I have thus found that there are altogether fifteen conditions or series of conditions which may govern the combinations of three terms, forming the premises of fifteen essentially different kinds of arguments. The following table contains a statement of these conditions, together with the numbers of combinations which are contradicted or destroyed by each, and the numbers of logically distinct variations of which the law is capable. There might be also added, as a sixteenth case, that case where no special logical condition exists, so that all the eight combinations remain. +---------+-------------------------------+-----------+------------+ | | | Number of | Number of | |Reference| Propositions expressing the | distinct |combinations| | Number. | general type of the logical | logical |contradicted| | | conditions. |variations.| by each. | +---------+-------------------------------+-----------+------------+ | I. | A = B | 6 | 4 | | II. | A = AB | 12 | 2 | | III. | A = B, B = C | 4 | 6 | | IV. | A = B, B = BC | 24 | 5 | | V. | A = AB, B = BC | 24 | 4 | | VI. | A = BC | 24 | 4 | | VII. | A = ABC | 24 | 3 | | VIII. | AB = ABC | 8 | 1 | | IX. | A = AB, *a*B = *a*B*c* | 24 | 3 | | X. | A = ABC, *ab* = *ab*C | 8 | 4 | | XI. | AB = ABC, *ab* = *abc* | 4 | 2 | | XII. | AB = AC | 12 | 2 | | XIII. | A = BC ꖌ A*bc* | 8 | 3 | | XIV. | A = BC ꖌ *bc* | 2 | 4 | | XV. | A = ABC, *a* = B*c* ꖌ *b*C | 8 | 5 | +---------+-------------------------------+-----------+------------+ There are sixty-three series of combinations derived from self-contradictory premises, which with 192, the sum of the numbers of distinct logical variations stated in the third column of the table, and with the one case where there are no conditions or laws at all, make up the whole conceivable number of 256 series.