Logic as a discipline has developed A LOT since aristotle developed the syllogism. basibally, logic used to be "if it follows these rules, then its true" but since Boole, but more importantly Frege and Russell, logic has become more or less a mathematical topic. In math, you gotts sit doen with yoyr statement and proove that it's true using theorems and reasoning by reference to rules. Hegels logic on the other hand has a more mystical bent (not exactly mystical, but vauge enough to where the term fits). Logic for hegel is much more about a vague sense of the flow of reason in the develoent of historical time. It sounds really cool and nice and deep, but the more you dig into it, and try to put it in toyr own words, the less sense it makes).