For example, right-libertarians have a natural law basis for their ideology (they believe in inalienable rights granted by God, threatened by the state), while left-liberals have a positivist legal theory (rights are established by the state).
This is just one example of the flaws in Lakoff's framework. I suggest you read Anarchy, State, Utopia by Robert Nozick for a better understanding of true libertarianism, as opposed to the Ayn Rand cartoon version.
>>Can you show me a specific problem with the definitions?
I don't just disagree with the definitions, I disagree with the entire idea that one may map ideologies on two arbitrary dimensions.
Why not: map all ideologies on the dimensions "loyalty" and "frivolity"? Or "Pascal" and "Descartes"?
It's a meaningless parlor game.