Logical positivism and legal positivism connection?

Logical Positivism is defined as have a positive outlook on life but using the force of logic to observe and describe the things around you that are happening.

the only worthwhile theories, ideas, assertions, or statements are those that can be verified empirically.

need some help here in my question regarding : How is legitimate science consistent with logical positivism?

Positivism is a philosophical and ontological (what exists) position in which there can be something which is 'positive', 'truthful' or 'known'. It often espouses that there is an external reality...

is the theory that claims there are no natural law, and therefore no natural right. All human rights, it holds, are derived from the state, from contracts, from each person's freedom, or from custom.