A Guide to Cases of Possibility in Syllogism

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Case I: When we know that All X are Y

(i) No X is Y — not possible

(ii) Some X are Y — certain

(iii) Some X are not Y — not possible

(iv) All X are not Y — not possible

Case II: When we know that No X is Y

(i) All X are Y — not possible

(ii) Some X are Y — not possible

(iii) Some X are not Y — certain

(iv) All X are not Y — certain

Case III: When we know that Some X are Y

(i) All X are Y — possible

(ii) No X is Y — not possible

(iii) Some X are not Y — possible

(iv) All X are not Y — possible

Case IV: When we know that Some X are not Y

(i) All X are Y — not possible

(ii) No X is Y — possible

(iii) Some X are Y — possible

(iv) All X are not Y — possible

Case V: When we have no conclusion between X and Y

(i) All X are Y — possible

(ii) No X is Y — possible

(iii) Some X are Y — possible

(iv) Some X are not Y — possible

(v) All X are not Y — possible

Note: Since certainty means 100% possibility, all cases of certainty also qualify to be considered as possible.