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What, to start with, are the grounds for supposing that phenomena do not have a scientific explanation? Phenomena of two kinds can be shown not to be explicable scientifically. First, there are phenomena which are too odd to be fitted into the established pattern of scientific explanation, and secondly there are phenomena which are too big to be fitted into any pattern of scientific explanation. To show phenomena too odd to be explicable scientifically the theist needs to show that there is good evidence for a scientific system h covering a certain range of phenomena, but that it is not a consequence of h that certain phenomena (within the general range of h) occur; and that any attempt to amend or expand h to allow it to predict e would make h so complex or for other reasons to have such low prior probability that it would be very improbable that it is true. Theists have claimed various particular phenomena to be too odd to be scientifically explicable. Among these, if we assume that they occur, are violations of laws of nature such as levitations, or people getting better from polio in a minute, or blood suddenly liquefying, or men walking on water, events which theists claim to be miracles. A somewhat different example of a particular event which, if it occurred, would be scientifically inexplicable, would be the first event or initial state of the universe.
But the oddness of events need not be confined to the particular; there may be events of certain kinds which cannot be explained by science. There may be much evidence for a certain scientific system, and yet it be a consequence of this system that a scientific explanation of certain kinds of event is ruled out. Theists have sometimes claimed that the occurrence of living organisms or of conscious human beings are scientifically inexplicable. I do not think that much of a case can be made out for the former, but I do think that a substantial case can be made out for the latter . The kind of argument used to show phenomena to be too odd to be scientifically explicable. Here I have only sketched it in schematic outline. The other phenomena which cannot be explained scientifically are phenomena which are too big for science, and too big not merely for some particular well-established scientific system, but for any scientific system. In considering, the nature of scientific explanation, we saw that science explains why some event or state of affairs occurs. It does this, on the Hempelian model, in terms of a prior state of affairs and some natural law. It also explains why certain natural laws operate, and it does this in terms of more general laws of nature—e.g. it explains the operation of Galileo's law in terms of the operation of Newton's laws. But what, science could not explain is why there are any states of affairs at all; it can explain only why, given that there are such states, this state is followed by that state. Nor could it explain, why the most general natural laws of all hold. Either these are brute facts about the world, or they have an explanation of a different kind. We shall see that the scientifically inexplicable, the odd and the big, form the normal starting-points for arguments to the existence of God. Cosmological and some teleological arguments argue from phenomena allegedly too big for science to explain; whereas most other arguments argue from phenomena allegedly too odd for science to explain. The arguments need to show also that there is no personal explanation in terms of the action of an embodied agent. This done, what has been shown is that an explanation in terms of a very powerful non-embodied agent is the only possible explanation of the phenomena. It then follows that either theism or something like it is true, or that the phenomena are just brute inexplicable facts, the stopping-point of explanation.
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