CERTAIN UNITIES IN SCIENCE
By Professor R. D. CARMICHAEL
UNIVERSITY OF ILLINOIS
THAT the several sciences taken as a whole form one science is a proposition which has often been urged, sometimes apparently as an article of faith and sometimes as a reasoned conclusion. To an individual who holds, with nearly religious fervor, the doctrine that the universe is one and that the truth of science asymptotically approaches the absolute truth about the universe, there can be no doubt of the oneness of all science; there is no room or opportunity, except through error, for that diversity which destroys the oneness of the whole. To an individual of such an outlook it may be almost or quite an article of faith that all science is one. But to him whose universe is not so tidy, in whose thought there is the ever-present possibility that after all we may be building on insecure foundations, the assertion of the unity of science can be made only on a reasoned analysis of its characteristics and on the established fact of the presence in it of such dominant qualities as bind the whole indissolubly into one. To exhibit such elements and to show that they have such qualities is a task of large proportions, for beyond the possible achievements of a single paper. Our purpose is the more modest one of exhibiting certain common elements, certain unities, in science as a whole and of partially analyzing the way in which their presence affects the character of scientific truth.
The unities in science, however far-reaching, can never be absolute. Whatever is common to two domains of knowledge appears in each of them colored by the dominant light of the particular discipline. Per haps the most obvious unity of all is that of experimentation and observation; its presence in natural science is almost universal. But in mathematics it is partially obscured from view by a universal insistence upon logical connection in exposition, so that the processes of experimentation and observation which were employed in discovery are not in evidence in the finished product. In the case of empirical theorems stated as conjectures (such as have occurred frequently in the history of the theory of numbers) we have the most notable partial exception to what is the general rule. The results conjectured are genuine empirical theorems. Mathematics differs from the natural sciences in refusing to accept these conjectured theorems without a logical demonstration. In thousands of cases it has been observed,
