The first formulation under which the question was asked represents, in my opinion rather characteristically, the type of question teachers should move towards as much as possible, either with the purpose of stimulating the student to reflect, or with the purpose of testing the condition of his knowledge. The best questions, for both purposes, are the ones that refer to the prediction of a specific fact, those where, after describing a given situation and a series of specific operations to the student, we ask what he would expect to find or to obtain if he were to perform them, or how he would act if he wanted to achieve a specific result given the circumstances.

Learned man, teachers, pedagogy scholars would refuse with horror the idea of taking part in three lectures a day, were it only for a week and only on topics they are deeply interested in. But they do not see how absurd it is, from an educational but also psychological and even hygienic point of view, to oblige students aged from 10 to 18 to remain riveted at least five hours a day for the whole year, as if there were no other means to attain the goals that should be reached in this way. For the result of this system of intensive culture - so similar to the barbaric nutrition system that is applied in the plain of Lombardy to obtain the exquisite goose liver - comes down to this, to cultivate in the students, especially in the most intelligent ones, such a repugnance for everything that is connected to school, or to what is taught in schools, that one might be glad that a large part of the school programmes is not worth being known.

Researches relating to the introduction and the changes in meaning of the technical terms of philosophy and logic present a striking contrast to analogous researches about the terminology of the physical sciences. Whereas, in the latter, the introduction of a new term, or of a new meaning for a term already in use, is generally due to the need of giving expression to some new idea or distinction, or of giving a name to some new object hitherto unknown; in the field of philosophy, on the contrary, the chief impulse to transformations of nomenclature arises from a totally different cause, viz.: from the inability of the terms referring to the more abstract ideas, which occur in philosophical researches, to retain for long the precise and well-defined meaning originally attributed to them, and from their tendency to become imbued with associations incompatible with the function assigned to them by those who introduced them. That is, the majority of the changes in philosophical nomenclature are due to the need of substituting, for expressions that have become unfit to express a given idea clearly and with sufficient definiteness, other expressions in which the same idea or the same distinction is characterised in a form less apt to give rise to confusions or misunderstandings. This is not the least important of the causes that combine to bring about the result that the contribution made by each philosopher, the advances and the improvements represented by his work, compared with that of his predecessors, are more difficult to recognise and appraise than the degree of originality of scientists properly so-called.

It is certainly not one of the least of the merits of the 'Leonardo' that it has established lines of communication and encouraged the exchange of ideas between exponents of philosophical studies belonging to the most diverse and distant intellectual fields - between logicians and estheticians, between moralists and economists, mathematicians and mystics, biologists and poets. Pending the possibility of a comparative examination of the results obtained, or prepared, by the development and exchange of ideas in all these various directions, it will not be irrelevant to summarize here in a schematic synopsis such of these results as relate to one of the most important lines of communication which the 'Leonardo' has helped to construct and keep in operation, that is, the line which joins the various domains of Pragmatism with those occupied and cultivated by the "mathematical logicians." A significant indication of the intimate connection between these two fields of philosophical research may be deduced from the fact that the sponsor of the denomination and concept of "Pragmatism" (Charles S Peirce) is himself likewise the initiator and promoter of an original trend in logico-mathematical studies. It is not, however, from the labours of the school of Peirce, but rather from those of the Italian school, headed by Peano, that I purpose here to take my material for the determination of what might be called the "pragmatic characteristics" of the new logical theories.

To discover differences and contrasts between things that resemble each other and to find points of similarity between dissimilar things are two kinds of mental activity which, although they appear opposite and contrary, are often found united. To employ them by turns is no less indispensable to progress in any kind of knowledge than are the two opposite movements of a piston to the rotation of the wheel which it sets in motion. Their relative importance, however, varies in the different fields of research, and as there are sciences, or phases of scientific development, in which the first predominates, so there are others in which the tendency prevails to distinguish or establish oppositions and contrasts among facts instead of connections or analogies.