  This has too little structure to be particularly useful, and so it is not commonly used. According to Alonzo Church, this modern view probably originated sometime in the late nineteenth  century.[1]  This representation of the four forms is now generally accepted, except for qualms about the loss of subalternation in the left-hand column. Most English speakers tend to understand ‘Every S is P’ as requiring for its truth that there be some Ss, and if that requirement is imposed, then subalternation holds for affirmative propositions.  Every modern logic text must address the apparent implausibility of letting ‘Every S is P’ be true when there are no Ss. The common defense of this is usually that this is a logical notation devised for purposes of logic, and it does not claim to capture every nuance of the natural language forms that the symbols resemble. So perhaps  ‘∀x(Sx → Px)’ does fail to do complete justice to ordinary usage of ‘Every S is P’, but this is not a problem with the logic.  If you think that ‘Every S is P’ requires for its truth that there be Ss, then you can have that result simply and easily: just represent the recalcitrant uses of ‘Every S is P’ in symbolic notation by adding an extra conjunct to the symbolization, like this:  ∀x(Sx  → Px)  &amp;  ∃xSx.