Not all that glitters is gold. That is, unless you’re Smash Mouth or a rich lady in a Led Zeppelin song. The aforementioned quote is quite a famous and rather cliche one featured in the likes of Shakespeare’s plays and Chuck Norris jokes, and many things inbetween.
At a glance one may say yes, the statement is logical. I mean, this argument just breathes soundness. Or does it?
To turn this statement into a syllogism one may arrange it so that it says:
Not all that glitters is gold
Gold glitters
Therefore, gold is not all that glitters
Bam. Valid. I’m sure we can all agree that not all that glitters is gold, however, looking at the other premise now begs the question: does gold really glitter?
And the answer to that, dear readers, is not always. Here is an example of a fallacy of presumption, where it is assumed that all gold glitters when gold, particularly in its raw and impure form, does not always glitter. So then, how could one save this syllogism?
Not all that glitters is gold
Gold does not always glitter
Therefore, gold is not all that glitters
It’s interesting because even though one of the premises are untrue, the conclusion that can be drawn is the same for both syllogisms.
In your first syllogism, is the second premise really necessary? The conclusion is essentially a restatement of the first premise.
Same question for the second one, now that I think of it. Even accepting both premises of the first as necessary, then “Gold does not always glitter” doesn’t prove the conclusion.