pg050 CHAPTER III. _REPRESENTATION OF TWO PROPOSITIONS OF RELATION, ONE IN TERMS OF x AND m, AND THE OTHER IN TERMS OF y AND m, ON THE SAME DIAGRAM._ The Reader had better now begin to draw little Diagrams for himself, and to mark them with the Digits "I" and "O", instead of using the Board and Counters: he may put a "I" to represent a _Red_ Counter (this may be interpreted to mean "There is at least _one_ Thing here"), and a "O" to represent a _Grey_ Counter (this may be interpreted to mean "There is _nothing_ here"). The Pair of Propositions, that we shall have to represent, will always be, one in terms of x and m, and the other in terms of y and m. When we have to represent a Proposition beginning with "All", we break it up into the _two_ Propositions to which it is equivalent. When we have to represent, on the same Diagram, Propositions, of which some begin with "Some" and others with "No", we represent the _negative_ ones _first_. This will sometimes save us from having to put a "I" "on a fence" and afterwards having to shift it into a Cell. [Let us work a few examples. (1) "No x are m'; No y' are m". Let us first represent "No x are m'". This gives us Diagram a. Then, representing "No y' are m" on the same Diagram, we get Diagram b. pg051 a b ·---------------· ·---------------· |(O) | (O)| |(O) | (O)| | ·---|---· | | ·---|---· | | | | | | | | |(O)| | |---|---|---|---| |---|---|---|---| | | | | | | | |(O)| | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· (2) "Some m are x; No m are y". If, neglecting the Rule, we were begin with "Some m are x", we should get Diagram a. And if we were then to take "No m are y", which tells us that the Inner N.W. Cell is _empty_, we should be obliged to take the "I" off the fence (as it no longer has the choice of _two_ Cells), and to put it into the Inner N.E. Cell, as in Diagram c. This trouble may be saved by beginning with "No m are y", as in Diagram b. And _now_, when we take "Some m are x", there is no fence to sit on! The "I" has to go, at once, into the N.E. Cell, as in Diagram c.