Clarification needed for "some"

[NATURE.M]

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.

 

[Simon Bridge]

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.

 

[NATURE.M]

Thanks Simon.

 

[Simon Bridge]

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

 

[blue_raver22]

In mathematical logic, the term "some" can refer to a non-empty subset of a set, and it does not necessarily imply a single element. Therefore, "some" can refer to multiple elements that satisfy a given property. However, it is also possible to prove that there exists at least one element that satisfies a property, which can be interpreted as "some" in a more general sense. Ultimately, the use of "some" in mathematical logic can be ambiguous and may require further clarification in certain contexts. It is important to carefully define and specify the meaning of terms in order to avoid misunderstandings and ensure clear communication in mathematical logic.