Chapter 35
_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'.
[For example, we might say "Let Univ. be 'books'"; and we might imagine the Diagram to be a large table, assigned to all "books."]
[The Reader is strongly advised, in reading this Chapter, _not_ to refer to the above Diagram, but to draw a large one for himself, _without any letters_, and to have it by him while he reads, and keep his finger on that particular _part_ of it, about which he is reading.] pg023 Secondly, let us suppose that we have selected a certain Adjunct, which we may call "x," and have divided the large Class, to which we have assigned the whole Diagram, into the two smaller Classes whose Differentiæ are "x" and "not-x" (which we may call "x'"), and that we have assigned the _North_ Half of the Diagram to the one (which we may call "the Class of x-Things," or "the x-Class"), and the _South_ Half to the other (which we may call "the Class of x'-Things," or "the x'-Class").
[For example, we might say "Let x mean 'old,' so that x' will mean 'new'," and we might suppose that we had divided books into the two Classes whose Differentiæ are "old" and "new," and had assigned the _North_ Half of the table to "_old_ books" and the _South_ Half to "_new_ books."]
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").
[For example, we might say "Let y mean 'English,' so that y' will mean 'foreign'", and we might suppose that we had subdivided "old books" into the two Classes whose Differentiæ are "English" and "foreign", and had assigned the North-_West_ Cell to "old _English_ books", and the North-_East_ Cell to "old _foreign_ books."]
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.
[For example, we might suppose that we had subdivided "new books" into the two Classes "new _English_ books" and "new _foreign_ books", and had assigned the South-_West_ Cell to the one, and the South-_East_ Cell to the other.]
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.
[Thus, if we say "Let Univ. be 'books'," we mean that we have assigned the whole Diagram to "books." In that case, if we took "x" to mean "old", the phrase "the x-Things" would mean "the old books."]
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.
pg026