No doubt when it is said that the laws of thought are also laws of things, the laws are contemplated in what we have regarded as their secondary forms: A is A ; A is not not-A ; Everything is A or not-A. But even so it is difficult to give them any meaning regarded as real propositions. By “A” we mean “A” neither more nor less; and by “not-A” we mean “that which is not A but includes everything else.” The laws do not profess to give any 464 material knowledge, and their validity is in no way dependent upon material conditions.
The question raised in this section has in substance been already dealt with in rather more detail in special connexion with the law of identity.
421. Mutual Relations of the three Laws of Thought.—If the validity of the ordinary processes of immediate inference is granted, it can be shewn that the three laws of thought mutually involve one another.
Starting from the hypothetical proposition,
| If A is true then C is true | (i), |
we obtain as its (true) disjunctive equivalent,
| It cannot be that A is true and C is not true | (ii), |
and as its alternative equivalent,
| Either C is true or A is not true | (iii). |
If now for C, we write A we have the following set of equivalent propositions: