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My logic prof told me that "some are" does NOT necessarily mean "some are not".... Ie. it could possibly mean "ALL are", but not necessarily (ie. we are not certain that all are) However, recently I was reading a book that was using Aristotelian logic and they said that "some are" entails "some are not". My former logic prof wrote this off as a careless/uninformed error. But is it in fact a difference in classical/modern definitions?

I tried to google search this, but couldn't find a clear answer.

  • It is possible that an author had a convention where "some are" presupposes "some are not", but that would be rather idiosyncratic. But there is a difference, although not on your issue, with some classical versions of the syllogistic. In modern logic "some" always implies existence, i.e. "some men are liars" means that male liars exist. However, in Mill's Logic it does not mean that, see In logic, do propositions default to true or false when objects in them do not exist? – Conifold Sep 9 at 22:00
  • @Conifold thank you! – Lily Sep 9 at 23:59
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What you want to research is Aristotle's 'Square of oppositions':

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As you can see above, 'Some S is P' is related to 'Some S is not P' by the relation of "subcontrariety." Two items are subcontraries if both may be true but both cannot be false. Hence, according to Aristotle, it is possible for both to be true, but it is not necessary. So, this means that 'Some S is P' does not imply 'Some S is not P.'

To understand Aristotle's position on these issues, you'll want to further investigate the square of opposition.

  • Thank you very much! I am familiar with the square of opposition, but I wasn't sure if it had been developed over time such that it wasn't 100% Aristotle's views anymore. So this clarification helps. :) – Lily Sep 10 at 0:00

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