"All", "Majority/Most" and "Some"? Forum

[ScottRiqui]

This is related to an earlier question I had, but I'm trying to move from evaluating specific examples to coming up with general rules I can use anywhere.

If I have:

A -> B (All A are B)
A -> C (All A are C)

I can't say that B -> C, or that C -> B.

But am I correct that I *can* say that "B some C" and "C some B" (Some B are C, and some C are B)?



Likewise, if I have:

A most B (Most A are B)
A most C (Most A are C),

then I should be able to infer that "some B are C" and "some C are B", right?


In general, I'm thinking that if have A related to B with an "All", "Most" or "Majority" relationship, and A related to C with an "All", "Most" or "Majority" relationship, then I can relate B to C with a "Some" relationship.


Does this sound right? I've run across a few LR questions where being able to assume this would make evaluating the answers easier.

[boblawlob]

Sounds right to me.

[bp shinners]

Rules of thumb:
1) I can never combine two some statements, or a most and a some statement.
2) I can always combine any other two statements as long as the Sufficient condition of the Stronger statement is Shared, resulting in a Some statement (I call this the 4 Ss). If the two statements are tied for strength, then the shared term must be in the sufficient condition of both.
3) This isn't an exception to the above, but it is an addition. On top of the some statement you can form, if you have the sufficient condition of an all statement lined up with the necessary condition of a most statement, you get a most statement. I don't have a good mnemonic/alliterative rule for this one (though if you come up with one, let me know).

Using those 3 rules, you can get to any valid inference between quantified statements (outside of a straight-forward, transitive combo).

[ScottRiqui]

Thanks!