ideas? And now we come to the more purely logical attempts to give a formal answer to the question: What is the connotation of the term “individual”?
To this question, viewed in this second way, the formal answer accepted by Duns Scotus, and traceable, of course, to Aristotle himself, seems indeed well applicable. A logical universal is capable of logical division into partes subjectivas. A logical individual is an object incapable of such division. This, as a merely formal definition, appears, I repeat, fair enough. In a very recent book, viz., in Schroeder’s admirable Algebra der Logik, in that very interesting chapter of the second volume which is devoted to the formal logic of the individual, a variation of this classic definition appears, in two or three different symbolic forms. The substance of Schroeder’s definition is, that by an individual, in the formal logic of extension, one means (1) a class, or “Gebiet,” different from zero, or from the “Null-Classe,” i.e. from a non-existent class; and then one also means (2) that this existent class is further incapable of being at once partially included within each of any two classes that exclude each other. Thus, if Socrates is an individual, he is conceived as incapable, as long as he exists, of being at once partially within and partially without the class defined as Athenians, or as incapable of being at once partially within each of the mutually exclusive classes, Athenian and Milesian. On the other hand, the class philosopher, which is not a logical individual, can exist as partly Athenian and partly not, or as partly Athenian and
