. The hypothesis that all sets are constructible is the axiom of constructibility (V = L). Gödel showed that if ZF is consistent, then ZF + V = L is consistent, and that AC and CH are provable in ZF + V = L.
Logic in the 19th century
Authors: Dipert Randall R.
Published: September 2018

The nineteenth century was one of the most active periods for logic in Western philosophy. It is regarded foremost as being the first time logic became ‘symbolic’ and ‘mathematical’.

There was tremendous diversity and conflict in logic in this period – indeed there were substantial debates over whether there even is a subject called ‘formal logic’ and over what the most basic logical forms were. There was an explicit discussion in the early part of the century of whether logic should be extensional or intensional, opinion eventually settling on a purely extensional conception. By the end of the century, many of these debates had been resolved or had withered away, and the most widespread conception and practice of logic coalesced in the early twentieth century into a view we now identify with the works of Frege, Russell and Whitehead.

The nineteenth century brought, for the first time, from Boole and Frege, distinct proposals on how to symbolize logic that were both extensively developed and had widespread influence. Boole is correctly regarded as the father of modern symbolic logic. Frege shared two concerns of many nineteenth-century mathematicians – avoiding incorrect derivations and providing rigorous and clear foundations for the infinitesimal and derivative calculus – and therefore sought to develop a very clear notion of mathematical ‘proof’. His notation has not been taken up but his influence, especially on the move towards symbolization, has been considerable.

De Morgan was the first logician extensively and symbolically to discuss the logic of relations. However, a systematic algebraic notation for relations was provided only later by Peirce, and developed also by Schröder.
Relevance logic and entailment
Authors: Read Stephen
Published: September 2018

‘Relevance logic’ came into being in the late 1950s, inspired by Wilhelm Ackermann, who rejected certain formulas of the form A→B on the grounds that ‘the truth of A has nothing to do with the question whether there is a logical connection between B and A’.

The central idea of relevance logic is to give an account of logical consequence, or entailment, for which a connection of relevance between premises and conclusion is a necessary condition. In both classical and intuitionistic logic, this condition is missing, as is highlighted by the validity in those logics of the ‘spread law’, A &∼A→B; a contradiction ‘spreads’ to every proposition, and simple inconsistency is equivalent to absolute inconsistency. In relevance logic the spread law fails, and the simple inconsistency of a theory (that a set of formulas entails a contradiction) is distinguished from absolute inconsistency (or triviality: that a set of formulas entails every proposition). The programme of relevance logic is to characterize a logic, or a range of logics, satisfying the relevance condition, and to study theories based on such logics, such as relevant arithmetic and relevant set theory.
Free logics
Authors: Bencivenga Ermanno
Published: September 2018

We often need to reason about things that do not – or may not – exist. We might, for example, want to prove that there is no highest prime number by assuming its existence and deriving a contradiction. Our ordinary formal logic, however (that is, anything including standard quantification theory), automatically assumes that every singular term used has a denotation: if you can use the term ‘God’ – if that term is part of your language – automatically there is a denotation for it, that is, God exists. Some logicians have thought that this assumption prejudges too many important issues, and that it is best to get rid of it. So they have constructed logics free of this assumption, called ‘free logics’.
Dynamic logics
Authors: Friedrichsdorf Ulf
Published: September 2018

Dynamic logics have been designed by Pratt as formal systems for reasoning about computer programs. The main ingredients discussed are programs, operations on programs, states and properties of states. In particular one can formalize that every execution of a program p starting in state s terminates in a state with a given property. Thus correctness statements for programs can be dealt with. According to Segerberg (1980) programs might be viewed more generally as actions of some agent so that certain aspects of human action theory can also be formulated and studied in these systems.
Inductive definitions and proofs
Authors: McGee Vann
Published: September 2018

An inductive definition of a predicate R characterizes the Rs as the smallest class which satisfies a basis clause of the form (β(x)→Rx), telling us that certain things satisfy R, together with one or more closure clauses of the form (Φ(x,R)→Rx), which tell us that, if certain other things satisfy R, x satisfies R as well. ’Smallest’ here means that the class of Rs is included in every other class which satisfies the basis and closure clauses.

Inductive definitions are useful because of inductive proofs. To show that every R has property P, show that the class of Rs that have P satisfies the basis and closure clauses.

The closure clauses tell us that if certain things satisfy R, x satisfies R as well. Thus satisfaction of the condition Φ(x,R) should be ensured by positive information to the effect that certain things satisfy R, and not also require negative information that certain things fail to satisfy R. In other words, the condition Φ(x,R) should be monotone, so that, if R ⊆S and Φ(x,R), then Φ(x,S); otherwise, we would have no assurance of the existence of a smallest class satisfying the basis and closure conditions.

While inductive definitions can take many forms, they have been studied most usefully in the special case in which the basis and closure clauses are formulated within the predicate calculus. Initiated by Yiannis Moschovakis, the study of such definitions has yielded an especially rich and elegant theory.
Logicism
Authors: Stein Howard
Published: September 2018

The term ‘logicism’ refers to the doctrine that mathematics is a part of (deductive) logic. It is often said that Gottlob Frege and Bertrand Russell were the first proponents of such a view; this is inaccurate, in that Frege did not make such a claim for all of mathematics. On the other hand, Richard Dedekind deserves to be mentioned among those who first expressed the conviction that arithmetic is a branch of logic.

The logicist claim has two parts: that our knowledge of mathematical theorems is grounded fully in logical demonstrations from basic truths of logic; and that the concepts involved in such theorems, and the objects whose existence they imply, are of a purely logical nature. Thus Frege maintained that arithmetic requires no assumptions besides those of logic; that the concept of number is a concept of pure logic; and that numbers themselves are, as he put it, logical objects.

This view of mathematics would not have been possible without a profound transformation of logic that occurred in the late nineteenth century – most especially through the work of Frege. Before that time, actual mathematical reasoning could not be carried out under the recognized logical forms of argument: this circumstance lent considerable plausibility to Immanuel Kant’s teaching that mathematical reasoning is not ‘purely discursive’, but relies upon ‘constructions’ grounded in intuition. The new logic, however, made it possible to represent standard mathematical reasoning in the form of purely logical derivations – as Frege, on the one hand, and Russell, in collaboration with Whitehead, on the other, undertook to show in detail.

It is now generally held that logicism has been undermined by two developments: first, the discovery that the principles assumed in Frege’s major work are inconsistent, and the more or less unsatisfying character (or so it is claimed) of the systems devised to remedy this defect; second, the epoch-making discovery by Kurt Gödel that the ‘logic’ that would be required for derivability of all mathematical truths can in principle not be ‘formalized’. Whether these considerations ‘refute’ logicism will be considered further below.
Constructivism in mathematics
Authors: McCarty David Charles
Published: September 2018

Constructivism is not a matter of principles: there are no specifically constructive mathematical axioms which all constructivists accept. Even so, it is traditional to view constructivists as insisting, in one way or another, that proofs of crucial existential theorems in mathematics respect constructive existence: that a crucial existential claim which is constructively admissible must afford means for constructing an instance of it which is also admissible. Allegiance to this idea often demands changes in conventional views about mathematical objects, operations and logic, and, hence, demands reworkings of ordinary mathematics along nonclassical lines. Constructive existence may be so interpreted as to require the abrogation of the law of the excluded middle and the adoption of nonstandard laws of constructive logic and mathematics in its place.

There has been great variation in the forms of constructivism, each form distinguished in its interpretation of constructive existence, in its approaches to mathematical ontology and constructive logic, and in the methods chosen to prove theorems, particularly theorems of real analysis. In the twentieth century, Russian constructivism, new constructivism, Brouwerian intuitionism, finitism and predicativism have been the most influential forms of constructivism.
Gödel, Kurt (1906–78)
Authors: Dawson John W.
Published: September 2018

The greatest logician of the twentieth century, Gödel is renowned for his advocacy of mathematical Platonism and for three fundamental theorems in logic: the completeness of first-order logic; the incompleteness of formalized arithmetic; and the consistency of the axiom of choice and the continuum hypothesis with the axioms of Zermelo–Fraenkel set theory.
Gentzen, Gerhard Karl Erich (1909–45)
Authors: Peckhaus Volker
Published: September 2018

The German mathematician and logician Gerhard Gentzen devoted his life to proving the consistency of arithmetic and analysis. His work should be seen as contributing to the post-Gödelian development of Hilbert’s programme. In this connection he developed several logical calculi. The main device used in his proofs was a theorem in which he proved the eliminability of the inference known as ‘cut’ from a variety of different kinds of proofs. This ‘cut-elimination theorem’ yields the consistency of both classical and intuitionistic logic, and the consistency of arithmetic without complete induction. His later work was aimed at providing consistency proofs for less restricted systems of arithmetic and analysis.
Post, Emil Leon (1897–1954)
Authors: Scanlan Michael
Published: September 2018

Emil Post was a pioneer in the theory of computation, which investigates the solution of problems by algorithmic methods. An algorithmic method is a finite set of precisely defined elementary directions for solving a problem in a finite number of steps. More specifically, Post was interested in the existence of algorithmic decision procedures that eventually give a yes or no answer to a problem. For instance, in his dissertation, Post introduced the truth-table method for deciding whether or not a formula of propositional logic is a tautology.

Post developed a notion of ‘canonical systems’ which was intended to encompass any algorithmic procedure for symbol manipulation. Using this notion, Post partially anticipated, in unpublished work, the results of Gödel, Church and Turing in the 1930s. This showed that many problems in logic and mathematics are algorithmically unsolvable. Post’s ideas influenced later research in logic, computer theory, formal language theory and other areas.
Neumann, John von (1903–57)
Authors: Rosmaita Brian
Published: September 2018

Von Neumann was one of the great mathematical minds of the twentieth century. His work has affected philosophy on several fronts, including logic and the philosophy of science. He also had great influence upon developments in the philosophy of mind: the computer model of mind employed during the middle-to-late twentieth century was explicitly based upon the von Neumann computer architecture. Although late twentieth-century philosophy of mind has largely rejected the von Neumann machine as a model of brain activity, his pioneering work in cellular automata has provided a basis for subsequent development in ‘distributed’ or ‘connectionist’ computer architectures.
Fanon, Frantz (1925–61)
Authors: Appiah K. Anthony
Published: September 2018

Fanon’s views (and often various misinterpretations of them) on the nature of colonialism, racism and the role of violence in Third-World revolutions were enormously influential. The main themes of all his writing are the critique of ethnopsychiatry and the Eurocentrism of psychoanalysis, the critique of négritude and the development of a political philosophy for Third-World liberation.

Frantz Fanon was born in the French Antilles on the island of Martinique and was educated there and in France. He served in the Free French army during the Second World War, both in north Africa and in Europe. He went on to study medicine and psychiatry at the University of Lyons between 1947 and 1951. In 1953 he was appointed chief of service of the psychiatry department of a hospital in Algeria (which was then still a French territory). He joined the Algerian liberation movement in 1954 and began to work for its underground newspaper El Moudjahid a few years later. His political activities caused him to leave his job, after which he moved to Tunisia where he practised psychiatry from 1957 to 1959. In 1961 he was appointed ambassador to Ghana by the Algerian provisional government. He died of leukaemia in 1961.
Yoruba epistemology
Authors: Hallen Barry
Published: September 2018

The Yoruba of west Africa have articulated systematic criteria that are used to assign varying degrees of epistemic certainty to experience. What one views with one’s own eyes and experiences at first-hand (ìmò) are judged as reliable ways of knowing the truth, providing there is conscious comprehension of what one is perceiving. Only propositions describing such experiences are regarded as true, or òótó. Less reliable is information received via books, other people, the media and the oral tradition. If such comparatively second-hand information, or ìgbàgbó, can be experimentally tested and accordingly verified, it has the potential to become ìmò.If verification cannot be attested, discussion, analysis and good judgment are essential tools for distinguishing the more reliable information from the less reliable.
Ethical systems, African
Authors: Appiah K. Anthony
Published: September 2018

Ethical thought in sub-Saharan Africa grows largely out of traditions that are communalistic, not based in individual consent, anti-universalizing, naturalistic, and humanist. Within such thought, the general vocabulary of evaluation, like such English words as ‘good’ and ‘bad’, does not strongly differentiate between narrow moral assessments, on the one hand, and technical or aesthetic evaluation on the other. This is true of places where Islam has been present for many centuries. The substantial exposure, in the colonial and postcolonial periods, to European moral ideas (both through various forms of Christian missionary evangelism and as a result of contact with secular moral and political traditions from elsewhere), along with the changes produced by the modern economy, have produced a wide range of ethical ideas. However, the residue of precolonial ethical theory remains the most distinctive, if not always the most important, component and is the main topic of this entry.
African traditional religions
Authors: Appiah K. Anthony
Published: September 2018

Religion has been at the centre of recent philosophical debate in Africa for two major reasons. The first is that the answers to many central canonical philosophical questions in precolonial African societies take a religious form. As a result any attempt to construct an African philosophy begs attention to the epistemological and ontological standing of claims of this general sort. The second reason religion has been central to African philosophy is that one of the major issues in modern African philosophy is whether distinctively African modes of thought exist. Within this debate influential positions have been argued by reflecting on the character of traditional religious thought and practice and contrasting it with modes of thought purportedly associated with Western science.
Ethiopia, philosophy in
Authors: Sumner Claude
Published: September 2018

Ethiopia is a unique phenomenon in Africa for three reasons. First, because of its historical continuity and political independence; second because of its written language and third because of its written philosophy. Ethiopian philosophy in the broadest sense is expressed in both oral and written language. In this entry only the written documents are dealt with. This methodological approach limits the investigation to linguistic and cultural phenomena as it deals with the ancient Semitic language known as Ethiopic and the Christian zones of influence on the high plateaus of Ethiopia.

There are five basic texts of Ethiopian philosophical literature: the Physiologue (the Fisalgwos) (c. fifth century ad), The Book of the Wise Philosophers (1510/22), The Life and Maxims of Skendes (c. eleventh century ad), The Treatise of Zar’a Ya‘ecob (1667) and The Treatise of Wäldä Heywåt (c. eighteenth century). The first three are adaptations of works transmitted from Greek sources through Arabic; the latter two (appearing in modern publications in a combined form) are original works of a rationalist flavour.
Douglass, Frederick (1818–95)
Authors: Boxill Bernard R.
Published: September 2018

Frederick Douglass was an escaped slave, an abolitionist, an orator, an agitator for black civil and political rights, an editor, an ambassador, a lecturer, a feminist, a journalist, a confidant of John Brown and also of William Lloyd Garrison, and a self-educated intellectual and philosopher who never had a single day of formal schooling in his life. His Narrative of the Life of Frederick Douglass, an American Slave, Written by Himself, published in 1845 when he was 27 years old and only seven years out of slavery, is a literary classic, and sold more than 4,500 copies in the first six months after it appeared. His My Bondage and My Freedom, published ten years later, is the best philosophical analysis of human nature in slavery ever written.
Senghor, Léopold Sédar (1906–2001)
Authors: Taoua Phyllis
Published: September 2018

Léopold Sédar Senghor is one of the most influential African poets of the modern era. He also left his mark as a controversial cultural theorist and president of his native Senegal from 1960 until 1981. The poet and statesman participated with Aimé Césaire and Léon Gontran Damas in founding the négritude movement during the interwar period in Paris. Négritude was a cultural revolution that affirmed black African culture across geographical borders, combining a political vision of social justice for all peoples of African origin with an innovative poetic idiom. Senghor’s distinctive contribution to this avant-garde effort was a set of inter-related concepts with which he developed his theory of black African culture. The first was a notion of cross-cultural creativity entailing an interpenetration of African and European cultures. The second was a selective assimilation of certain aspects of French culture into an African conceptual framework. The third was an African version of socialism that integrated a community-centred ethics with a traditional African spirituality. Senghor believed that African culture had unique contributions to make to European thought, and worked to define a theory of culture based on dialogue, reciprocity and an inclusive humanism, which would pave the way for Africa’s integration into a civilization of the universal. His philosophy of culture is unsystematic; it appears as a collection of insights derived from various sources on the central theme of négritude.
Anti-positivist thought in Latin America
Authors: Weinstein Michael A.
Published: September 2018

Anti-positivist philosophy arose in Latin America at the turn of the twentieth century in response to the dominance of closed positivistic systems of historical development in the climate of intellectual opinion. Argentina, Mexico and Uruguay were all centres of anti-positivist theorizing. Philosophers such as Mexicans Antonio Caso and José Vasconcelos, the Argentinian Alejandro Korn and the Uruguayan Carlos Vaz Ferreira attacked Auguste Comte’s positivism, as well as deterministic forms of scientific Marxism and Herbert Spencer’s social Darwinism for their denials of creative freedom and spiritual values. Latin American anti-positivism is characterized as a form of modernism although it incorporates elements of traditionalism. It is self-consciously critical of the limitations of modern progressivism and willing to supplement the modern paradigm with premodern discourses. Anti-positivist philosophy is also firmly committed to the modern embrace of process over fixed form.

Latin American anti-positivism is founded in a comprehensive interpretation of experience that embraces phenomena such as creative freedom, tentative and experimental thinking, imaginative coordination and charitable love. These aspects are excluded from the purview of what positivists allow to be objects of scientific knowledge. Anti-positivists interpret experience as a bi-polar struggle in which the free side of life battles to prevail over the forces of necessity, system, abstraction and egoism.

South American anti-positivists concentrated on issues of knowledge and the structure of thought and experience, whereas Mexican anti-positivists, who were products of a formal education modelled on Comte’s prescriptions, undertook a more total revolt. This revolt had metaphysical, moral and political dimensions.

For the most part anti-positivists did not fully escape the doctrines they criticized. They took from these doctrines descriptions of unredeemed, degraded and mechanized life which they opposed to redemptive practices of struggle.
Feminist thought in Latin America
Authors: Oliver Amy A.
Published: September 2018

Any analysis of feminist thought in Latin America is burdened by the task of combatting the frequent assumption that feminism is an ideology imported from the USA or Europe. One could begin by arguing that in certain senses autocthonous feminist thought has existed in Latin America for centuries. The thought of Sor Juana Inés de la Cruz, a seventeenth-century Mexican writer and nun, had certain qualities, themes and perspectives that can be called feminist. Her autobiographical essay, ‘Reply to Sor Filotea de la Cruz’, is a brilliant defence of a woman’s right to engage in intellectual pursuits and includes many feminist strategies and dimensions.

Among the Latin American feminists through the centuries, exemplary passages are easily found, such as the following from the Peruvian Flora Tristán, who said ‘Without liberation of woman, there will be no liberation of man’ (1843). Revisionist reappraisals of underappreciated women thinkers have grown more common. Venezuelan Teresa de la Parra’s important writings which have been re-examined as texts by women continue to be rescued from relative obscurity. Rosario Castellanos, Rigoberta Menchú and Domitila Barrios de Chungara count among those whose work has enjoyed increased critical attention. Concurrently, the voices of traditionally voiceless women are being heard through expanding oral history projects, such as those of domestic workers in Bogotá: ‘It is not enough to have rights. We must raise consciousness and organize ourselves to defend those rights’.

In recent years, particularly after the international year of the woman in 1975 and the decade of the woman sponsored by the United Nations from 1976 to 1985, women and men have continued to develop feminist philosophies appropriate for Latin American contexts.

Professional feminist philosophy has been practised in Latin America since the early part of the twentieth century. Perhaps surprisingly, a theoretically sophisticated feminist philosophy was practised in Uruguay at this time by male social philosopher, Carlos Vaz Ferreira (1871–1958). His work had significant impact on women’s rights in Latin America. Vaz Ferreira was a pioneer in feminist theory.
Cultural identity
Authors: Loughney John A.
Published: September 2018

If cultural identity means that a person achieves the fullest humanity within an accepted context of traditional symbols, judgments, values, behaviour and relationships with specific others who self-consciously think of themselves as a community, then it must be seen as a great contemporary challenge to many Western philosophical assertions about the person, society, meaning and truth.

This sense of cultural identity, as well as more extreme forms, can amount to classic determinism: individuals are subsumed under the relations with meaning and people surrounding them. Advocates of the centrality of cultural identity often make an argument rooted in an ‘authenticity’ which purports that, to fully encounter oneself, each of us must grasp and fully accept one’s psychological and social location within a specific group of people who interpret life in terms of the particular civilization that contains them.
Literature, philosophy in Latin American
Authors: Gomez-Martinez Jose Luis
Published: September 2018

Within the Latin American intellectual community, the relationship between philosophy and literature constitutes one of the most interesting chapters in its development. Much Latin American literature is characterized by profound philosophical concerns, focusing on the question of identity. From the time of the conquest and colonization of the American continent in the 1500s, a debate regarding the humanity of the recently discovered inhabitants began in Spain. This debate would prove to be one of the most revealing controversies of sixteenth-century Europe. At the point of colonial expansion, Europe projected a logocentric vision which would incite a unique Latin Americanist philosophical discourse relating to the question of identity.

During the nineteenth century, philosophical discourse was formulated principally through literary expression. At first the quest for a cultural identity was the philosophical focus, although two conflicting positions were evident: the desire to achieve cultural independence from Europe and a yearning for Latin America to become European. This latter position inspired the urge to identify with European culture and from the mid-1900s, with the political and economic success of the USA.

In the twentieth century, from the time of the University Reform of 1918, an academic philosophy emerged close to that of Europe and began to diversify the Latin American philosophical panorama. From the various philosophical stances which arose at that time, one that dominated the cultural arena, despite its occasional relegation to a secondary position in academia, was the urge to articulate a Latin Americanist philosophical discourse which would succeed in transcending its own frontiers through liberation philosophy, beginning in the 1960s.
Marginality
Authors: Oliver Amy A.
Published: September 2018

Traditional definitions of marginal persons include those who live in two worlds, but do not feel well integrated into either and those who live in societies which are in the process of being assimilated and incorporated into an emerging global society. The influence of Anglo-American and European cultures has brought this situation into existence. A broader, more contemporary understanding of marginality is the condition of feeling marginal in relation to various concepts of the centre. This state produces a stigmatized identity, which either aspires to inclusion or assimilation into the centre, or demands recognition of and respect for a separate but equal existence. This condition of marginality can be experienced in varying degrees by many kinds of people.

Often gender, sexual preference, age, ethnicity, geography and religion are factors which can influence perceptions of marginality. Those who perceive themselves, or who are perceived by others to be marginal are often female, dark-skinned, very young or elderly, poor, disabled, nonheterosexual, displaced, exiled, immigrant, rural, indigenous, ‘foreign’, outcast, persecuted, or otherwise ‘different’ from those who occupy positions of privilege in the centre, or the metropolis. Critics of the term ‘marginality’ believe it has become overused to the point of losing descriptive precision because, they argue, almost everyone has experienced some form of marginality. In philosophy, however, the phenomenon of feeling, or being, perceived as peripheral, or on the margin, has generated critical perspectives which have enlightened discourse on social integration and stratification; personal suffering and economic, political, and cultural inequality. In addition, analyses of marginality have called into question notions of the ‘universal’ and the ‘objective’ set forth by many Western philosophers.
Una propuesta del área de Matemáticas para el Taller de Arquitectura: Percepción del espacio mediante parámetros asociados a la visibilidad
Authors: Abajo Casado Encarnación , Delgado Sánchez Juan Manuel
Published: September 2018

El objetivo de este artículo es introducir al lector en el análisis de la percepción espacial y visual de una obra arquitectónica utilizando para ello una metodología desarrollada en las útimas décadas. Partiendo del concepto de isovista, región plana visible para un individuo situado en una determinada localización de una planta arquitectónica, esta metodología se basa, por una parte, en la interpretación del algunas medidas asociadas a la geometría de las isovistas; por otra parte, en el uso de herramientas o parámetros asociados al denominado grafo de visibilidad o grafo de localizaciones intervisibles. El uso de esta metodología permite la integración de las Matemáticas en asignaturas de carácter transversal presentes en los planes de estudios en Arquitectura. 
Estabilizador de Sistemas de Potencia usando Control Predictivo basado en Modelo
Authors: Duarte-Mermoud Manuel A , Milla Freddy
Published: September 2018

Se propone un estabilizador de potencia predictivo para amortiguar oscilaciones de potencia en un sistema eléctrico de potencia(SEP) formado por una sola máquina conectada a una barra infinita (Single Machine Infinite Bus, SMIB). Este enfoque considera un análisis de estabilidad de pequeña señal, usando un modelo incremental alrededor de un punto de operación. El estabilizador proporciona señales de control óptimas, debido a que además de utilizar el controlador predictivo basado en modelo (Model Predictive Controller, MPC) sus parámetros se optimizan fuera de línea empleando un algoritmo de optimización por enjambre de partículas (Particle Swarm Optimization, PSO). Su comportamiento se compara con un estabilizador del sistema potencia convencional, con parámetros también optimizados con PSO fuera de línea. Para validar la metodología propuesta, se presentan numerosas simulaciones de respuestas dinámicas del SMIB, para diferentes condiciones de operación y perturbaciones.
The effect of purslane hydroextract and zinc on performance, antioxidant capacity and immunity of broiler chickens during summer conditions
Authors: Kazemi Rojin , Sheikhahmadi Ardashir , Sadeghi Ghorbanali
Published: September 2018

Abstract. Due to negative effects of high ambient temperature, the present study was conducted to investigate the effects of Portulaca oleracea hydroextract (PHE) and zinc (Zn) on the growth performance and immunity of broiler chickens reared under high summer ambient temperature conditions. A total of 420 day-old male broiler chickens (Ross 308) were randomly allocated to seven dietary treatments each replicated four times with 15 birds per replicate. The basal diet as the control diet was supplemented with 100 mg kg−1 butylated hydroxytoluene (BHT), or 300 and 600 mg kg−1 of PHE, 100 mg kg−1 of zinc and 100 mg kg−1 of zinc plus 300 or 600 mg kg−1 of PHE (ZP300 and ZP600). The result of the present study showed that Zn, PHE and their combination did not alter daily feed intake and feed conversion ratio. Although there was a tendency toward an increase in broiler body weight at 24 and 44 days of age (P=0.059 and P=0.061), the body weight of birds fed the basal diet supplemented with Zn reduced at day 10. The birds fed diets supplemented with BHT or ZP600 showed lower aspartate aminotransferase (ASAT) and lactate dehydrogenase activity at 24 days of age (P<0.05), but it remains lower in the ZP600 group only for ASAT activity level at day 44. The results of the present study suggest that dietary PHE and Zn supplementation partially improved body weight and serum antioxidant capacity, superoxide dismutase activity and antibody titer against sheep red blood cells and Newcastle diseases in the broiler chickens during summer conditions.