Here is part of the result, cited from an Atheist correspondent of CMI:
To begin with, I must point out that just because something has a logical basis, that does not mean that it is necessarily true. Logic is more concerned with the validity of reasoning and the nature of arguments than with the truth values themselves. For example, I could construct a logical argument for the moon being made of cheese, but that would not necessarily prove that the moon was indeed made of cheese. Here’s a perfectly “logical” argument for the moon being made of cheese:
Premise 1: Every object in the sky is made of cheese.
Premise 2: The moon is an object in the sky.
Therefore: The moon is made of cheese.
As you can see, a logical argument can also be an absurdly misguided one. Obviously it is the premises here that you want to worry about more than the logical validity.
Cited from here:
CMI : Feedback archive → Feedback 2012
Atheism—no objective morality?
Logic as Aristotle taught it was sufficiently concerned with Semantics to check some points of validity of sentences before coming up with an absurdity like "Every object in the sky is made of cheese."
To a logician such as Aristotle, the given syllogism is an example that a true conclusion does not necessarily follow from premisses one of which is false.
But it is symptomatic that when Atheists use this quip, they are literally saying "logic is not enough" in cases when what they really need would be a "logic is not necessary".
Not enough and not necessary are not the same thing.
But the syllogism given is not sth which you risk coming up with if you have learned logic, unless you were looking for cases when valid form of syllogism either gives no true conclusion (i e one of the premisses at least must be untrue for that) or for cases of what happen when one of the premisses isn't true (a false conclusion is one of the things you risk).
When the syllogism is valid AND both premisses are true AND correctly formulated so as to avoid equivocations or a bad formulation screwing the logic form of the syllogism, then the conclusion is true.
There are two cases for accepting something : if it is obvious or if the things that are lead to it through a valid syllogism or series of such.
Hans Georg Lundahl
St John Chrysostom
PS - not citing the context of my quote, since the rest was answered very well on site AND there are more occasions than that there when atheists lack either an obvious and direct or a logically syllogistic and less direct foundation for their claims and try to cover it up with "logic is not enough".