Are the Gospels Historically Reliable?

In his book 'Sense and Goodness Without God: A Defense of Metaphysical Naturalism' Richard Carrier gives three criteria that distinguish a good historian from a bad one.

The first of these criteria is showing "a critical awareness of problems with his sources or with the intrinsic believability of an event." In the case of the gospels however, sources are not even mentioned, and miraculous stories are written as if they are nothing out of the ordinary.

The second criteria is that they should "engage in logical historical argument various forms of evidence and assessing their merit." In the case of the gospels however, no arguments are made and no evidence is addressed, the stories are just reported as being so.

The third criteria is that they will be correct on some matters. In the case of the gospels however, there are many instances where they are dead wrong. A notable example is the massacre of the innocents attributed to Herod by Matthew. If we look at more than one gospel at a time (e.g. Matthew and Luke) we find instances where they don't agree with each other, with no way of telling which of them are correct, if either of them are at all.

So the gospels are not historically reliable, as none of them even come close to meeting these three criteria of a good historian to a sufficient level. Many Christians claim that they gospels are believable because they 'read like eyewitness accounts', which is possibly the worst argument on earth. There is simply no evidence that they were written by eyewitnesses, and in any case eyewitness testimony is often unreliable. This is why these criteria mentioned by Richard Carrier are worthwhile, because you can't just take someone's word for something, especially when it happened centuries or millennia ago.