The Argument from Miracles - Refuted

These are the standard objections to argument #9 on the list provided here...

http://www.peterkreeft.com/topics-more/20_arguments-gods-existence.htm

The argument states:

1. A miracle is an event whose only adequate explanation is the extraordinary and direct intervention of God.
2. There are numerous well-attested miracles.
3. Therefore, there are numerous events whose only adequate explanation is the extraordinary and direct intervention of God.
4. Therefore God exists.

Common Objections

There are alleged instances of multiple incompatible miracles which are used to provide evidence for different religions. Not all these can be correct. Therefore the initial assumption of what a miracle is fails.

The first premise is assuming the existence of God in order to arrive at the conclusion that God exists. This is therefore a circular argument. 

Occam's Razor suggests that God is unnecessary to explain miracles for which natural explanations can be found. For example, the reports of miracles in Lourdes are (according to the church) supernatural cures. But all of the recorded cures consist of diseases which may have healed by themselves without the need for divine intervention.

The initial assumption that a miracle as an intervention by God is open to doubt and cannot be stated as fact.

A miracle is defined as something that is not naturally possible (hence it is the result of supernatural intervention). This is impossible to demonstrate. Without an explanation of how it can be proven that a natural cause for an event is impossible, the argument fails. 

Even if we assume for the sake of argument that a “miraculous” event is indeed exceptional enough to warrant an exceptional explanation, it cannot be assumed that this requires the existence of God. It could be argued that extraordinary events are caused by the incredible powers of human mind. This explanation is no less credible than the existence of the mind of a questionable God.

To propose one supernatural, paranormal, or unusual explanation for an exceptional event, one has to be willing to consider every other supernatural, paranormal, or unusual explanation. But how is it possible to compare all these different explanations? How can one reasonably support the idea that something