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My memory seems to be failing me at the moment, but I seem to recall Russell saying something like the following on some occasion:
The consistency of mathematics does not show that it is true but only that it could be true.
I think he might have said something like this in his book The Philosophy of Logical Atomism, but I can't seem to find it there. Anyone care to lend a hand by giving the exact phrasing and source?
Ah! I found it! It was in his book The Philosophy of Logical Atomism (see the chapter entitled Logical Atomism (1924), which starts on page 126):
The only way in which work on mathematical logic throws light on the truth or falsehood of mathematics is by disproving the supposed antinomies. This shows that mathematics may be true. But to show that mathematics is true would require other methods and other considerations.
The passage reads a little differently from I remember. I must say, I rather like my pithy paraphrase of what Russell is saying.
I could not find your quote. However, I found one which suggests that Russell might have believed the opposite.
Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.
http://www.azquotes.com/quote/739801, citing Bertrand Russell (2013), “History of Western Philosophy: Collectors Edition”, p.38, Routledge.
Although "eternal and exact truth" seems at odds with the less certain statement in the quote, it is not clear whether Russell was offering his own conclusions, or merely describing the history of this particular belief.
See the set of Russell quotes about mathematics at http://www.spaceandmotion.com/mathematical-physics/famous-mathematics-quotes.htm
