What are Political Philosophy & the Philosophy of Law?:
The Philosophy of Politics and the Philosophy of Law (jurisprudence) are often studied separately, but they both come back to the same thing: the study of force. Politics is the study of political force in the general community and jurisprudence is the study of how laws can and should be used to achieve political and social goals. Many religious theists believe that both law and politics should be based on a religious foundation, and in particular on the commands of some alleged god. Without that foundation, they argue, both law and politics will be illegitimate uses of force.
Why Should Atheists Care About Political and Legal Philosophy?:
Most atheists recognize that the separation of church and state are important to their ability to be free of having religion imposed upon them. Not all realize that separation is based upon a more fundamental political and legal philosophy which theocrats on the Christian Right don't accept. Debates over church/state separation are thus debates over political and legal philosophy and one reason why such debates often don't go anywhere is because, in not realizing all this, people fail to address the more fundamental disagreements that are really at issue like the legitimate authority of government, for example.
What is Political Philosophy?:
Political Philosophy is primarily constrained to the workings of governments and nations how they developed, why they developed, which systems are better than others, what the purpose of government should be, etc. All of this is closely related to Ethics, because so much is dependent upon what actions are right; but there is the added element of what actions can and should be constrained by outside human forces. There is much debate in America over how much separation there can or should be between politics and people's religious beliefs. Can people, for example, base public policy on private religious revelation?
What is Legal Philosophy or the Philosophy of Law?:
Legal Philosophy focuses on laws and legal systems: how laws came to be, what laws are better than others, what the purpose of law should be, whether or not laws should be obeyed, etc. Because political systems are dependent upon the law, legal philosophy is at the heart of political philosophy. Legal Philosophy is often studied in an effort to elucidate the way in which human nature and social nature need to be expressed and controlled through the law. There is significant effort from some Christians, especially Christian Reconstructionists, to re-make American law along the lines of Old Testament religious law.
What is an Atheist Political or Legal Philosophy?:
An atheist political and legal philosophy need not be secular because not all atheists are also secularists; in practice, though, atheists tend to favor secularism and a separation between religious and civil authority in society. They are most likely to support basing the authority of government and public institutions on the consent of the governed and the participation of the public in the political process. There are, however, great disagreements between atheists on specifics. Atheist may follow conservative, liberal, communist, socialist, libertarian, or any one of a number of different political philosophies.
Questions asked in Political and Legal Philosophy:
Why do governments and laws exist?
Why should we obey governments or laws?
Are laws created by humans, or derived from natural laws?
Should ethics and laws be the same or separate?
Is anyone above the law?
Should religious and civil authority be separated? What role should intention play in legal judgments?
Important texts in Political and Legal Philosophy:
On Liberty, by John Stuart Mill
Leviathan, by Hobbes
The Republic, by Plato
Politics, by Aristotle
Social Contract, by Jean Jacques Rousseau
Philosophy of Right, by GWF Hegel