Singular Predication and the Syllogism

Aristotle’s categorical syllogistic is the first formal deductive system in the history of formal sciences. Most parts or elements of the system are validated by modern (first-order) mathematical logic, but the system is quite limited in scope, as it is incapable of analyzing inferences other than the ‘figure syllogisms’ consisting of a couple of a-e-i-o premises and an a-e-i-o conclusion, containing three ‘moderately’ universal terms – terms that express neither a highest genus nor a lowest species – each of which is common to a different couple of propositions out of the three. Logicians in the following ages dealt with various questions concerning the addition of various (novel) logical forms into this limited system, among which are singular predications, i.e. categorical propositions with a singular term as subject, and the most common choice has been interpreting singular predications as universal predications. This paper tries to take a strictly formal perspective on the system of categorical syllogisms, and argues in detail for a much simpler and fairly effective assimilation or translation scheme for singular predications. The key to the proposed scheme is the preservation of the supposed inferential relation between opposite singular predications, namely contradiction. It is argued that the resulting singularized syllogistic moods, which are also validated by first-order logic (under its standard renderings of a-e-i-o and singular predications), promote in turn the mentioned type of treatment, since they call for the employment of two of the four subaltern moods of the system, disregarded by Aristotle, which are formally there.