V GROWTH IN TIME OF THE TOTAL ORGANISM I7I 



fall in line by taking into account complicating factors, as for example air 

 resistance, which in turn become amenable to exact law. Furthermore, Galileo's 

 law leads to Newton's law, the derivation of Kepler's laws of planetary motion 

 to the development of modern astronomy and mechanics in general, and from 

 classical mechanics eventually to relativity theory and modern physics. 



What Galileo and his colleagues did was to establish a mathematical inodel, that 

 is, a conceptual construct representing allegedly "essential" factors in the process 

 in question, and allowing deductions which can be tested in experiment or 

 observation. The law refers to an "ideal" case, approached in certain experimental 

 situations (cannon-balls and, still better, bodies falling in vacuo), but may be very 

 unsatisfactory in others. Galileo's law does not provide a very satisfactory mathe- 

 matical description for falling leaves, feathers, or cats. The same applies to any 

 law of physics. There is, strictly speaking, no ideal gas, no absolutely rigid body, 

 etc., and the respective laws refer to "ideal" cases or cases which experimentally 

 have been made nearly ideal. The essential feature of a model is that it forms the 

 basis of a hypothetico-deductive system yielding "dividends" (to use an illustrative 

 phrase of Rapoport, 1955b), that is, results mathematically implied in the model 

 but not ascertainable and amenable without the logical machinery. By mathema- 

 tical reasoning and insertion of appropriate conditions consequences can be 

 derived which explain a range of observed phenomena and even predict still 

 unobserved ones. (The classic exposition on the nature of scientific theory is still: 

 Kraft, 1926.) 



A first consequence from the nature of scientific theory is that the relation 

 between observation and law is by no means simple. If the alleged law is contra- 

 dicted by observation, it naturally has to be discarded. However, mere fit of 

 observed data does not prove a mathematical expression to be a law of nature. 

 Particularly in complicated phenomena (p. 174), good fit may be obtained by 

 formulas which are without meaning, or by different formulas. On the other 

 hand, unsatisfactory fit of certain observations does not necessarily disprove the 

 model and law. It may be that complicating factors have to be introduced as in 

 the case of Galileo's law and air resistance; that the original model was too 

 simple and needs amendment, as in the case of Bohr's model of the atom which 

 allowed deduction of the spectrum of hydrogen but was not adequate for more 

 complicated atoms; or that the initial theory eventually becomes a special case 

 in a more general one as was the case with classical mechanics compared to the 

 theory of relativity. In such instances, the original theory is not exactly refuted but 

 rather turns out to be a special case, valid under certain restrictive conditions, of 

 some more general theoretical framework. It is indeed the criterion of a good 

 scientific theory that it leaves room for further developments, in contrast to "cover- 

 all" concepts or panchresta (Hardin, 1956) such as the entelechy of the vitalists, 

 natural selection {cf. Bertalanffy, 1932, p. 72; 1952, p. 89^), etc. which "explain" 

 everything and for precisely this reason nothing. 



The transition from simple to more complicated cases and corresponindgly to 

 more elaborate theories is the progress of science. Here, like the beginner's luck 

 in a gamble, accident often plays an important role. Mendel was able to state 

 his basic laws because he happened to cross peas which represented a schematic 



Literature p. 253 



