What happens if you replace the statements of the Traditional Square of Opposition with "percentages of the subject term"? Do all the relationships from the Traditional Square of Opposition still apply?

A: 100% of x have y. -- ("All dogs have fur.")

E: 0% of x have y. -- ("Not some dogs have fur.")

I: >0% of x have y. -- ("Some dogs have fur.")

O: <100% of x have y. -- ("Not all dogs have fur.")

Square of Percentages

Traditional Square of Opposition

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    Yes: the basic relation of contradiction still holds: 100% = not < 100% and 0% = not > 0%. – Mauro ALLEGRANZA May 2 '18 at 18:27
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    The A proposition is indeed 100%. The E proposition is indeed 0%. The I proposition expresses the values 1% up to 99%. The O proposition expresses a negative claim & atleast 1% up to 99% does not apply. Your NOT ANY Is incorrect. To say not any is still vague & can be either an E proposition OR an O proposition depending on the context. Not all men are married does not mean no men are married. Not all birds are reptiles means no birds are reptiles. Note the proposition No birds are reptiles does not imply some birds are reptiles. – Logikal May 2 '18 at 18:30
  • @Logikal "The I proposition expresses the values 1% up to 99%" No, else there'd be no subalternation. "(A proposition) ⇒ (I proposition)" and "(E proposition) ⇒ (O proposition)". – Geremia May 6 '18 at 4:51
  • @Green is, please explain why you think this. If something is 100% true then there is at least one subject that a proposition hold the same value which is an I proposition. If all women are humans then some women are humans must also be true. That is subalternation. The universal makes the particular true as well. – Logikal May 6 '18 at 5:07
  • @Geriemia, please see my comment above with the wrong name Green is.. The auto correct change my spelling of your name. The idea I am expressing is that some can not be 100% --That is what All expresses. if both quantifiers expressed the same amount confusion would be possible. – Logikal May 6 '18 at 13:31

The statement "some are" means "there exists at least one". The statement "there exists at least one" is consistent with the statement "all are". This consistency between Some and All has to be accounted for. Thus the I statement, "Some S are P" becomes: "The ratio of subject S, in relation to predicate P, (1) is larger than zero percent, but (2) is less than or equal to one hundred percent".

A similar adjustment appears in the O statement, "Some S are not P". The statement becomes, "The ratio of subject S, in relation to predicate P, (1) is smaller than one hundred percent, but (2) is larger than or equal to zero percent".

The zero and one hundred points are the E and A statements.

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