We have a universally shared assumption that there is an external world, an assumption that science cannot itself certify.

We rely on experiment and observation to certify our judgments in science. But experiment and observation are reliable only in virtue of the truth of basic assumptions about causation and optics that we rely on science itself, and nothing more basic, to certify. 

And of course our judgments about the nature of the external world all depend, even more fundamentally, on a universally shared assumption that there is an external world, an assumption that science cannot itself certify.

. As I said, everything in science, including the importance of shared observation, hangs together: it rests on nothing outside science itself. Logic and mathematics are different still. Consensus about the validity of a complex mathematical argument is in no way evidence of that validity.

Value is different still. If value is objective, then consensus about a particular value judgment is irrelevant to its truth or anyone’s responsibility in thinking it true, and experience shows, for better or worse, that the human community can survive great discord about moral or ethical or aesthetic truth. For the religious attitude, disagreement is a red herring.

said, just now, that the religious attitude rests finally on faith. I said that mainly to point out that science and mathematics are, in the same way, matters of faith as well. In each domain we accept felt, inescapable conviction rather than the benediction of some independent means of verification as the final arbiter of what we are entitled responsibly to believe. This kind of faith is not just passive acceptance of the conceptual truth that we cannot justify our science or our logic or our values without appealing to science or logic or value. It is a positive affirmation of the reality of these worlds and of our confidence that though each of our judgments may be wrong we are entitled to think them right if we have reflected on them responsibly enough.

I mean to suggest that convictions of value are also complex, sui generis, emotional experiences. As we will see [in a later section of the new book, Religion Without God], when scientists confront the unimaginable vastness of space and the astounding complexity of atomic particles they have an emotional reaction that matches Otto’s description surprisingly well. Indeed many of them use the very term “numinous” to describe what they feel.

They find the universe awe-inspiring and deserving of a kind of emotional response that at least borders on trembling

You may think that if all we can do to defend value judgments is appeal to other value judgments, and then finally to declare faith in the whole set of judgments, then our claims to objective truth are just whistles in the dark.

t someone is in pain, or threatened with danger, I have a moral responsibility to help if I can. Just the plain fact of pain or danger appears to generate, all by itself, a moral duty. But the appearance is deceptive: the pain and danger would not generate a moral duty unless it was also true, as a matter of background moral truth, that people have a general duty to relieve or prevent suffering. Very often, as in this case, the background principle is too obvious to need stating or even thinking. But it must still be there, and it must still really connect the ordinary judgment with the more concrete moral or ethical or aesthetic judgment it is supposed to support.

I agree that the existence of a personal god—a supernatural, all-powerful, omniscient, and loving being—is a very exotic kind of scientific fact. But it is still a scientific fact and it still requires a pertinent background moral principle to have any impact on value judgments. That is important because those background value judgments can only themselves be defended—to the extent they can be defended at all—by locating them in a larger network of values each of which draws on and justifies the others. They can only be defended, as my account of the religious attitude insists, within the overall scheme of value.