Science cannot explain the existence of physical phenomena and laws
This argument is used in the debate Does God exist?.
This argument is an objection to God is but the name of our ignorance.
Summary
Quotes
“Dawkins' argument presupposes that all forms of ignorance can be overcome by mathematical physical science. But this is not the case. Scientists' wishful thinking that "with the progress of science, everything will one day be explained" is not always justified. [...] no, there really are questions that we can know in advance, for logical reasons, that science will never be able to answer. By right, science can explain all physical phenomena on the basis of laws and initial conditions. But it is by definition impossible for science to explain the existence of physical phenomena in general. Similarly, it is impossible for it to explain the existence of laws. Certainly, it can derive certain laws from other more fundamental laws, but in the end (assuming a fully realized science) there will be a few laws, or even a single fundamental law (described by the future and hypothetical Theory of Everything) from which all others will derive, and which will itself not be explained by science. This law, by hypothesis, would comprise a certain number of constants, and would apply to arbitrary quantities of matter that would appear as brute facts without explanation. Similarly, the intelligibility, beauty and simplicity of the laws of nature are inexplicable by science. These "ignorances" are not ignorances that can be filled by science: they cannot be overcome by science. To say: "One day science will tell us why something exists rather than nothing" makes no more sense than saying "one day geometry will tell us where space is". Science is only valid within the sphere of physical phenomena; it cannot address the question of whether or not the totality of physical phenomena has a cause. While science asks how the universe transforms itself, metaphysics asks whether the existence of the universe itself has an explanation. To answer this question, or attempt to do so, is in no way to answer a question that science could (or might) have answered: it is not, therefore, to fill a hole. The God of metaphysics is not a God of the gaps.”
References
Justifications
Objections
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The inexplicability of a phenomenon by science lends credence to the thesis of a filler god
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Religious answers will always be more biased than scientific ones
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It's more rational to admit our ignorance than to invent an explanation out of nowhere.
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Science has never claimed to have all the answers.