D O C . 4 6 5 P L A N N E D L E C T U R E B U E N O S A I R E S 7 2 5 The fact that a concept in the presence of experience, even if originated from ex- perience, has a certain logical independence is appreciated by considering extrasci- entific thought. The observation of the existence of similar objects has given rise to the notion of number, but has not created it. In fact, people in some cultures have not gone any further than an understanding of only the smallest of numbers. Returning to the ideas and fundamental laws of physics, it is easy to show that starting from the facts of experience there is no fixed road taking us back to those ideas and fundamental laws. Let us consider, for example, the laws of motion of which classical astronomy rests. Using logical and mathematical methods we can deduce from Kepler’s laws Newton’s law on the [inverse][4] proportionality of force on the square of the distances.[5] Kraft auf mathematisch-logischem Wege abzuleiten. Aber Galileis Setzung, dass die Kraft der Beschleunigung proportional sei, entstammt selbst unmittelbar keiner Erfahrung, sondern ist logisch betrachtet eine freie Festsetzung. Sie ent- stammt der intuitiv gewonnenen Erkenntnis, dass die Phänomene der Bewegung sich dadurch besonders einfach auffassen lassen, dass man in der Beschleunigung dasjenige Grundphänomen sieht, für welches man gesetzmässige Ursachen zu su- chen hat. Dass dies nicht an und für sich selbstverständlich bzw. notwendig ist, er- kennt man an der Geschichte der Mechanik von Galilei. Man wird sich der logischen Willkür dieses Gesichtspunktes neuerdings auch besonders dadurch be- wusst, dass die allgemeine Relativitätstheorie[6] has found it necessary to modify it. Not only are fundamental laws the result of an act of imagination that cannot be controlled, but so are their ingredients, the ideas derived from those laws. Thus, the concept of acceleration was in itself an act of free creation of the mind which even if supported by the observation of the motion of solid bodies, assumes as a precon- dition nothing less that the infinitesimal calculus. It follows from here that fundamental laws can be refuted not only by showing that the consequences attributed to them are wrong, inexact, or not generally appli- cable, but also can be refuted by showing that the concepts introduced for them do not suit the observed facts. In this respect the history of modern theoretical physics offers beautiful exam- ples. In the kinetic theory of heat, temperature is an elementary concept that stands out in a discussion on fundamental relations in that science. The development of thermodynamics showed that, in a body isolated from exchanges with its surround- ings for any length of time, energy fluctuates permanently around a fixed average value the smaller the portion of the body considered, the larger the fluctuations. If we observe parts that are sufficiently smaller, a precise distinction between its ther- mal and mechanical energy loses its meaning. The apparent incongruence of all