http://www.religiouseducation.co.uk/school/alevel/philosophy/cosmological/Kalam_summary.htm
Let's begin with (1): the universe either had a beginning or did not have a beginning. Craig offers three arguments in support of a universe with a beginning. Two are philosophical; one is scientific. Here is the first philosophical argument:
1. An actual infinite cannot exist.
2. A beginningless series of events in time is an actual infinite.
3. Therefore, a beginningless series of events in time cannot exist.
Premise One
In contemporary set theory, an actual infinite is a collection of things with an infinite number of members, for example, a library with an actually infinite set of books or a museum with an actually infinite set of paintings. One of the unique traits of an actual infinite is that part of an actually infinite set is equal to whole set. For example, in an actually infinite set of numbers, the number of even numbers in the set is equal to all of the numbers in the set. This follows because an infinite set of numbers contains an infinite number of even numbers as well as an infinite number of all numbers; hence a part of the set is equal to the whole of the set. Another trait of the actual infinite is that nothing can be added to it. Not one book can be added to an actually infinite library or one painting to an actually infinite museum.
This fundamentally misrepresents set theory by conflating two infinities as being equal - like zero, infinity is not a number it's a mathematical concept, and there are different infinities. This fails to establish that an infinite series is impossible, and therefore fundamentally undermines the first premise.
While these counter-intuitive paradoxes might make sense at the level of mathematical theory, they do not make much sense in the real world of books and libraries.
This particular line seems disengenuous to me - we aren't talking about the everyday, we're talking about the entirety of existence and the potential for an all-powerful creator - these are outside of the boundaries of the day-to-day intellectual short-cuts and estimates that normally suffice.
Having given three arguments to show that the universe had a beginning, we can move on to the second dilemma posed by the KCA: if the universe had a beginning, the beginning was either (a) caused or (b) uncaused. Before discussing the (a) option, we should consider what is becoming a common response to this dilemma from those critical of the cosmological argument. Some theorists speculate that before Plank's time (10 to the negative 43 seconds after the universe began) the universe came into existence out of a quantum mechanical fluctuation. Hence some argue that the universe came out of nothing. Moreland, however, rightly points out that identifying nothingness with something, in this case a mechanical fluctuation, is a mistake; nothingness does not cause anything, let alone fluctuate or bring a universe into existence. Astronomer Hugh Ross notes that one of these theorists, Alan Guth, remarked that "such ideas are speculation squared." Put more concretely, there are three main problems with the quantum fluctuation speculation: it is based upon (1) a non existent theory of quantum gravity, (2) the use of imaginary numbers, and (3) the assumption that the universe was in a quantum state in its early beginning and thus had an indeterminate beginning.
Oh boy. Actually, quantum theory, and experimental observation, supports the contention that something can, and indeed does, come from nothing on a regular basis. At least part of the flaw, here, is seeing 'nothing' as some sort of ground state from which every 'something' is up. Nothing is the balance point, and can be split into equal parts matter and anti-matter - no net change, but localised and specific differences. Something (and anti-something, which is still not nothing) spontaneously emerging.
All of which is to fail to appreciate that the contention the universe 'came from nothing' is a shorthand for 'came from nothing within the universe', which is the current limit of science's remit. It says nothing about what might or might exist outside of the universe, or how that might have been involved in the start of any universes.
Under the Copenhagen interpretation of quantum physics, there needs to be someone to observe the quantum fluctuation that produced the universe.
Another misunderstanding, not confined to Lane-Craig - the 'observer' in this depiction doesn't need to be a conscious, or even living, thinking being. The observer is whatever 'device' is measuring in the experiment, and when translated to behaviour in relating correlates with whatever physical interaction comes next in the chain - it could be an electron waiting to either change energy levels and emit a photon or remain where it is, it's the 'observer'.
Further, this entire section is a 'gaps' argument - there are questions about various scientific interpretation of a natural cause for a universe, but nothing actually supporting the idea of a conscious creator, just scepticism about the current (or in the case of Professor Hawking's quote, a very dated) scientific commentary. At best that reduces to 'we still don't know' - specifically:
Put more concretely, there are three main problems with the quantum fluctuation speculation: it is based upon (1) a non existent theory of quantum gravity, (2) the use of imaginary numbers, and (3) the assumption that the universe was in a quantum state in its early beginning and thus had an indeterminate beginning.
That we don't have a theory of quantum gravity yet doesn't mean there isn't one.
If the use of imaginary numbers discounts science, why doesn't the use of imaginary gods discount religion? Imaginary numbers are well-validate, well-established part of the mathematical framework that operate in more than the four-dimensional space we currently intellectually operate in; that said, I don't actually see any reference to imaginary numbers in the account, I think this is a misunderstanding of the concept of infinity only being partially operable as a number.
There are a number of promising ideas that are based on the extrapolation back from our earliest information on the state of the universe which lead to ideas around a quantum state, but until there's a break-through that's just one type of hypothesis.
First, what does it mean to say that the cause of the universe is a natural one? Natural causes exist within the universe, not outside of it. If something preceded the universe, then by definition it is not a natural cause, because the laws of nature came into existence after whatever preceded the universe.
Do they? None of Oxford, Merriam-Webster or Cambridge online dictionaries mention 'the universe' (or a synonym) in their definition of 'natural'. Natural causes do exist within the universe, but there is nothing to say they are limited to it. That we, in normal conversation, tend to mean it to refer to things within the universe is an artefact of the fact that we reside entirely within the universe, not as a deliberate attempt to differentiate.
Second, if the cause of the universe is a sufficient cause, meaning that the existence of the cause alone guarantees the existence of the universe, the universe would always have existed.
Depending on whether you see Block Time as valid, the universe may have always existed for it's full extent, but regardless of that... there is a presumption in this that the extra-universal reality is static, somehow - perhaps it is, but we have no way to know. If Block Time is invalid, then the universe has still 'always' existed to the extent that particular dimension of time that we're referring to is part of the universe and came into existence with the universe - it's literally exactly as old as time itself.
This fails to establish why only a conscious necessary agent is not static; it's a failed argument, but even then it's still an argument against a particular theory of a natural cause and not an argument in favour of a conscious one.
Overall, this particular framing evades the most egregious special pleading variants that William Lane-Craig's typical variations do, but it's still flawed at every single stage.
O.
