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I like the replacement of "All" with "Every" that Mauro ALLEGANZA has been systematically using. The change prevents the need for a difference in number agreement (is/are) in the propositions, which reduces the amount of interpretation of what is changing from one proposition to another; and this change effectively eliminates the suggestion of a whole having properties that its parts may not share. ("The whole is greater than the sum of its parts" is something Aristotle coined.)

I like the replacement of "All" with "Every" that Mauro ALLEGANZA has been systematically using. The change prevents the need for a difference in number agreement (is/are) in the propositions, which reduces the amount of interpretation of what is changing from one proposition to another; and this change effectively eliminates the suggestion of a whole having properties that its parts may not share. ("The whole is greater than the sum of its parts" is something that Aristotle made famous.)

May 5:

Corrected the statement that "exists" requires existential import to say instead that "every" requires existential import.

What I do not see in any of the responses here or in the common presentations of obversion and contraposition is any treatment of existential import (i.e., which quantifiers should evaluate as true/false when one entity or the other or both is empty). SEP makes a good argument that "exists" necessarily has existential import (i.e., "exists" is not satisfied when the subject is empty) and that the O-proposition must not have existential import.

None of these necessary clarifications of the meaning of the proposition types is apparent in the examples or definitions of obversion that is currently presented on Wikipedia, for example. So, the common presentations of this aspect of so-called Aristotelean logic are indeed woefully incomplete, just as I worried on Apr 30. (I say so-called because I understand from SEP that Aristotle did not endorse contraposition and wrote about a few forms of obversion, but mainly these transformations were added between the 12th and 14th centuries CE and were then taught as part of "Aristotelean logic".)

Regarding paraconsistent logics, if the logical system evaluates correctly when empty entities are included, then it is compatible with a Kleene logic. Kleene logics and Priest logics are operationally identical but have different interpretations: Kleene nulls are unknown or undetermined, while Priest nulls are contradictory or overdetermined. A Priest logic need not be explosive and would therefore be paraconsistent. Consequently, a logic that is valid in the presence of empty entities could be paraconsistent. However, I was really wondering if there might be a more substantial difference between "not" and "non-" that might have led to something more interesting; but, obviously, that wonder is forlorn.

What I do not see in any of the responses here or in the common presentations of obversion and contraposition is any treatment of existential import (i.e., which quantifiers should evaluate as true/false when one entity or the other or both is empty). SEP makes a good argument that "every" necessarily has existential import (i.e., "every" is not satisfied when the subject is empty) and that the O-proposition must not have existential import.

None of these necessary clarifications of the meaning of the proposition types is apparent in the examples or definitions of obversion that are currently presented on Wikipedia, for example. So, the common presentations of this aspect of so-called Aristotelean logic are indeed woefully incomplete, just as I worried on Apr 30. (I say so-called because I understand from SEP that Aristotle did not endorse contraposition and wrote about a few forms of obversion, but mainly these transformations were added between the 12th and 14th centuries CE and were then taught as part of "Aristotelean logic".)

Regarding paraconsistent logics, if the logical system evaluates correctly when empty entities are included, then it is compatible with a Kleene logic. Kleene logics and Priest logics are operationally identical but have different interpretations: Kleene nulls are unknown or undetermined, while Priest nulls are contradictory or overdetermined. A Priest logic need not be explosive and would therefore be paraconsistent. Consequently, a logic that is valid in the presence of empty entities could be paraconsistent. However, I was really wondering if there might be a more substantial difference between "not" and "non-" that might have led to something more interesting; but, obviously, that wonder is forlorn.

May 5:

Corrected the statement that "exists" requires existential import to say instead that "every" requires existential import.