them, the medievals invented the following Latin rhyme: adfirmat, negat , sed universaliter ambae; firmat, negat , sed particulariter ambae. It affirms that and are not neither both true nor both false in each of the above cases. The same applies to and . While the first two are universal statements, the couple / refers to particular ones. The Square of Oppositions was used for the categorical inferences described by the Greek philosopher Aristotle: conversion, obversion and contraposition. Each of those three types of categorical inference was applied to the four Boethian logical forms: , , , and . The problem of existential import Subcontraries ( and ), which medieval logicians represented in the form 'quoddam est ' (some particular is ) and 'quoddam non est ' (some particular is not ) cannot both be false, since their universal contradictory statements (no is / every is ) cannot both be true. This leads to a difficulty firstly identified by Peter Abelard (1079 – 21 April 1142). 'Some is ' seems to imply 'something is ', in other words, there exists something that is . For example, 'Some man is white' seems to imply that at least one thing that exists is a man, namely the man who has to be white, if 'some man is white' is true. But, 'some man is not white' also implies that something as a man exists, namely the man who is not white, if the statement 'some man is not white' is true. But Aristotelian logic requires that one of these statements (more generally 'some particular is ' and 'some particular is not ') is necessarily true, i.e., they cannot both be false. Therefore, since both statements imply the presence of at least one thing that is a man, the presence of a man or men is followed. But, as Abelard points out in the Dialectica, surely men might not exist? For with absolutely no man existing, neither the proposition 'every man is a man' is true nor 'some man is not a man'. Abelard also points out that subcontraries containing subject terms denoting nothing, such as 'a man who is a stone', are both false. If 'every stone-man is a stone' is true, also its conversion per accidens is true ('some stones are stone-men'). But no stone is a stone-man, because neither this man nor that man etc. is a stone. But also