# Star Test for Syllogisms

1. Sep 30, 2014

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.

2. Sep 30, 2014

### 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.

3. Sep 30, 2014

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.

Last edited: Sep 30, 2014
4. Sep 30, 2014

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

5. Sep 30, 2014

### 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.

6. Sep 30, 2014

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.

7. Sep 30, 2014