MODERN CONCEPTS IN PHYSICS LANGMUIR 229 



mathematical form. We have no guarantee ^vhatever that nature is 

 so constructed that it can be adequately described in terms of ine- 

 chanicid or electrical models; it is much more ])robable that our most 

 fundamental relationships can only be expressed mathematically, if 

 at all. 



In analyzing our attempts to describe nature, we have discussed 

 concepts, models and mathematical theories. We iind that they are 

 all alike in that they represent hunum abstractions which are found 

 convenient in describing nature. Going back a step further we must 

 recognize that words themselves constitute elementary concepts. 

 They are, it is true, much more vaguely defined than our concepts of 

 physics and chemistry, but qualitatively they are very much like the 

 latter; in fact, most of our misunderstandings in science arise from 

 assigning reality to concepts wiiose main reason for existence is the 

 fact that they are represented by a word. Logically we should aim 

 to deline our words in terms of operations. We should have in mind 

 speciHcatioiis by which we can test whether or not the word is prop- 

 erly applicable. 



The progress of science depends largely upon (1) giving to words 

 meanings as precise as possible; (2) dehnition of concepts in terms 

 of operations; (3) development of models (mechanical or mathe- 

 matical) which have properties analogous to those of phenomena 

 which we have observed. 



MEANINGLESS QUESTIONS 



A great deal of time and eflfort is wasted in scientific circles as 

 well as in the world at large through failure to give sufliciently 

 definite or useful definition of words and concepts. Bridgman em- 

 phasizes this in connection with his discussion of " meaningless 

 questions." 



In some cases questions fail to have meaning because of the more 

 or less inherent fuzziness of the concepts involved. For example, 

 if we compare two trees of about the same size it may have no 

 meaning to ask which tree has the larger diameter, for no one has 

 defined the diameter of a tree with tlie necessary precision. 



A more important class of meaningless questions arises when 

 there are no conceivable operations that could be performed to 

 arrive at a decision. For example, what is the meaning of the 

 question, "Would the United Stales have entered the World War 

 if the Lusitania had not been sunk? " Such a question may be a 

 good subject for a school debating society, but no one is apt to 

 think that the question has thereby been answered. 



A study of meaningless questions may serve a very useful purpose 

 in science. A statement that a certain question has no meaning may 

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