#help In conditional premises, if we change the binding in the second idea to something weaker and indefinite like "may", does that remove the necessary condition from the relationship altogether?

for example: If one is a Jedi, then one may be on the Jedi Council.

But this doesn't imply that everyone on the Jedi council is a Jedi. I think visually this would look like a Venn Diagram, but I am not sure if that is accurate or if this example is outside the scope of conditional relationships.

Maybe this is me overthinking it, but I am trying to find ways that I might confuse your advice.

If we have a conditional statement and there is an indefinite binding word present, I believe that makes said statement ineligible for a contrapositive.

Ex: Some Presidents are Democrats

it logically follows as well that "Some Democrats are Presidents". But it does not follow that "if one is not a President, then one is not a Democrat" or "if one is not a Democrat, then one is not a President".

This is even the case with other indefinites, such as: most, a few, almost all, etc.

Here we have bilateral sufficiency, with no possible contrapositive.

This kind of makes me realize as well that the conditional argument from before is different in that it has unilateral necessity. If one is a cat, then one MUST be a mammal. Because of the binary strength of necessity, we can create a contrapositive. Indefinites, however, are gradient.