Why Protestants Shouldn't Dismiss Purgatory

I've been reading Houston Baptist professor, Jerry Walls' book, "Purgatory: The Logic of Total Transformation."  It's his third book in his trilogy on Hell, Heaven, and Purgatory.  It's interesting in particular because Walls is a Protestant who believes in Purgatory (he gave a very brief argument for it in his book on heaven).  Ever since thinking through C.S. Lewis's thoughts on the matter--himself a believer in Purgatory--I've found myself inclined to believe as well.  (Aside: I don't know if I do believe, however, since it's sometimes hard to tell whether one is merely inclined to believe or inclined such that one is believing.  But if forced to choose I'd bet on it.  Have there been any Inquisitions for being inclined to bet on something?)

So I hope to post some of Jerry's thoughts on the matter as I get the chance.  But I'll begin by trying to show why I think an all too common Protestant objection to Purgatory is terribly wrongheaded, and why Protestant's shouldn't dismiss the notion in the way they often do.  Unfortunately, I have heard Protestant-Evangelical theologians, apologists, and Biblical scholars who should know better (and perhaps do!) make this very objection. 

The objection is that Purgatory is not mentioned in Scripture.

This is a good objection if the following proposition is true:
(P) The only propositions to believe or have an opinion about are mentioned in Scripture. 

But if this proposition is true then no one should believe or have an opinion about the following:

that...
Satan is a fallen angel
Infants who die go to heaven
Infants who die don't go to hell
Unbaptized infants who die go to hell
There is time where one goes from unaccountable to accountable
One is not accountable for original sin
Everyone inherits original sin
Mary inherited original sin
Infant baptism should not be practiced
Heaven is not miles away in outer space such that if we only built a big enough rocket we could fly there
Sola Scriptura
Humans have free will
Everything in the Bible is true
The original autographs contained no errors
God does not radically deceive us all the time, including telling us he's a God of Truth when he is not
God knows every detail of the future
God loves everyone including Esau
Deacons are not deacons for life
Pastors are to be appointed by a congregational vote
Jesus is in no way specially present at Communion
There have been no Apostle's since the first century
God's major revelation to humankind ceased in the first century
God believes a 19th-century German hermeneutic is the best one
God disapproves of aborting zygotes
God is telling me to become a minister
Everyone who dies either goes straightaway to heaven or hell

The list could go on and on. 

Now of course, some or all of the above propositions are reasonable to believe and moreover should be believed.  But none of them flies off the pages of Scripture.  None of them are explicitly stated in Scripture.  At best, some of them are implied.  Moreover there is probably not a decent deductive argument from statements mentioned in Scripture to the truth of these statements.  Rather there are inductive, probabilistic arguments.   But isn't that going to be the case with most theological propositions--important propositions pertaining to faith and morals?  So shouldn't we expect that the case for or against the existence of Purgatory will be a probabilistic one, and perhaps a complicated one at that?   Just because something is not obvious does not mean that it is false or not worth having an opinion about.

As far as inductive arguments go, this one is a howler:

1. P is about God or something supernatural and P is not mentioned in Scripture.
2. (Probably) P is false.

If that argument is cogent then it turns out that God doesn't know math.  Any proposition of the form "God believes that [insert mathematical proposition]" would be one which God would know is probably false.  But one can't know that P if one knows that P is probably false (given the definition of knowledge).