Intellectual Rigor in the Non-Empirical

I ran across a blog post I found very interesting at the following link: http://www.ordinary-gentlemen.com/2009/02/falsifying-the-unfalsifiable/

Here's a taste of what the writer was arguing: "There is, to be blunt, no scientific way to prove or disprove the existence of God. Both theists and atheists would serve their causes much better if they kept this in mind. " C.S. Lewis said much the same thing in a quote I can't find right now.

Yet . . . One of the ideas that I am wanting to develop more fully comes from the observation that many (although not all) humans in the course of the centuries have had experiences of the Numinous, or the Divine, or the Transcendent.

If the principal error of the Medieval centuries was to put too much in the category of "God's unchanging and revealed truth," I sometimes think the error of the 20th Century was to discount categorically any accounts of the Transcendent.

In a time where the scientific method reigns unchallenged, those things that are not able to be accounted for via the scientific method have no place in orthodox intellectual life. Without intellectual rigor, popular culture began to be give every description of something vaguely supernatural the same level of credibility -- from the theology of Thomas Aquinas, to UFO sitings, to hauntings of English manor houses, to Apocalyptic literature, to the Hindu gods.

This mindset disturbs me, because I think that reality may be bigger than we can describe exclusively using the scientific method. However, what sort of intellectual rigor is appropriate when approaching issues of faith (and revelation)?