There are certain purely logical principles which are useful in regard to structure. When we are dealing with inferred entities, as to which, as explained in Part II., we know nothing beyond structure, we may be said to know the equations, but not what they mean: so long as they lead to the same results as regards percepts, all interpretations are equally legitimate. Let us take an example. Suppose we have a set of propositions about an electron which we will call . According to the subject-predicate logic, and according to the view that matter is a substance, there is a certain entity which is mentioned in all statements about this electron. According to the view which resolves an electron into a series of events, the propositions in question will be differently analyzed. Assuming a certain schematic simplicity, we might set the matter out as follows: there is a certain relation which sometimes holds between events, and when it holds between and , and are said to be events in the biography of the same electron. If belongs to the field of , "the electron to which belongs" will mean the relation with its field limited to terms belonging to the -family of ; and the -family of consists of together with the terms which have the relation to and the terms to which has the relation . "This electron" will mean "the electron to which this belongs." "An electron" will mean "a series such that there is an such that the series is the electron to which belongs." In order to mention some particular electron, we must be able to mention some event connected with it, e.g. the scintillation when it hits a certain screen. Thus, instead of saying "the event happened to the electron " we shall say "the event happened to the electron to which happened," or, more simply, " belongs to the -family of ." The formal properties of the propositional function " belongs to the -family[Pg 288] of " ( being constant) are the same as those of " belongs to the electron ." If we want any two electrons to be mutually exclusive, in the sense that no event can happen to both, we can insure it by assuming that if has the relation (or the converse relation) to both and , then belongs to the -family of . If we do not want this, we do not make this assumption about . It is because of the identity in formal properties that the one propositional function can be substituted for the other. Whenever we suggest a new view as to structure, we have to make sure that it does not falsify any of the old formulæ, though it may give them a new interpretation.