If “some men are doctors” and “some doctors are tall”, does it follow that “some men are tall”?

Question

If it is stated that "some men are doctors" and "some doctors are tall," can we conclude that "some men are tall"? Please clarify the logical relationship between these statements and whether the conclusion necessarily follows.

Anonymous · Accepted Answer

Sort of.  Define tall&hellip;.Actually, it&rsquo;s a RESOUNDING YES!

Anonymous · Answer

1

Anonymous · Answer

No.

Because while some men may be doctors and some doctors may be tall, there is no guarantee that there is any overlap in the two.

Maybe only short men become doctors. The statement "some men are doctors" remains true.

Maybe only tall doctors are women. The statement "some doctors are tall" remains true.

But, in this situation, as only short men became doctors and all tall doctors are women, then it does not logically follow that "some men are tall."

(Except in relation to the shorter men that became doctors, I guess. But still, ALL men could be shorter than ALL women in the above statements without violating any arguments and then none would be "tall.")

Anonymous · Answer

Set aside the semantics;
M=men, D=doctors, T=tall (tall people)
Some M are D
Some D are T
So, Some M are T
Reorder the premises so that the predicate of the conclusion is in the first premise:
Some D are T
Some M are D
So, Some M are T
This ‘syllogism’ has the form III-1
It is invalid since the middle term is not distributed; Fallacy of undistributed middle.

Anonymous · Answer

If some men are doctors and some doctors are women, does it follow that some men are women?

Anonymous · Answer

Not if all the tall doctors are WOMEN!

Anonymous · Answer

No.
John, that argument only seems valid because we assume (reasonably enough) that all women are humans.  That’s why the flaw in the argument (that the short-haired women might not be human) isn’t so obvious.

Jaylan Prohaska Jr. · Answer

If some humans are women, and some women are have short hair, then some humans have short hair.

Anonymous

If “some men are doctors” and “some doctors are tall”, does it follow that “some men are tall”?

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