There absolutely is logic in the arguement you so blithely dismiss. That is if Logic means based in observable and verifiable fact and tied to a system or reasoning with internally consistent rules.

Science has grown in knowledge and understanding. What of it? Non-science and illiterates have grown in knowledge over the centuries as well.

Again, all depends on your definition of "knowledge". If knowledge means the aggregation of data into facts, and facts into patterns and patterns into knowledge - then no, illiterates haven't particularly grown in knowledge over the centuries.

On the contrary, science has only solidified the claims of the eternal. They have fully witnessed and examined the bleeding wooden statue of Mary in Akita, Japan.

So I searched both Google and Bing for SCHOLARLY articles on the Mary in Akita Japan - and there simply IS NO SUPPORT to INDEPENDENTLY docment the claims you are making here. And I doubt you can point me to any. What you CAN point us to is story's by BELIEVERS who BELIEVE a thorough scientific examination has been made.

But then how come the town or the statue's owners aren't $1 million richer? There simply isn't any corroborable evidence that there really is a miracle going on.

This is the Christian God witnessing to the believer and unbeliever alike.

No more than it was the Christian God witnessing to unbeleivers as the sun rose at the Vernal Equinax in Chichen Itza as the Snake descended from the top of the temple

Science cannot explain how three young children could predict a great miracle for all to see to the exact day, 90 days in advance.

Sure it can. And it does

That is why 70,000 people showed up in the pouring rain and mud on a field in Portugal in 1917

There is no actual verifiable evidence that corroborates all of the specific details you claim. This is appocryphal at best.

PS – You say miracles have subsided as science has advanced? You are reading the wrong books because you are mistaken.

Well yes. Of course. But simply because something is in a book doesn't make it fact.