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Clarification needed for "some"

  1. Sep 14, 2014 #1
    In mathematical logic, can "some" refer to "one".
    Namely can you prove a 'some … satisfy Property A', by proving there exists one that satisfies property A. The term just seems really ambiguous.
     
  2. jcsd
  3. Sep 14, 2014 #2

    Simon Bridge

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    If we say that

    1. all people are either men or women,
    2. and that not all people are men,

    then we can conclude

    3. some people are women.

    You mean like that?

    Here statement 3 is basically another way of writing statement 2. It's a tautology.

    You are correct - if there were only one woman in the group "people" then statement 3 applies.
    It reads the same as "there is at least one".

    You are also correct that it is informal - there are contexts where you want to distinguish between "some", "several" and "many". But usually you will want to be more careful than that. Where there is danger of confusion, say what you mean: if you mean "at least one" then say so.

    It usually gets clearer if you write it out in math symbols:
    P := people, M := men, W := women.
    $$\text{if}\; P=\{M,W\}\land |M|<|P|\; \text{then}\; |W|>0$$... or something like that.
     
    Last edited: Sep 14, 2014
  4. Sep 15, 2014 #3
    Thanks Simon.
     
  5. Sep 16, 2014 #4

    Simon Bridge

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    No worries - check the context and the meaning should appear.
     
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