Atheists are often very aggressive when it comes to attacking Christianity, and one of the topics they often criticize is prayer. Since they believe (deny, lack belief, etc.,) that there is no God, therefore prayer cannot work--no matter what is said. The problem is that atheists who attack Christianity regarding prayer have three major problems. First, they need to deal with their own false assumptions that constrain their objectivity. Second, how would they judge if prayer works. Third, they don't understand how prayer works.
In the first case, atheists can only assume that God does not exist. They cannot know for sure that God does not exist because it is not possible to know all arguments and evidences for and against God's existence--which means there could be arguments and evidences they have not yet heard. So, ultimately, his position is held by faith--even if he wants to say it is an informed "faith." Once his belief is in place, all evidence and arguments for God must be filtered through that paradigm. Prayer, then, could not possibly work because it would mean that God existed.
Second, how would atheists judge whether or not prayer works? Do they want repeatable experiments and regular quantifiable data so that the efficacy of prayer can be tested and measured? That would be a problem. If prayer "A" resulted in effect "B," then we would see a correspondence of prayer and result--something the atheist could see and verify. But if this were the case, such a phenomena would not be a demonstration that God exists. Instead, it would be a demonstration that uttering certain words in certain patterns brings certain results. This would imply that a new property of the universe has been discovered, and that by saying certain words certain results occur. This would not demonstrate that God exists. Besides, we call this phenomena sorcery.
Third, prayer doesn't work the way the atheists imply it should. Biblically speaking, prayer is offered to a Living Being who, according to Christianity, works all things after the counsel of his will (Ephesians 1:11) and not ours. God, like any rational being, may or may not answer a request from someone. Think about this: if my child asks me for ice cream and I don't want to give it to her, does it mean I don't exist, or that her asking me for things doesn't work? Of course not.
That doesn't stop the atheist from citing "studies" where the efficacy of prayer is measured and found to be useless--according to them. But that is what you'd expect if God, in his infinite wisdom, refused to be quantified by those who deny him and want him, essentially, to perform parlor tricks by responding to prayers in such a regular and man-centered manner so that his "performance" (and prayer's efficacy) can be measured. In other words, atheists, who deny God, want God to do what they want him to do, so they can be convinced. But God doesn't submit to his creation--especially to those who deny him.
But still, does prayer work? Yes it does. I've experienced profound answers many times. But, of course, if I were to offer my experiences and answered prayers, the atheist would say it's too subjective and not quantifiable. Therefore, they would reject it. So we are at an impasse. The atheist requirement of observation, testability, etc., can't affirm or deny prayer's efficacy. So, it isn't possible to win with the atheist when he sets up a criteria that is impossible to satisfy and especially when all answers have to be filtered through his atheistic worldview which requires that prayer will not work.
The atheist, in my opinion, has arrogantly challenged God by viewing non-answered prayer as evidence that he does not exist. The Bible says that God hides himself from the proud (James 4:6). So according to Scripture, atheists cannot and will not see that prayer works, and they will continue to deny God and elevate their own sense of truth and reality.
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