This attitude is problematic in many ways, but worst of all is this: the Bible itself doesn't take such a strict view about itself. On the contrary, there are passages in scripture which apparently take for granted that God and his will can be known wholly apart from revelation. In particular consider the following passage from Jesus' sermon on the mount:
You have heard that it was said, ‘You shall love your neighbor and hate your enemy.’ But I say to you, Love your enemies and pray for those who persecute you, so that you may be children of your Father in heaven; for he makes his sun rise on the evil and on the good, and sends rain on the righteous and on the unrighteous (Mt 5:43-5).Notice that the point about God's goodness is something that can be observed and learned from natural phenomena: God himself is good to both the righteous and to the wicked, as is evidenced by the fact of both groups benefiting from the regularity of the rain cycle. This is a bit about God's character that can be understood by anyone who has even passing familiarity with the moral diversity of human beings and their dependence upon the earth.
Consider also what Paul tells the pagans about God:
In past generations he allowed all the nations to follow their own ways; yet he has not left himself without a witness in doing good—giving you rains from heaven and fruitful seasons, and filling you with food and your hearts with joy (Acts 14:16-17).Paul affirms that God has not left himself without witness as regards his treatment of the nations, through the fact that he has provided for them through the natural world. But it would absurd to think that he could have left himself without witness, and yet it would be in principle impossible to realize the truth of the matter. What kind of a witness is that, which I could not discern even if I wanted to? I am hardly blameworthy for failing to be thankful in that case, since I had no way to know from whom the gift had come!
Finally, in the first chapter of Romans, speaking about the wickedness of sinners, Paul affirms: what can be known about God is plain to them, because God has shown it to them (Rom 1:19). He is not talking about the Bible, but about the natural world as a means of revelation of God's will, however imperfect: Ever since the creation of the world his eternal power and divine nature, invisible though they are, have been understood and seen through the things he has made. So they are without excuse (v. 20). He makes the argument in that section of Romans that the various things about God and about right and wrong can be known to human beings, and indeed at some point were known. But because they rejected the truth and preferred a lie, God left them in the darkness of their minds and they were gradually, increasingly degraded through various perversions.
In these various passages, then, we see the natural world put forth as a means of revelation. It doesn't follow from anything I've said that the natural world is a perfect or complete source of revelation, since clearly it cannot be. However, it is clearly put forth as a genuine source of at least some of God's truth, which is enough to defeat the exaggerated Bible-onlyism of much evangelical Protestantism. This is an important concession, because from this point forward a lot of theological changes follow. Now the material world is a means through which God reaches out to the human person and tries to relate to him; now the material world is a means through which God acts, rather than acting entirely apart from it only in revelation; now salvation and restoration to God involves the material world in which we live and through which God intended to relate to us from the beginning.