Are Miracles Logically Impossible?
I was surprised by your defense of the value of eyewitnesses. It's not up to your regular level of scholarship. You should review David Hume's "On Miracles" (from an Inquiry Concerning Human Understanding).
In short, no amount of personal testimony is sufficient to establish a violation of natural law (or even the presence of natural law). Physicists don't believe the facts of physics because of personal testimony from other physicists; rather, they believe because they can do the experiment for themselves. Furthermore, if you don't believe, you can do the experiment and see for yourself. No lesser standard of proof is acceptable for scientific explanations of the world.
The miracles of the Bible are not a legalistic claim (did Judas really sell Jesus out?) but a natural claim (did Jesus violate the laws of buoyancy and walk on the water?). Personal testimony is sufficient for the law, mostly because it has to be (prosecutors prefer DNA when they can get it); but it is insufficient for any kind of description of physical reality. Only replicability can stand for that, and miracles, by definition, aren't replicable...
Thank you for writing. You bring up a very interesting argument - one that has been quite resilient over the years. As you said, David Hume wrote _Philosophical Essays Concerning Human Understanding_ in 1748 and Section X was entitled "Of Miracles". The chapter argues very deftly that if rational people have a choice to believe more than one explanation of an event, they should choose to believe that explanation which is most probable
In fact, Hume argues that miracles are by definition unbelievable. He writes, "A miracle is a violation of the laws of nature. There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation. And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle." Hume further argues that because the only evidence offered for miracles is eyewitness testimony, and eyewitnesses have been know to be wrong, any reasonable man would assume the eyewitness testimony in error rather than believe an abrogation of something as consistent throughout time as natural law. The probabilities demand it!
The Problem of Hume's Argument
As I said, Hume's argument seems quite formidable- but it's not without its problems. Whenever someone asks if miracles are probable (or believable) they are really asking is there a God, and that is the crux of the problem. You see, Hume at the start of his inquiry dismisses God as a criterion for support. Hume says we should judge miracles only on the basis of natural evidence - what we find occurring in nature as repeatable. The less common an instance, the less rational it is to believe.
If one assumes that nature is the standard for judging the reasonableness of an event occurring, then Hume may have a point. But by assuming this, one assumes there is no God that rules over nature. What he does is in effect is beg the question.
The Reasonableness of Believing in Miracles
However, if we have strong logical reasons for believing the existence of the Christian God - apart from miracles - then a belief in miracles is not illogical. The argument can be stated thusly:
- The Bible asserts that an omnipotent God created the universe ex nihilo and governs natural laws.
- If God governs natural laws, God can suspend natural laws
- A suspension of natural laws is a definition of a miracle.
- Therefore if the God of Christianity exists, He can perform miracles.
Using the above argument, one can see that miracles are not placed outside the realm of logic as Hume would have it. The question really becomes does the God of the Bible exist.
Hume Proves Too Much
The other problem with Hume's argument is it is so sweeping in scope; it proves too much. According to Hume, any event that would be considered singular in nature (unrepeatable) is by definition irrational to hold. Yet, this cannot be. Take for example the creation of the universe. The universe began to exist or it has existed for infinity. Now, an infinitely existing universe is illogical . However, Hume would state that a universe that had a beginning is also illogical. Thus we are left with a quandary of only two choices available to us, neither being reasonable by Hume's standards. Yet the universe is here and it is in time! It did have a beginning. Therefore, Hume must be wrong.
Norman Geisler notes that Hume's argument fails because it "equates quantity of evidence and probability. It says, in effect, that we should always believe what is the most probable. What Hume seems to overlook is that wise people base their beliefs on facts, not simply on odds. Sometime the 'odds' against an event are high (based on past observation), but the evidence for the event is otherwise very good (based on current observation or reliable testimony). Hume's argument confuses quantity of evidence with quality of evidence. Evidence should be weighed, not added." 
I hope you can see that a belief in miracles is not illogical at all. Hume has made an argument that starts with a denial of a God who can work outside nature, then he goes on to argue that it is unreasonable to believe in violating nature's laws because it is unusual. But, we have seen that both counts of this argument are flawed.
I pray that you will continue to investigate the truth-claims of Christianity. Weigh the evidence for the resurrection and see if it can stand an objective study.
2 - I lay out the argument for why an infinitely long universe is illogical in my article "The Kalam Cosmological Argument". For a more in-depth treatment, you may also see "The Existence of God and the Beginning of the Universe" by William Lane Craig at http://www.leaderu.com/truth/3truth11.html.
3 - Geisler, Norman "Miracles & The
Modern Mind" In Defense of Miracles Geivett &
Intervarsity Press, Downers Grove, Ill 1997 p.79