What does claims mean here?

Context:

Having no pretensions to the high and commanding claims of my predecessors, whose names are so much more conspicuously identified with our Revolution, and who contributed so preeminently to promote its success, I consider myself rather as the instrument than the cause of the union which has prevailed in the late election. In surmounting, in favor of my humble pretensions, the difficulties which so often produce division in like occurrences, it is obvious that other powerful causes, indicating the great strength and stability of our Union, have essentially contributed to draw you together. That these powerful causes exist, and that they are permanent, is my fixed opinion; that they may produce a like accord in all questions touching, however remotely, the liberty, prosperit

More:
http://www.presidency.ucsb.edu/inaugurals.php