More on Universe of Discourse

Håkan sent me a quick email on universe of discourse in which he says he’s encountered it primarily within set theory and logic. He also included some quotes, of which the following two made the most sense for me:

The term universe of discourse denotes the overall domain within which all interesting arguments are made. The entities contained within the universe of discourse comprise a complete vocabulary. All correct, consistent statements that can be made within the universe of discourse, then, use only symbols that are available within that universe.

And:

The concept of dichotomy allows for the enabling of a frame of reference, a universe of discourse, where classes are created such that, for example, an object is symbolized as either being in ‘A’ (in the class) or in ’~A’ (outside the class).

The link for the first one doesn’t work right now, but Google’s cache does. The second one is from a page on the principle of dichotomy.

Jay McCarthy also chipped in and says his understanding of the concept comes from studying mathematics “with particular reference to theory classes—like proof creation and number theory.” He continues:

So, for me, “universe of discourse” really says to me: When you make a statement, be honest with yourself about the assumptions you are making and try to make those assumptions clear to the reader.