A free market in this construction must necessarily lack monopolies. There is no counterfactual observation that could falsify the proposition because the definition of free market doesn't admit a counterexample.
Congratulations. That's an epistemic trap.
There are many examples of natural monopolies, which is a concept that has been recognized in economic theory for at least two centuries. Walter is either being deliberately obtuse or is ignorant of history.
AT&T, Western Union, most railroads, many local utilities—all examples of monopolies that formed "naturally" i.e. without state intervention.
Insofar as there was state intervention in the formation of these monopolies, it was because the state intervened on the company's behalf to suspend antitrust law—such as in the case of AT&T, where the government decided it would be most efficient to permit AT&T to continue operating as a monopoly (until it didn't, and broke AT&T up).
I'm honestly fine with whatever definitions, but they need to be able to cross the chasm from concept to criterion in conjunction or disjunction to be useful as a means of discriminating. So far, Walter's proposed definitions for monopolies and free markets together fail this test even if they're separately some measure of fine, inaccuracies relative to their term-of-art counterparts notwithstanding.
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