You can't really identify a logical fallacy unless someone makes a claim, and the only claim your question describes is this:

Mr. Black denies all claims that cannot be proved by evidence.

Mr. Black is committing the fallacy of over-generalisation. Because it is clear that there are some claims that must be 'accepted' without evidence.

Otherwise Mr. Black must deny all the axioms of mathematics and science. There is no evidence that x always equals x. There is no evidence that if a =b and b=c then a=c. These are Axioms that we take to be true without evidence.

You can't really identify a logical fallacy unless someone makes a claim, and the only claim your question describes is this:

Mr. Black denies all claims that cannot be proved by evidence.

Mr. Black is committing the fallacy of over-generalisation. Because it is clear that there are some claims that must be 'accepted' without evidence.

Otherwise Mr. Black must deny all the axioms of mathematics and science. There is no evidence that x always equals x. There is no evidence that if a=b and b=c then a=c. These are Axioms that we take to be true without evidence.