Structuralism

Structuralism in the Philosophy.

Structuralism is the study of what structures (mathematical objects) are, and how the ontology of these structures should be understood. This is a growing philosophy within mathematics that is not without its share of critics.

Paul Benacerraf's "What Numbers Could Not Be" (1965) is a seminal paper on mathematical structuralism in an odd sort of way: it started the movement by the response it generated. Benacerraf addressed a notion in mathematics to treat mathematical statements at face value, in which case we are committed to an abstract, eternal realm of mathematical objects. Benacerraf's dilemma is how we come to know these objects if we do not stand in causal relation to them. These objects are considered causally inert to the world. Another problem raised by Benacerraf is the multiple set theories that exist by which reduction of elementary number theory to sets is possible. Deciding which set theory is true has not been feasible. Benacerraf concluded in 1965 that numbers are not objects, a conclusion responded to by Mark Balugar with the introduction of full blooded platonism (FBP is essentially the view that all logically possible mathematical objects do exist). With FBP it does not matter which set-theoretic construction of mathematics is used, nor how we came to know of its existence, since any consistent mathematical theory necessarily exists and is a part of the greater platonic realm.

The answer to Benacerraf's negative claims is how structuralism became a viable philosophical program within mathematics. The structuralist responds to these negative claims that the essence of mathematical objects is relations that the objects bear with the structure.

Important contributions to structuralism in mathematics have been made by Bourbaki.

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Structuralism in the Literary Theory and Literary Criticism

Main article: Semiotic literary criticism

In literary theory structuralism is an approach to analysing the narrative material by examining the underlying invariant structure. For example, a literary critic applying a structuralist literary theory might say that the authors of the West Side Story did not write anything "really" new, because their work has the same structure as Shakespeare's Romeo and Juliet. In both texts a girl and a boy fall in love (a "formula" with a symbolic operator between them would be "Boy +LOVE Girl") despite the fact that they belong to two groups that hate each other ("Boy's Group -LOVE Girl's Group") and conflict is resolved by their death. The versatility of structuralism is such that a literary critic could make the same claim about a story of two friendly families ("Boy's Family +LOVE Girl's Family") that arrange a marriage between their children despite the fact that the children hate each other ("Boy -LOVE Girl") and then the children commit suicide to escape the arranged marriage; the justification is that the second story's structure is an 'inversion' of the first story's structure: the relationship between the values of love and the two pairs of parties involved have been reversed. Structuralistic literary criticism argues that the "novelty value of a literary text" can lie only in new structure, rather than in the specifics of character development and voice in which that structure is expressed.

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Structuralism after World War II

Throughout the 1940s and 1950s, existentialism like that practiced by Jean-Paul Sartre was the dominant mood. Structuralism surged to prominence in France after WWII and particularly in the 1960s. The initial popularity of structuralism in France led it to spread across the globe.

Structuralism rejected the concept of human freedom and choice and focused instead on the way that human behavior is determined by various structures. The most important initial work on this score was Claude Lévi-Strauss's 1949 volume Elementary Structures of Kinship. Lévi-Strauss had known Jakobson during their time together in New York during WWII and was influenced by both Jakobson's structuralism as well as the American anthropological tradition. In Elementary Structures he examined kinship systems from a structural point of view and demonstrated how apparently different social organizations were in fact different permutations of a few basic kinship structures. In the late 1950s he published Structural Anthropology, a collection of essays outlining his program for structuralism.

By the early 1960s structuralism as a movement was coming into its own and some believed that it offered a single unified approach to human life that would embrace all disciplines. Roland Barthes and Jacques Derrida focused on how structuralism could be applied to literature.

Blending Freud and De Saussure, the French (post)structuralist Jacques Lacan and, in a different way, Jean Piaget, applied structuralism to the study of psychoanalysis and psychology each respectively.

Michel Foucault's book The Order of Things examined the history of science to study how structures of epistemology, or episteme shaped how people imagined knowledge and knowing (though Foucault would later explicitly deny affiliation with the structuralist movement).

Blending Marx and structuralism another French theorist Louis Althusser introduced his own brand of structural social analysis. Other authors in France and abroad have since extended structural analysis to practically every discipline.

The definition of 'structuralism' also shifted as a result of its popularity. As its popularity as a movement waxed and waned, some authors considered themselves 'structuralists' only to later eschew the label.

The term has slightly different meanings in French and English. In the US, for instance, Derrida is considered the paradigm of post-structuralism while in France he is labeled a structuralist. Finally, some authors wrote in several different styles. Barthes, for instance, wrote some books which are clearly structuralist and others which clearly are not.

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Reactions to structuralism

Today structuralism is less popular than approaches such as post-structuralism and deconstruction. There are many reasons for this. Structuralism has often been criticized for being ahistorical and for favoring deterministic structural forces over the ability of individual people to act. As the political turbulence of the 1960s and 1970s (and particularly the student uprisings of May 1968) began affecting academia, issues of power and political struggle moved to the center of people's attention. In the 1980s, deconstruction and its emphasis on the fundamental ambiguity of language - rather than its crystalline logical structure - became popular. By the end of the century Structuralism was seen as a historically important school of thought, but it was the movements it spawned, rather than structuralism itself, which commanded attention.

Date: 2015-01-02; view: 774