Some have argued that the first premise of the Kalām Cosmological argument commits the fallacy of composition.
As a reminder, here is the first premise of the Kalām
1. Whatever begins to exist, has a cause.
But just what is the fallacy of composition? “The fallacy of composition involves inferring that because every part of a thing has a certain property, therefore the whole thing has that property. For example, somebody might say because every part of an elephant is light in weight therefore the whole elephant is light in weight. That would obviously be fallacious. That commits the fallacy of composition.”
In support of the first premise of the Kalām, Dr. Craig gives three reasons in support of the premise (link). In his third reason he says that “This third point that I am making – that common experience and scientific evidence support the truth of premise (1) – doesn’t reason by composition. It doesn’t infer because every part of the universe has a cause therefore the whole universe has a cause. It doesn’t even refer to parts of the universe!”
“Rather this third point is a case of what is called inductive reasoning which underlies all of science. One infers from a random sample of items some property which is shared by items of that sort. In this case the sort in question is things that begin to exist. When we look at things that begin to exist, scientific evidence and common experience is that they always have causes. The generalization “Whatever begins to exist has a cause of its beginning” is a very powerful inductive inference. You infer this general truth based upon a random sample of typical cases. This objection is, I think, just based on a confusion between inductive reasoning (which is sound reasoning) and reasoning by composition (which is fallacious reasoning). This third argument is not an instance of reasoning by composition.”
You can find the full response from Dr. Craig here: link.
Here is another webpage where Dr. Craig response to charges of the composition fallacy: link.