Some and Most

[samuelfbaron]

Could someone aid me with understanding "Most."

This issue comes up a lot in flawed parallel reasoning questions.

For instance:

Most A are B
Most B are C
Therefore some A are C.

I realize we don't know if these groups overlap. Is that all I need to know?

Likewise if we were to have:

All A are B
All B are C
Therefore Some A are C?

How come we can infer some (at least one) A are C ?

[ohthatpatrick]

Everything you said was correct.

With Most/Most, do you also know the VALID inference?

Most A are B
Most A are C
========
Some B are C (Some C are B)

Here, we DO now that B and C overlap because both Most statements are about group A.

To give you a quick example of why we can't chain together Most statements, consider this:
Most 20th century US Presidents are male.
Most males do not live in the White House.
-------------------
thus, some 20th century US presidents do not live in the White House?

Clearly this is no good.

Your second one:
All A are B
and
All B are C
, so some A are C.

This is true, but we could really infer that ALL A are C.

If I said:
All my friends are democrats.
and
All democrats are liberal.

Then it's totally fair to say that all my friends are liberal. It is still true to say "at least one of my friends is liberal". So both are true. The "some" statement is just a weaker version of the inference.

Besides
Most A are B
Most A are C
========
Some B are C

the other quantity overlap inference you want to look out for is
All A are B
Some A are C
========
Some B are C

Let me know if you have any questions about any of this.

[chike_eze]

I found that drawing intersecting circles helped a lot with visualizing the relationships.

You may even want to memorize the forms, if that works for you.