Page:Schlick - Gesammelte Aufsätze (1926 - 1936), 1938.djvu/235

 logically interconnected, i. e. every single one of them can be deduced from (= is logically contained in) certain others.

It is possible to select a group of propositions such that all other propositions of the system can be derived from them the laws of nature which form this group are called axioms. The choice of axioms is arbitrary within certain definite limits, which is to say that there are many ways of singling out a set of axioms from which all the other propositions can be deduced; there are consequently, many different forms in which the system can be represented; a law of nature which plays the role of an axiom in one of these forms appears as a derivative proposition in another one. These different forms differ only in their outward appearance, not in their essential nature, for all of them are expressions of the same facts in the world. It is a matter of convenience, economy and — last, not least — beauty to make the set of axioms as small and as simple as possible — which means that ordinarily of all the possibilities of choice that one is preferred which makes the set of axioms consist of a minimum of simple propositions. (The two postulates of simplicity and of the smallest number are not always compatible, by the way, but we are not concerned with these questions here, which are sometimes considered to form the subject of a special logical discipline called "axiomatics". But it is important to keep in mind that the word "axiom" is used in a relative, not in an absolute way. In the old systems of philosophy, that of Spinoza for example, "axiom" meant a self-evident principle forming the natural and necessary formulation of all other propositions, but we do not attach this philosophical dignity to the word any longer, it is, in principle, a matter of arbitrary selection wether a certain law of nature plays the part of an axiom or is regarded as derived from a set of axioms. The only thing that counts in the mutual logical relation between the propositions of the system, the possibility of deriving each one from a set of others.)

Outwardly the propositions appear as sentences composed of certain words or as formulae composed of figures and letters representing measured quantities. Now, all the work of the theoretical physicist is done entirely on his paper, all his calculations are done by jotting down long rows of symbols and shifting them about, according to the rules of mathematics. As long as he is really only calculating, i.e. considering the logical relations between