it is true that the outcome of Mathematics in Psychology has been small. And it is unfortunately true that the inroads of Mathematicians into the field of Psychology has for the most part resulted in a tangle of more or less meaningless formulæ; but the examples given by Dr. Münsterberg to show the absurdity of Mathematics in Psychology are not wholly convincing. He says, for instance (p. 52), "We know, if two quantities are equal to a third, they are equal to each other. Now the sensation from a sound stimulus of 500 vibrations a second, is like the sensation of 500.2; in the same way the sensation of 200.4 vibrations is like that of 200.2; consequently the sensation of 500 vibrations a second is like that of 500.4 — which experiment shows to be false." But this argument hinges on the use of the word 'like,' which in German also means equal (gleich): when the psychologist applies the word 'like' to sensations it is simply as a shorthand expression for the phrase, 'Not to be distinguished from one another in respect to some quality.' Inserting this qualification in the place of the word 'like' in the above reasoning, the logic of words and facts agree.
Having determined the problem of Psychology and ruled out unproductive methods, Dr. Münsterberg discusses the methods that he considers fruitful, and first of all self-observation. It will scarcely surprise those who have read the article on the "Time-sense" in the Beiträge to find that a very broad scope is given to the method of introspection. The rejection of self-observation as an independent method in Psychology is held to spring from the theory which regards consciousness as made up of contents, and activities related to these contents; as an activity cannot make itself the object of its own action, it can only be examined in the more or less deceptive memory image. Against this, the author holds that consciousness is the content of consciousness; that attention is not an activity which determines states of consciousness, but is in itself a state of consciousness composed of feeling of muscular tension joined to the consciousness that the sensation or mental images are rising or sinking, and growing dimmer or clearer.
Self-observation consists in these feelings, along with the directive idea that the discrimination and retention involved in them are necessary to scientific purposes.
Attention, discrimination, and comparison, and the other so-called activities of consciousness, are for the most part open to observation as being made up of changes in conscious states along with a certain integrating play of associative elements. Dr. Münsterberg grants that direct self-observation is not always practicable: the mental phenomena may be too dim or fleeting, or they may be overpowering as in wrath (p. 168), but of the sum total of those psychical processes, he finds but a scanty number which cannot be observed in transitu,
