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The full sentence is 数学的性質をもつ現象はすべてこの科学の対象となるうるわけであるから、それは数限りなくあり、また日々増えていて、これらをもらさず解説することは不可能に近い。

But I can't parse "なるうるわけ". Ignoring that part, I interpret the sentence as "All phenomena with mathematical properties are the objects of study of this science, and these are innumerable and increasing day by day, and are therefore near-impossible to list without omission."

If it were "なりうる", as in なり得る, that would make sense to me. Then, any phenomenon with mathematical properties could be an object of study of this science, so therefore [...] there are too many to list without omission.

When I Google "となるうるわけ", I get over 1000 results, but none that make it any clearer. I would have assumed that these were typos that should have been "となりうるわけ" but the sentence I quote above is from a published science book, which has surely been proofread.

So: what am I missing? Can you really join 得る in this way?

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    It's a typo for なりうるわけ. 明らかにtypoですぅ～^^
    – user1016
    Jan 26, 2013 at 14:50
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    I think you've been misled by "over 1000 results". If you scroll down, you'll see there are only 2 pages of results, and when you click to the second page, it says there are only 13.
    – user1478
    Jan 26, 2013 at 14:58
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    Hmm. Should have clicked to the second page. Thanks.
    – infinitecardinal
    Jan 27, 2013 at 5:30
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    A message from Google count police: Google counts may not be as reliable as you imagine.
    – Tsuyoshi Ito
    Jan 27, 2013 at 5:54

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