Teddy Roosevelt was an authentic military hero, ridiculously courageous in battle. What is it, 60% of American Presidents that have been elected out of notable military service?
He loved nature, was a "manly man," hated Big Government, stood for rugged individualism. In terms of his personality, and in terms of iconic Americans, he works for me :- )
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As to whether his achievements are comparable to Washington's, well, there are only so many 7-star generals to go around. ;- ) But as to you main point Jonezie: I would NOT sign a debate proposition against you on Teddy Roosevelt as one of the 4 (or 25) greatest Americans. Good 'puts.
I'm curious: do you consider it relevant that America, as a group, has little problem with the 4 faces on there?
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Odd coincidence: One of my best friends, himself a military man, thinks Honest Abe was Abe-ominable also.