Long ago Thucydides argued that a primary cause of the Peloponnesian War was the mutual fear that Athens and Sparta had of each other. Being afraid of Sparta, Athens kept increasing its armed might, which, in turn, convinced Athens that its fears were justified. Under these circumstances, according to Thucydides, a clash became inevitable. Evidently Thucydides was espousing a theory that an arms race and, by implication, war are self-sustaining processes of the sort now familiar to us in some self-catalyzing chemical reactions. There are, of course, other theories of international conflict; for example, those that place the sources of arms races and wars in economic or political dynamics. One may well ask how any such theories can be supported by evidence.
Arguments about "what causes what" can sometimes be resolved if they occur in a context where controlled observetins can be made. For instance, specific diseases are attributed to specific pathogenic organisms on the basis of expertmental results. Obviously, no such controlled observations can determine the "causes of wars." Ideas about such matters are backed by personal convictions rather than by objective evidence. No doubt such convictions sometimes stern from observations and their interpretations, but the line of reasonin which leads from hypothesis to observation to conclusion is never sharp. The mathematic-deductive method is spewcivically designed to sharpen this reasoning and to set clearer limits as to what may or must or may not be inferred from available evidence.
The foundation of the deductive-deductive method is the so-called mathematical model--a statement in mathematical language of the assumptions underlying a theory. If, for example, one speaks about levels of armaments, one has to specify how these levels are to be measured. More generally, if one espouses an idea that the "hostility" of one nation toward another elicits (or inhibits) reciprocal hostility, one must specify how "hostility" is manifested in measurable quantities. Also one must specify what one means by eliciting (or inhibiting) hostility.