Logic, Mathematics, and Knowledge of Nature

Abstract

Even a cursory glance at the propositions of physics shows us that there is evidently a great difference in nature between them.¹ There are such propositions as “If a taut string is plucked, a sound is heard” and “If sunlight is made to pass through a glass prism, a coloured band interrupted by dark lines is seen on a screen behind it”, which can at any time be verified immediately by observation; but there are also such propositions as “There is hydrogen in the sun”, “The satellite of Sirius has a density of about 60,000”, “A hydrogen atom consists of a positively charged nucleus with a negatively charged electron rotating about it”, which cannot in any way be verified by immediate observation, but which can be advanced only on the basis of theoretical considerations and verified only by means of theoretical considerations. And this brings us to the burning question: what is the relative position of observation and theory in physics - and not just in physics but in science as such, for there is only one science, and wherever science is pursued, it is pursued in the final analysis by the same methods; only in physics everything is most clearly visible since it is the most advanced, the tidiest, the most scientific science.²