Here are six reasons, from Puritan John Flavel, why we shouldn't dismiss providence as being the mere outworking of natural causes.
1. Naturalism cannot explain why so many of the mercies given to the saints are clearly above the power of and against the course of natural causes.
2. Naturalism cannot explain how so many natural causes can unite and associate themselves in such strange ways for the relief and benefit of God's people.
3. Naturalism cannot explain how the most powerful means directed to destroy God's people are rendered ineffectual, while the weakest means employed for their defence and comfort are crowned with success.
4. Naturalism cannot explain how the good and evil directed towards God's people are often temporaly rewarded and punished accordingly.
5. Naturalism cannot explain the sensitive timing of the deliverences experienced by God's people.
6. Naturalism cannot explain the concommitence of prayer and such deliverences.
Flavel offers numerous examples to support each proposition. Definitely worth the read - "The Mystery of Providence" by John Flavel