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I am reading about categorical syllogism in Copi's Introduction to Logic. I was wondering what differences are between the following statements:

  • No S is P.
  • All S are not P.

Am I correct that

  • Their quantities are both universal, instead of particular?
  • Their qualities are both negative, instead of affirmative?
  • they mean the same?

Does the book answer my question somewhere?

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  • Normally(?) they're interchangeable, though "hyperintensionally" they might not be the same. Or, then, intuitionist negation theory might not support the interchange, for example.
    – Kristian Berry
    Sep 25 at 11:55
  • See Aristotle's Logic and see also this post. Yes, they are both Universal.
    – Mauro ALLEGRANZA
    Sep 25 at 12:09
  • @KristianBerry can you elaborate?
    – Tim
    Sep 25 at 12:45
  • @Mauro do they mean the same? Why are the two links in your comment the same?
    – Tim
    Sep 25 at 12:46
  • If some S is P, then, "No S is P," is false. So classically/per the opposition-square, at least, the truth condition of, "No S is P," is the same as of, "All S are not P." Or at least that's my understanding of the matter, qualified by reasons to divest certain vectors of the square of existential import, etc. (again e.g. intuitionism's insight that the absence of a term for the presence of some X is not absolutely the same as the presence of a term for the absence of that X).
    – Kristian Berry
    Sep 25 at 13:17

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