Sunday, June 05, 2005

More on concept, referent, term

A commenter asks in the thread below:

"I'm not sure I see how this would be a "triangle". If there's a real thing (an actual bear), what I think about bears (presumably somewhat idiosyncratic, though also presumably coloured by society &c to some debatable degree), and some linguistic intermediary I use to work between one and the other, that seems like a straight line. Everyone could have their own straight line between their thoughts and the bear, perhaps, but I don't see the triangle."

I've put up a couple of illustrations, but haven't yet gotten them to work in Blogger. One issue is that they are too big. I can shrink them in PhotoShop when I go in to school tomorrow, but for the moment, I'll just put links to them. Sorry that they take so long to load; that will be fixed tomorrow.

The first illustration is of the semantic triangle after Ogden and Richards. But the commenter raises a very good question: why a triangle? We could draw a straight line with the concepts on that line; wouldn't that suffice?

Let's try it and see. First of all, we'll make a minor change to the illustration, by changing the representation from a triangle to a concept graph. In my discipline, biomedical informatics, concept graphs are used frequently to illustrate structures, relationships, processes, and more. A concept graph consists of nodes (also called vertices), which are the circles representing entities, and of edges, which are the lines between nodes, representing relationships.

So converting the semantic triangle to a concept graph, we get this illustration. The entities are concept, referent, and term, and the bidirectional labeled edges a, b, and c are the relationships among them. For example, the referent may inform the concept by demonstrating an extremely protective maternal instinct, leading us to think of bears as fierce yet good mothers. That concept may inform the referent when, out of that concept, we pass laws forbidding the killing of mother bears with cubs. The referent may inform the term, as for, in example, the Russian медведь, which comes from "honey-eater" (cf. our English word mead. Similar relationships can be drawn so that each of the elements of meaning can be shown to inform each of the others in some way.

So now that we have the concept graph representation of the triangle, let's try the straight-line representation, to see if they are equivalent.

Notice that I have placed "concept" between term and referent. That implies that the referent informs my concept, which informs my term, and vice versa. The commenter asked the question in such a way that the term forms an intermediary between the concept and the referent, a perfectly good alternative way of arranging the three points on a straight line. The other alternative, where the referent is the intermediary between the concept and the term, is perhaps a little harder to visualize in terms of the physical world, but is, strictly logically, just as viable as the other too.

So we have three unique possible straight-line representations, as follows:

1) Referent <== a ==> Concept <== c ==> Term

2) Referent <== b ==> Term <== c ==> Concept (Update: this arrangement mirrors the strong form of the Sapir-Whorf hypothesis. Benjamin Lee Whorf: "We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organised by our minds - and this means largely by the linguistic systems in our minds. We cut nature up, organise it into concepts, and ascribe significances as we do, largely because we are parties to an agreement that holds throughout our speech community and is codified in the patterns of our language. The agreement is, of course, an implicit and unstated one, but its terms are absolutely obligatory; we cannot talk at all except by subscribing to the organisation and classification of data which the agreement decrees.")

3) Term <== b ==> Referent <== a ==> Concept

Notice that rotation of any of these yields the an equivalent line--we can also write 1) as Term <== c ==> Concept <== a ==> Referent. There is no physical reason why either representation is more correct, so we consider the rotation of any line above to be the equivalent of the line. The only way to get a uniquely different line is to change which of the three entities is at the center.

Notice that while any of the straight lines manages to account just fine for all three entities, it only accounts for any two sets of relationships, but not all three. That is why Ogden and Richards used a triangle (a 2-dimensional representation)--in order to be able to account for three different kinds of relationships among the entities. A line (a 1-dimensional representation) does not have sufficient power to represent the relationships among all the entities, just among any two which are connected to each other.

But perhaps there is a way in which this line representation can work. In this illustration, I have drawn the b relationship in. Now all the relationships are accounted for, although the representation is no longer 1-dimensional, but now 2-dimensional, like the triangle.

Is our new representation the same as the triangle, then? Well, yes and no. Geometrically, it is very different. Topologically,, however, it can be proved to be the same. Further, if we take any of our 3 unique lines described above, and add the missing relationship, we can prove that they are topologically no longer unique, but are equivalent to each other, as well as to our original triangle.

So if geometry says that they are different, and topology says that they are the same, how do we know which one to go with? The subject matter is the deciding factor. Geometry is a very numeric branch of mathematics, which deals with exact lengths, angles, and such. Topology, on the other hand, looks at those non-numeric properties which remain invariant under transformation. Since the relationships we are talking about, such as how a term influences a concept, are very non-numberic, topology seems like a more appropriate domain--and indeed, the topology of graphs and networks is a very big research area in computer science and bioinformatics.


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