Cake Space
1887: Lewis Carroll, mathematician and author of Alice in Wonderland, publishes his "Game of Logic" -- a kind of Natural Language Bingo game that allows its players to translate certain kinds of language expressions into an arrangement of colored tokens on a diagram. The game board he describes is a conceptual space for organizing things according to attributes. Each attribute creates a means of dividing the universe of things in two -- those which have the attribute and those which do not.
Carroll begins his discussion with the following statements, or propositions in the language of formal logic:
Some new cakes are nice. No new Cakes are nice. All new Cakes are nice.
He continues:
- Now please to look at the smaller Diagram on the Board, and suppose it to be a cupboard, intended for all the Cakes in the world (it would have to be a good large one, of course). And let us supposed all the new ones to be put in the upper half (marked x), and all the rest (that is, the not-new ones~ into the lower half (marked x'). Thus the lower half would contain elderly Cakes, aged Cakes, ante-diluvian Cakes -- if there are any: I haven't seen many myself -- and so on. Let us suppose all the nice Cakes to be put into the left-hand half (marked y)...
So here the "universe" is the world of all possible cakes, and being "new", and "nice" are two attributes. The "space" of all possible cakes according to these two attributes can be represented in the game diagrammatically as follows:
GameOfLogic.png
The game tokens then are used to mark of portions of this conceptual space based on the information of the propositions. For instance, the statement that "All new Cakes are nice" would be represented then by placing a red token to mark "Nice New Cakes" as certainly occupied, and "Not Nice New Cakes" with a gray token to mean certainly empty.
http://www.cut-the-knot.org/LewisCarroll/bidiagram.shtml
http://www.cut-the-knot.org/LewisCarroll/bitable.shtml