The Kalam Cosmological Argument

[Belacqua]

Quoting from Wikipedia: 'The most prominent form of the Kalam cosmological argument, as defended by William Lane Craig, is expressed as the following syllogism:

Everything that begins to exist has a cause.
The universe began to exist.
Therefore, the universe has a cause.'

I find this argument laughable because it's supposed to be an argument for God but the conclusion is just that the universe has a cause.

William Lane Craig usually does elaborate on why this cause is God. He says that: 

a. Being the cause of spacetime, this cause must trascend space and time itself
b. All mechanical things are bound my cause and effect. Only a mind making a decision out of free will can bypass this cause and effect rule, so such decision could be uncaused.

It's a characteristic of all first cause arguments that they only get us to a first cause. Getting from there to the God of the Bible or of the Koran, or whatever, takes a number of separate steps. All the first cause arguments say that the cause must transcend space and time. 

You're right that Craig adds at least one step that's not included in the Kalam argument itself, by claiming that creation must be the result of a freely-willed decision. But still, that just leaves us with a decision-maker, and there's way more to prove before we get to Jehovah. 

Regarding (b), I am not sure that a mind making a decision can be said to be uncaused. A mind making a decision is usually caused by a previous mental state, not uncaused.

Craig also talks about an infinite series of past causes being impossible, because an actual infinite cannot exist. He claims that it leads to mathematical paradoxes and problems. I am not sure what to think of this.

Also, is the premise that everything that begins to exist has a cause reallly demonstrated? It seems true from our intuition but this is not the same as being formally proven.

Lastly, does the big bang theory really say that the universe as such began to exist, from a previous point of non-existing? Or does it just say that at some point all the matter and energy in the universe was together in the form of a singularity?

I don't think Craig has done us any favors by dusting off this old argument. He names it "Kalam" after a school of Aristotelian Muslim theologians who worked on the theory, but I don't know what they concluded about it, or how widespread it is among Muslims. 

The argument originally came from a Christian -- John Philoponus (490–570 AD). Christian theologians considered the argument and then almost all of them rejected it. Thomas Aquinas specifically points to its flaws when making his own first cause argument. And they rejected it in part because of the issues you raise. Thomas, in particular, thought that there was no empirical evidence that the universe had a beginning -- and he was right, according to what they knew at the time. He also knew of no logical argument why the universe had to have such a beginning. Therefore he thought the second premiss of Kalam was too weak. 

Sometimes on line I see people mixing up Craig's version of the Kalam argument with the Aristotelian/Thomist version. I think that Craig has not done a good job of clarifying the differences, and added unnecessary confusion to the issue. 

(To be fair, I have never read Craig's book. Perhaps what he wrote there is in fact better than the version of the argument that people offer on the Internet.)