During a conversation with my friend about cosmological argument for God, friend told me that cosmological argument is not even true because causal principle is outdated and not needed in modern physics. After the conversation, I searched for that by internet and found out Russell first argued like that and many contemporary philosopher of physics agreed that causality is at least not needed in our fundamental physics. I think if this kinds of argument succeed, then causal principle is undermined and as a result cosmological argument cannot be hold. So my question is, how do proponents of causal principle and cosmological argument answer to that?

I could be wrong, but I believe that few philosophers today would claim that causation (per se) can be eliminated in an adequate description and explanation of the world. Indeed, it would be hard to understand our communicating right now (my intentionally responding to you, using computational mechanisms) without making use of cause-effect relations. There are abundant philosophical treatments of causation ranging from those that appeal to laws of nature, counterfactuals, Humean regularities.... I myself favor the idea that causation is best not understood as fundamentally involving laws of nature; I suggest that what we think of as laws of nature are abstractions that rest on substances (things / particles) that have primitive or basic causal powers and liabilities, but this (like so many things in philosophy) is controversial.

There are still defenders of the cosmological argument for theism. You might look at what I think is the excellent entry on the cosmological argument in the free online Stanford Encyclopedia of Philosophy by Bruce Reichenbach or the work of Tim O'Connor. The Stanford entry has an excellent bibliography.

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