Chapter XII

we saw that the mind can at successive moments _mean the same_, and that it gradually comes into possession of a stock of permanent and fixed meanings, ideal objects, or conceptions, some of which are universal qualities, like the black and white of our example, and some, individual things. We now see that not only are the objects permanent mental possessions, but the results of their comparison are permanent too. The objects and their differences together form an immutable system. _The same objects, compared in the same way, always give the same results;_ if the result be not the same, then the objects are not those originally meant.

This last principle, which we may call the _axiom of constant result_, holds good throughout all our mental operations, not only when we compare, but when we add, divide, class, or infer a given matter in any conceivable way. Its most general expression would be "_the Same operated on in the same way gives the Same_." In mathematics it takes the form of "equals added to, or subtracted from, equals give equals," and the like. We shall meet with it again.

The next thing which we observe is that _the operation of comparing may be repeated on its own results_; in other words, that we can think of the various resemblances and differences which we find and compare them with each other, making differences and resemblances of a higher order. _The mind thus becomes aware of sets of similar differences, and forms series of terms with the same kind and amount of difference between them, terms which, as they succeed each other, maintain a constant direction of serial increase._ This sense of constant direction in a series of operations we saw in