One of the most common arguments forwarded casually by new atheists is called the "problem of silence." It will be phrased in the form of a question, like "Why should I believe in a God who is so difficult to see?" In essence, they are asking a rhetorical question that implies a syllogism:
P1: God is not manifestly evident to me.
P2: The Christian God, if true, wants me to know Him.
P3: A God who wants me to know Him would make Himself manifestly evident to me.
C: The Christian God is not true (does not exist).
There are several responses:
1) This only works against omnibenevolent theism (the idea that God exists, is active in the universe, and loves us - essentially, Christianity, Judaism, and Islam).
2) This doesn't work. The syllogism has a clear error in premise three: it is possible that the Christian God has a valid reason for not making Himself manifestly evident to me. At the point that the non-theist CANNOT refute that possibility (i.e. there's no way to say He COULDN'T have a valid reason) then the syllogism doesn't follow - premise three is false.
So the problem of silence isn't really a logical problem at all. It's an evidential problem - "I find it probabilistically less likely that the Christian God exists, because He has not made Himself manifestly evident to me."
But here's the thing: this is probabilistic argumentation without a probability. How much less probable is it? How does that weigh against other probabilistic argumentation (like the argument from design, which seems entirely built to demonstrate that God HAS made Himself manifest via the order of His creation)? How could a non-theist POSSIBLY weigh that data and, in any warranted way, determine that the probability from design is outweighed by the counter-probability from silence?
They can't. That's the point. They CHOOSE to accept the probability of the argument from silence, and NOT the argument from design. And they choose this based on a-priori assumptions (God's non-existence) that they bring to the debate. Be careful, though, because we do the same in reverse. We accept the argument from design, and deny the argument from silence, because of a pre-existing theism. And that's ok. All that means is that whether or not one accepts the argument from silence is ENTIRELY determined based on one's pre-existing beliefs. In other words, it offers nothing to move the discussion forward.
As such, it is no longer a relevant argument. It cannot persuade the theist to abandon theism, and serves no purpose of defense (i.e. it doesn't counter any theistic arugments) for the non-theist. It is a non-argument; a mere restatement of the non-theist's already-existing beliefs. Its no different than a theist saying: "Well, I know God. How can I know a God that doesn't exist?" The non-theist saying "Well, how come I don't know God - how can I know a God I don't experience?" is just a rhetorical way of saying "I don't believe in God. Why do you?" Immediately, we're on to the other arguments - the real arguments for and against God (from change, from consciousness, etc.)
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