What does "if only" mean?

Solution 1:

The most reasonable parsing of that particular sentence would be that "it was the sole dialogue available in Europe for almost 1,000 years" could plausibly be the only reason for "The influence of the Titnaeus among early philosophical thinkers" being "pervasive", without explicitly excluding any other reason.

Solution 2:

I think the sentence tells us There may be other reasons for Titnaeus' influence, but one of them is for sure ....

here are more people supporting this http://forum.wordreference.com/showthread.php?t=718222

Solution 3:

Based on your example sentence, "if only" is acting as a modifier to "because". Essentially, the line of text, when fully expressed is:

The influence of the Titnaeus among early philosophical thinkers was pervasive, [for at least the reason that] it was the sole dialogue available in Europe for almost 1,000 years [but not necessarily only for that reason].

"If only", in essence, makes the reasoning following "because" non-exclusive, while still aptly expressing the importance of that specific reason.