As Bob Black said, Left and Right are on either side of the same thing. It's hard to say what ultimately constitutes either one, as both claim the same virtues. When issues arise, however, they always have fundamentally different ontological interpretations of the same events.
It would, perhaps, be easy to categorize them metaphysically and metahistorically, regardless of where they sit in terms of the French Revolution. The Left is the beginning of modern politics. It is the institution of what it perceives as natural by way of force. The Right, on the other hand, is a product of modern politics--the institution of precisely what is apolitical in politics, or rather, the separation of life from the political; the praise of what is natural with the least amount of force. The Left looks to the future to get beyond politics while the Right looks to the future which is really a primordial condition like the past; but then, this is the Left too.
We could keep going further, but the more we do, we step away from an ultra-canonical definition and assess things case by case, which are never consistent. The Left and the Right are, at the end of the day, their own meta-political nations which are defined precisely by their incompatibility with one another. They are two gangs constantly beefing over turf and, every now and then, becoming emboldened by circumstances which see them in a position to slaughter the other side by the millions upon millions. These descriptions are useful in specific epochs as means of convenient group identification. They stop being useful when they prevent clarity from even occurring. These positions have changed before and they will change again. It's hard to imagine them going away and it's hard to imagine that everyone would have the same motivation in wishing for them to go away.