Tony Vargas said:I think a character with a scimitar in one hand and a longsword in the other could, indeed, by the PH rules, attack with either one.
Well the rule:
An off hand weapon is light enough that you can hold it and attack effectively with it while holding a weapon in your main hand.
implies that non-off hand weapons are not light enough to hold and attack effectively with while holding a weapon in your main hand.