1. Naturalism- the view that all of reality is reducible to matter and nothing else-is sufficient to explain everything we observe in the universe.By "New Atheism," he is most likely referring to the beliefs of Sam Harris, Richard Dawkins, Christopher Hitchens, Daniel Dennett, and others in that vein. I can't speak for their beliefs, but I would be very surprised if they agreed with this characterization of their "key principles." I certainly don't agree. There's a big problem with this whole idea, but I'll get to that later. First, let's take them one by one.
2. Absence of evidence for God is, indeed, evidence of absence when the evidence should be there and is not.
3. The Bible fails as a basis for morality and is unable to account for the problem of unnecessary suffering throughout the world.
4. The "way of nature" of nontheist beliefs of Buddha, Tao, and Confucius is far superior to the traditional supernatural monotheisms, which history shows can lead [to] evil.
1. Naturalism- the view that all of reality is reducible to matter and nothing else-is sufficient to explain everything we observe in the universe.
This begs the question: what is matter? If he means the traditional definition of "anything that takes up space" I'm certainly not comfortable making that statement with regards to something like light, of whose properties we only have the most basic understanding. And who's to say there is nothing else in the vastness of the universe that can't be classified as "matter." Isn't antimatter, a concept that's very popular in the scientific community, by definition, not matter?
2. Absence of evidence for God is, indeed, evidence of absence when the evidence should be there and is not.
This is just silly. Absence of evidence is never evidence of absence. There is no evidence of the absence of god. A rational person simply refuses to believe a positive claim that god exists because of this lack of evidence. Being an atheist (even a "New Atheist") doesn't mean making a positive claim as to the non-existence of god. It just means you lack such a belief.
3. The Bible fails as a basis for morality and is unable to account for the problem of unnecessary suffering throughout the world.
I agree with this. This likely accurately describes the beliefs of the "New Atheists" (although, include all holy books, scriptures, etc. Not just the Bible). But I don't think it's a prerequisite to being an atheist. Atheists don't disbelieve the Bible because it fails as a basis for morality. They disbelieve it because it's demonstrably false. Someone could easily believe that the Bible provides good moral lessons and still think it isn't true.
4. The "way of nature" of nontheist beliefs of Buddha, Tao, and Confucius is far superior to the traditional supernatural monotheisms, which history shows can lead [to] evil.
Wow. First of all, any belief system can lead to evil, including one based on atheism. Certainly Buddhism, Taoism, and Confucianism can, and have, led to something most people would describe as "evil" at certain points in history. Second of all, these belief systems, while plausibly described as nontheist, are certainly spiritual, and just as irrational as any supernatural monotheisms. While I may prefer Confucianism to Islam, I'm certainly not going to hold it up as an example of an ideal philosophy. I don't think the "New Atheists" would either.
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Apart from my specific objections noted above, I take issue with the idea that "New Atheism" has any "principles." New atheism is the same as the old atheism. It's just attracting attention now because people are writing books and not getting murdered for it by religious fanatics. Atheism, new or old, is not a belief system, code of conduct, or community. It has no beliefs, principles, or rules. Atheism is just a lack of belief in god. It is not a positive statement of anything. I wish people would stop trying to make it one.