Is the Star Test for Syllogisms a Valid Method?

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I'm reading a book by Harry J. Gensler in which he introduces his 'star test' for checking whether or not a syllogism is valid. According to the star method the premises;

all A is B
all A is C

has no valid conclusion. But wouldn't;

some B is C

be a valid conclusion?
Sorry if this is kind of a silly question, I'm just starting to learn this stuff.

 

[Borg]

Are you sure that you've copied it correctly? The closest that I could find was this fallacy - Undistributed Middle Term.

If the example is correct, perhaps the answer is elsewhere on that site.

 

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I'm pretty sure. Gensler says the star test works by putting a star above any distributed letters in the premises and any non-distributed letters in the conclusion. The test says it is valid only if:
1) each capital letter is starred exactly once and
2) there is exactly one letter on the right hand side that is starred.
In the premises of the examples I listed 'A' would be starred twice, once in each premise, so that should make it invalid but I don't see why 'some B is C' isn't a valid conclusion.

The example I gave wasn't from the book, it was something I though up which fails the test but appears to have a valid answer.

 

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Never mind, I think I figured it out. Is it because there isn't necessarily anything in A?

 

[Borg]

My first thought when I read your example was the following:

A = Ford
B = vehicle
C = 4 wheels

Substituting, using your example:
all Fords are vehicles
all Fords have 4 wheels

It looks like some vehicles have 4 wheels would be true.

 

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But if we take:

A = fairies
B = things that have wings
C = things that have magic wands

then some B is C only if fairies exist, if they don't then there isn't necessarily something that's common to both B and C so I can't say with certainty that some B is C.

 

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Wow, after I just posted I literally read two more pages and Gensler started to go into this, turns out it is because A may be empty.

 

[Borg]

Looks like we both learned something. :)