Ferdinand de Saussure
Let's start by talking about structuralism in general as a philosophical stance or worldview. Structuralists are interested in the interrelationship between UNITS, also called "surface phenomena," and RULES, which are the ways that units can be put together. An example is Tinkertoys. The "units" in a Tinkertoy set are all the partsin the box: the various colored rods of different lengths, the various kinds of connectors and wheels and attachments; the "rules" of Tinkertoy construction is that rods go into holes. That's the structure of tinkertoys: everything you can make out of tinkertoys, whatever that may be, is made by using the units according to the rules. A structuralist analysis of tinkertoys wouldn't look at what youmade (a building, a race car, a windmill, etc.) but would look only at the structure governing every possible combination of Tinkertoy elements. And that structure is that rods go into holes.
Tinker toy picture
That's what structuralist analysis does, whatever it's analyzing: looks at the units of a system, and the rules that make that system work, without regard for any specificcontent. In language, for instance, structuralists (like Saussure) the units are words (or, actually, the 31 phonemes which make all the sounds of words in English) and the rules are the forms of grammar which order words. In different languages the grammar rules are different, as are the words, but the structure is still the same in all languages: words are put together within a grammatical system tomake meaning.
An example of this idea of structure can be found in the game of "Mad Libs." In class I read an example, which asked for various nouns, adjectives, verbs, proper names, and exclamations. When plugged into a story, these randomly chosen parts of speech made a very silly narrative-- but one which was recognizable as a narrative because the parts of speech were appropriately placed:nouns went where nouns go, and verbs where verbs go, etc. In a sentence, any noun can replace any other noun and not change the grammatical structure: the sentence "My pencil ate my PT Cruiser" might not make any rational sense, but it's recognizable as a sentence because the parts of speech are all in the right places. Here's an example of this using literature. I'll give you three characters:princess, stepmother, and prince. Now you tell me the story. Many of you said "Cinderella," and others came up with other story titles. From a structuralist point of view, Cinderella is the same story as Snow White and as lots of other Disney stories and fairy tales: a princess is persecuted by a stepmother and rescued (and married) by a prince. The "units" here are the characters, and the "rules"are: stepmothers are evil, princesses are victims, and princes and princesses have to marry. Whatever details or added elements you supply, the basic structure of this story is always the same. And that's exactly what structuralist analyses of literature (or myth or other forms of narrative) are analyzing.
Structuralists believe that the underlying structures which organize units and rules intomeaningful systems are generated by the human mind itself, and not by sense perception. As such, the mind is itself a structuring mechanism which looks through units and files them according to rules. This is important, because it means that, for structuralists, the order that we perceive in the world is not inherent in the world, but is a product of our minds. It's not that there is no "reality outthere," beyond human perception, but rather that there is too much "reality" (too many units of too many kinds) to be perceived coherently without some kind of "grammar" or system to organize and limit them.
So structuralism sees itself as a science of humankind, and works to uncover all the structures that underlie all the things that humans do, think, perceive, and feel--in mathematics,...