and (ζ) by (2), so that there remain only
| ABC | (α) |
|---|---|
| a BC | (ε) |
| ab C | (η) |
| abc . | (θ) |
To describe any term under the conditions of the premises (1) and (2), we have simply to draw out the proper combinations from this list; thus, A is represented only by ABC, that is to say
| A | = ABC, | |
|---|---|---|
| similarly | c | = abc . |
For B we have two alternatives thus stated,
and for b we have
When we have a problem involving four distinct terms we need to double the number of combinations, and as we add each new term the combinations become twice as numerous. Thus
| A, B | produce | four combinations | |
|---|---|---|---|
| A, B, C, | " | eight | " |
| A, B, C, D | " | sixteen | " |
| A, B, C, D, E | " | thirty-two | " |
| A, B, C, D, E, F | " | sixty-four | " |
and so on.
I propose to call any such series of combinations the Logical Alphabet. It holds in logical science a position the importance of which cannot be exaggerated, and as we proceed from logical to mathematical considerations, it will become apparent that there is a close connection between these combinations and the fundamental theorems of mathematical science. For the convenience of the reader who may wish to employ the Alphabet in logical questions, I have had printed on the next page a complete series of the combinations up to those of six terms. At the very commencement, in the first column, is placed a single letter X, which might seem to be superfluous. This letter