The scientific experiement is a procedure in which an attempt is made to keep some aspects of an event constant, while the other (variable) aspects are studied. The pains scientists take in setting up their experiments and the skepticism that good scientists invariably show toward the results of most experiements indicate that they are aware of how difficult it is to keep all the conditions (except the chosen few to be studied) constant. (1, p. 133)

Where the man in the street (and the metaphysician) speak of causes and effects, the experimental psychologist is wary of assigning these roles to events. He speaks instead of independent and dependent variables. The independent variables are those which he himself manipulates or those which are not affected by the experiment, e.g., time; the dependent variables are those which are greado as the results of the experiment. In this way, one relates valuses of observed quantities (dependent variables) to values of manipulated quantities (independent variables). If these relations can be expressed mathematically, one has a compact statement -- a "result." (4, p. 142)

The paradigm of the cycle of scientific cognition -- namely the formulation of hypotheses, deduction of conclusions, testing the conclusions, acceptance, rejection, or modification of the hypotheses -- remains as valid in the social sciences as in the natural sciences and so makes the corresponding methodology (observation, induction, and deduction) as necessary in the former as in the latter. (D, p. 182)

The language of mathematics is eminently qualified to serve as the language of general systems theory, precisely because this language is devoid of content and expresses only the structural (relational) features of a situation. (F, p. 7)

If we follow the definition of "system" given above to its logical conclusion -- namely, as a specified set of entities and a set of relations among them -- then it would seem that the method of mathematical homology is the most natural foundation of a general systems theory. For an exact specification of relations is practically synonymous with a mathematical specification. The system is specified as a particular mathematical model and is seen at once to be isomorphic to all systems specified in terms of models of the same type. (C, p. 455)

Since the structure of ordinary logical operations has been shown to be strictly isomorphic to certain mathematical systems, e.g. Boolean algebra, with which certain networks of relays or electronic devices can in turn be made isomorphic. The existence of calculating and logically reasoning automata is the concrete consequence of these theoretical results. (A, pp. 94-95)

Now mathematics provides a way of developing a theory of such processes from a set of probabilities. There is a certain average probability that any two persons in a population will come in contact within a given interval of time. . . . The more conditions are specified, i.e., the more specifically the corresponding probabilities are defined, the more accurate will be the resulting model of the phenomenon. . . . The power and value of the mathematico-deductive approach is severly limited by the range of problems that can be solved in this way. (4, pp. 126-127)

It can be shown that

It is as legitimate to look for areas of inquiry in which an available tool is useful as to look for tools useful in a given situation. . . . This point is strongly disputed in some quarters. I have heard a philosopher of science whom I respect tell the sardonic parable of a man who went about the house looking for things to fix with only a screw driver. Having tightened all the loose screws, he found some protruding nails, whereupon he fetched a file and made a groove in the cap of each nail in order to use the screw driver. The barb is well aimed; still the abuse of any method does not invalidate its legitimate use. (3, pp. 59, 364)

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