Life Has Meaning, therefore God Exists (a closer look at the logic)

Yesterday we looked at simple argument for the existence of God. It was:

If Atheism is true, then the universe lacks meaning.
But the universe has meaning.
Therefore, Atheism is false.

We then went on to examine why an atheistic universe must lack meaning, at how we all must choose between meaning and atheism. Today, I'd like to look closer at this argument to see if it really succeeds.

This is a particular kind of syllogism is a hypothetical syllogism. To see if it works we'll use a little "symbolic logic" which is very easy, if a bit unfamiliar to most. In testing a hypothetical with symbolic logic we use the letter "p" for our antecedent (the "if" part of our "if...then" proposition) and "q" for our consequent (the "then" part of our "if... then" proposition). So our argument:

If Atheism is true, then the universe lacks meaning.
But the universe has meaning.
Therefore, Atheism is false.

 Is symbolized thus:

p ⊃ q
~ q
∴ ~ p

antecedent - atheism is true (let this be "p")
consequent - the universe lacks meaning (let this be "q")
⊃ - means this is a hypothetical syllogism (a "if... then" argument)
~ - negates the proposition (puts a "not" in front of it)
∴ - means "therefore" (signals our conclusion)

For this type of argument to succeed in proving its conclusion, the syllogism must either affirm the antecedent (the second line is "p") or deny the consequent (the second line is "~ q"), if it denies the antecedent (the second line is "~ p") or affirms the consequent (the second line is "q") the argument fails to conclusively prove anything (except for the poor logic of the arguer). Thus, all we have to do, once we put the argument into its symbolic form, is see if the second term is p or ~ q (which means its valid) or if it is ~ p or q (which means our argument has failed). Here, again is our argument, in symbolic form:

p ⊃ q
~ q
∴ ~ p

 Where we can see we've got "~ q" as our second term. We've denied the consequent and have a valid argument!

This proves that our argument works logically, that the logic is sound, that the conclusion must follow from our premises. As each term we used has only one meaning (and that a clear one) our poor atheist is left with only two options:

1) Admit God exits (i.e. accept our argument has worked)
2) Admit the universe lacks all meaning (i.e. deny the truth of our second premise)

As the second option is absurd and runs clear against every fiber of our being most atheists won't want to turn to option 2, leaving the abandonment of atheism the only other recourse.