A second important feature of the schematics is that they accommodate numerically specific quantifications and easily display solutions to what would otherwise involve very complicated patterns of reasoning. Indeed, my original motive for developing the schematics was to display how the Aristotelian syllogism becomes infinitely more powerful when the inherent numerical foundation of its quantifiers is made explicit and developed, and it is to this expanded version that we turn now.
Although the quantifier, "some," has long been interpreted to mean "at least one," Aristotle did not make that claim. But even if he had, I think it would not have led to a numerical interpretation of quantification because, on the one hand, for him number had to do with plurality while the unit—one—is singular. But probably of more consequence is the fact that there is no zero in the Greek (or Roman) numerals. Indeed it was in the Middle Ages when the concept of zero first found its way into Europe. So without even having the concept there was no way for a quantifier to be articulated in terms of zero; and then after the zero concept arrived the logic system that had stood for centuries without it continued without being successfully questioned in that regard.