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Any reliance placed on the inconceivableness of the contradictory as a criterion must lie, and indeed according to this theory does lie, in the way in which it has been produced, and this is the essential thing to be considered.
The criterion has its value because it is the effect, as supposed, of an experience infinitely greater than that of one individual: and thus when Mill objected that if the test got its value from experience, we had better appeal directly to experience, it was replied that the large experience represented by the test was inaccessible to the individual.
It is easy to see that the maximum logical worth of the test would be that of an induction drawn from all the instances which have occurred in the experience of the race, supposing these could be presented to one mind which would draw the inference. The induction has registered its conclusion automatically in the physical organism, and, through that, in the mind. The race has come to believe that all A must be B, because the constant experience through its history of instances of A which were B has so modified the organs that they cannot be used for thinking A except as B.
It has been inadvertently assumed that in axioms such a belief has been produced in one way only.
From the very assumptions about biological processes which this theory makes, it is clear that the sufficient and necessary condition that the belief 'all A must be B' should be produced, is not that every A should be B in the nature of things, but only that those instances of A which have acted on the organs of perception should have been B. And thus the conviction that A must be B could be perfectly well produced in the automatic way supposed, in a case where A was not necessarily B. The limitation of our experience to a certain species of A which would be necessary for this, would correspond to known facts. For
