In foreign policy, Rand Paul shares with his father — who warned that American power abroad was often not a force for good — an opposition to “nation building.” But rather than rethinking our entire foreign policy, Senator Paul has proposed a two-year, $190 billion budget increase in military spending. (He has urged corresponding cuts in domestic programs and foreign aid.) He repeats the mindless mantra that “radical Islam” must be fought — but he does not adequately say how, where or at what cost.

To Mr. Paul’s credit, he’s suggested slashing 20 percent from the Centers for Disease Control and Prevention, shrinking the National Science Foundation by 62 percent, and taking a 25 percent chunk out of NASA, among other cuts.

But such cuts are vulnerable to endless, piecemeal tinkering that will lead only to more out-of-control spending. Instead, Mr. Paul should consistently advance the core libertarian notion that some things just aren’t an appropriate function of the government at all. For a true libertarian, the government’s power to tax should be used only to protect our natural rights to our lives and property.

Libertarianism’s relevance to the problems that bedevil the Republican Party, and America, goes beyond spending. You can’t solve our foreign policy problems until you understand that the military’s purpose is to defend lives and property on the homeland — not fight international villainy. You can’t solve the immigration problem unless you understand that people, like goods and services, should be allowed maximum freedom of movement. (Mr. Paul, like other Republicans, instead wants to strengthen the borders.) You can’t make criminal justice truly just until you limit the reasons government fines and imprisons us to true crimes against persons or property, not minor “quality of life” infractions or life choices (like drug use) that the government simply disapproves of.

It seems Mr. Paul prefers the term “constitutional conservative” to “libertarian.” But it’s a fairly empty distinction. America’s government was conceived as a small island of limited powers in a sea of unenumerated rights. Mr. Paul has vowed to end the National Security Agency’s dragnet of phone data collection. But without arguing rigorously from a core libertarian philosophy, he will find it hard to answer the question: Why not give up some privacy in the name of “national security”? Mr. Paul needs to rigorously defend the principle that certain rights trump all other considerations — even public safety.