BOOK III.. The Biliteral Diagram.

THE BILITERAL DIAGRAM.

·-------------· | | | | xy | xy' | | | | |------|------| | | | | x'y | x'y' | | | | ·-------------·

CHAPTER I.

SYMBOLS AND CELLS.

First, let us suppose that the above Diagram is an enclosure assigned to a certain Class of Things, which we have selected as our 'Universe of Discourse.' or, more briefly, as our 'Univ'.

Thirdly, let us suppose that we have selected another Adjunct, which we may call "y", and have subdivided the x-Class into the two Classes whose Differentiæ are "y" and "y'", and that we have assigned the North-West Cell to the one (which we may call "the xy-Class"), and the North-East Cell to the other (which we may call "the xy'-Class").

Fourthly, let us suppose that we have subdivided the x'-Class in the same manner, and have assigned the South-West Cell to the x'y-Class, and the South-East Cell to the x'y'-Class.

It is evident that, if we had begun by dividing for y and y', and had then subdivided for x and x', we should have got the same four Classes. Hence we see that we have assigned the West Half to the y-Class, and the East Half to the y'-Class. pg024 [Thus, in the above Example, we should find that we had assigned the West Half of the table to "English books" and the East Half to "foreign books."

·-------------------· | old | old | | English | foreign | | books | books | |---------|---------| | new | new | | English | foreign | | books | books | ·-------------------·

We have, in fact, assigned the four Quarters of the table to four different Classes of books, as here shown.]

The Reader should carefully remember that, in such a phrase as "the x-Things," the word "Things" means that particular kind of Things, to which the whole Diagram has been assigned.

The Reader should not go on to the next Chapter until he is quite familiar with the blank Diagram I have advised him to draw.

He ought to be able to name, instantly, the Adjunct assigned to any Compartment named in the right-hand column of the following Table.

Also he ought to be able to name, instantly, the Compartment assigned to any Adjunct named in the left-hand column.

To make sure of this, he had better put the book into the hands of some genial friend, while he himself has nothing but the blank Diagram, and get that genial friend to question him on this Table, dodging about as much as possible. The Questions and Answers should be something like this:--

pg025 TABLE I.

·----------------------------------------· | Adjuncts | Compartments, or Cells, | | of | assigned to them. | | Classes. | | |------------|---------------------------| | x | North Half. | | x' | South " | | y | West " | | y' | East " | |------------|---------------------------| | xy | North-West Cell. | | xy' | " East " | | x'y | South-West " | | x'y' | " East " | ·----------------------------------------·

Q. "Adjunct for West Half?" A. "y." Q. "Compartment for xy'?" A. "North-East Cell." Q. "Adjunct for South-West Cell?" A. "x'y." &c., &c.

After a little practice, he will find himself able to do without the blank Diagram, and will be able to see it mentally ("in my mind's eye, Horatio!") while answering the questions of his genial friend. When this result has been reached, he may safely go on to the next Chapter.

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