Figuratively, one thinker's ideas mix with other ideas, combine, almost mate, and generate or give birth to other ideas in the minds of other thinkers. So, figuratively, you can construct a kind of family tree of great ideas, and talk about some ideas as being the ancestor of other ideas.
A "pedigree" means a formal, certified family tree that proves someone or some animal is "legitimate" and descended from noble ancestors.
When reading the passage above--I can imagine an argument that goes like this:
"The government has a responsibility to promote happiness."
"Nonsense."
"But that idea comes from the Declaration of Independence. Which was written by Jefferson. Who got the idea from Locke, who got it from [someone], who got it from [someone], who got it from Plato, who got it from Aristotle. I didn't make it up myself. It's a very legitimate idea with a very distinguished intellectual pedigree."
"I don't care about the intellectual pedigree, that idea is always a threat to human freedom."