the letters are altered.
The meaning of the above premises is difficult to interpret, but seems to be capable of expression in the following symbolic forms—
| A | = AB c ꖌ A b C, | (1) |
|---|---|---|
| De | = D e BC, | (2) |
| DE | = DE bc . | (3) |
As five terms enter into these premises it is requisite to treat their thirty-two combinations, and it will be found that fourteen of them remain consistent with the premises, namely
| AB cd E | a BCD e | ab C d E |
|---|---|---|
| AB cde | a BC d E | ab C de |
| A b C d E | a BC de | abc DE |
| A b C de | a B cd E | abcd E |
| a B cde | abcde . |
If we examine the first four combinations, all of which contain A, we find that they none of them contain D; or again, if we select those which contain D, we have only two, thus—
Hence it is clear that no A is D, and vice versâ no D is A. We might draw many other conclusions from the same premises; for instance—
or D and E never meet but in the absence of A, B, and C.
Fallacies analysed by the Indirect Method.
It has been sufficiently shown, perhaps, that we can by the Indirect Method of Inference extract the whole truth from a series of propositions, and exhibit it anew in any required form of conclusion. But it may also need to be shown by examples that so long as we follow correctly the almost mechanical rules of the method, we cannot fall into any of the fallacies or paralogisms which are often committed in