For those unfamiliar with Dr. Craig's work, he often uses deductive arguments when making his case for theism. He is an avid defender of the Kalam and Leibnizian cosmological arguments, the fine-tuning argument and the moral argument.
In his article The New Atheism and and Five Arguments for God, Dr. Craig explains what makes a good deductive argument:
"An argument is a series of statements (called premises) leading to a conclusion. A sound argument must meet two conditions: (1) it is logically valid (i.e., its conclusion follows from the premises by the rules of logic), and (2) its premises are true. If an argument is sound, then the truth of the conclusion follows necessarily from the premises. But to be a good argument, it’s not enough that an argument be sound. We also need to have some reason to think that the premises are true. A logically valid argument that has, wholly unbeknownst to us, true premises isn’t a good argument for the conclusion. The premises have to have some degree of justification or warrant for us in order for a sound argument to be a good one. But how much warrant? The premises surely don’t need to be known to be true with certainty (we know almost nothing to be true with certainty!). Perhaps we should say that for an argument to be a good one the premises need to be probably true in light of the evidence. I think that’s fair, though sometimes probabilities are difficult to quantify. Another way of putting this is that a good argument is a sound argument in which the premises are more plausible in light of the evidence than their opposites. You should compare the premise and its negation and believe whichever one is more plausibly true in light of the evidence. A good argument will be a sound argument whose premises are more plausible than their negations."1
As Dr. Craig notes, the power of arguing this way is that if a deductive argument is sound, the truth of the conclusion follows necessarily, whether you like the conclusion or not. Deductive arguments are a standard way of arguing. Which is why Dr. Krauss's strange attack on deductive arguments during this dialogue was so bizarre.
In his speech, Dr. Krauss warned the audience that they need to beware of syllogisms because they can lead to false conclusions. He offered the following example:
1. All mammals exhibit homosexual behavior.
2. William Lane Craig is a mammal.
3. Therefore, William Lane Craig exhibits homosexual behavior.2
As you can imagine, the audience got quite a chuckle from Krauss's argument! However, I fear that some missed the error in Krauss's sad attempt to undermine deductive arguments. There are two problems with Dr. Krauss's "homosexual mammal" argument: 1) It is self-defeating to use logic to refute logic 2) this argument is informally invalid because it uses terms equivocally. Dr. Craig explains:
1. William Lane Craig, The New Atheism and Five Arguments for God, 2010.
2. William Lane Craig and Kevin Harris, Reasonable Faith Podcast Transcript, "The Debate in Melbourne Part 2," Nov. 11, 2013
A Universe from Someone: Against Lawrence Krauss by Peter S. Williams
Counterpoints: Lawrence Krauss and J. Warner Wallace