I read a couple of short essays in "The Stone Reader in Modern Philosophy". One set of essays is an argument between Timothy Williamson (Professor at Oxford) and Alex Rosenberg (Professor at Duke) about the flaws (or lack thereof) of Naturalism. Some of the issues they discuss are similar to those in the "What is History" thread.
Rosenberg describes himself as a Naturalist: "Naturalism is the philosophical theory that treats science as our most reliable source of knowledge and the scientific method as the most effective route to knowledge." He goes on to state that science uses, "experimental / observational methods".
Williamson's objections (some of which mirror my objections in the other thread) include:
1) Mathematical proofs do not rely on observation or experiment. If mathematical proof is "a (reliable) route to knowledge", this would seem to suggest limits (at least) to Naturalism. Williamson says, "since the natural sciences depend upon mathematics, Rosenberg desires to find a place for it, but admits he doesn't know how."
2) Williamson quotes Rosenberg as saying, "We should be confident that it (physics) willdo better than any other approach at getting things right." "What things?" asks Williamson. "If he (R) means questions of physics, what reasonable person denies (it).... But if he means all questions, why should we be confident that physics will do better than history at getting right what happened at Gettysburg?" W. adds a literary example. Isn't knowing whether Mr. Collins is the "hero" of Pride and Prejudice a form of knowledge? Every normal reader who has read the book has the critical expertise to answer this question. But the question is metaphysical, depending on agreed definitions of "hero" and shared perceptions of literature. Physics (or science in general) cannot speak to them.
3) Williamson points out a paradox inherent to Naturalism. "If it is true that all truths are discoverable by hard science, then it is discoverable by hard science that all truths are discoverable by hard science.... But, 'Are all truths discoverable by hard science?' is not a question of hard science. Therefore the extreme naturalist claim is not true." W. goes on to say, "Such problems pose far less threat to more moderate forms of naturalism...... But we should not take for granted that reality contains only the kinds of things that science recognizes. (How can) we establish in any remotely scientific way that reality contains only those things we are capable of recognizing at all?"
4) From another essay in the same book: Suppose there was a color blind scientist, who saw the world only in black and white. Further suppose that said scientist was an expert in the cognition of color, a science which, because the scientist lived in the future, was so highly advanced that she knew everything science can know about color recognition in humans. Now suppose the scientist has an operation which cures her color blindness. The bandages are removed, and she sees "red" for the first time. Her experience of "red" clearly has taught her a fact about color that she did not know from her scientific research. We can gain scientific understanding about perception, or love, or pain; but this understanding is different in kind from the knowledge we gain by experiencing color or pain or love. Therefore, naturalism -- effective as it may be in gaining some forms of knowledge -- can never be the "best" way of gaining knowledge about certain things. There will always be knowledge -- even "facts" -- with which it cannot deal.