I studying graduate math (not very far into it) and I realized that some of the higher level math texts I would like to read are hard to access without a strong basis in logic. Now I've taken elementary courses (like general college first year) in philosophy with an emphasis in logic. So anyway, I just started reading an introductory logic bood/pdf titled forallx by P.D. Magnus, in order to strengthen myself.

  One of the first things covered is validity and its definition

An argument is valid if and only if it is impossible for all of the premises to be true and the conclusion false.

The author then provides an example of a valid argument, and then of an invalid argument, which is

London is in England.
Beijing is in China.
So: Paris is in France.

He then explains that this argument is invalid, based on his definition of valid

The premises and conclusion of this argument are, as a matter of fact, all true. But the argument is invalid. If Paris were to declare independence from the rest of France, then the conclusion would be false, even though both of the premises would remain true. Thus, it is possible for the premises of this argument to be true and the conclusion false. The argument is therefore invalid.

This quickly lead me to think that he's circumventing any subtlety. For example, there are arguments that I could make in the same style, but where the conclusion is impossible to make false. Consider

London is in England.
Beijing is in China.
So: This is an argument.

To summarize, I do believe there's some fundamental flaw in my reasoning in regards to creating this little paradoxical-seeming statement, but at the same time I don't think the author's logic was correct either.

I studying graduate math (not very far into it), and I realized that some of the higher-level math texts I would like to read are hard to understand without a strong basis in logic. Now I've taken elementary courses (like general college first year) that emphasized logic. 

I just started reading an introductory logic book titled Forall X by P.D. Magnus, in order to strengthen my skills. One of the first topics covered is validity and its definition:

An argument is valid if and only if it is impossible for all of the premises to be true and the conclusion false.

The author then provides an example of a valid argument, and then of an invalid argument, which is

London is in England.
Beijing is in China.
So: Paris is in France.

He then explains that this argument is invalid, based on his definition of valid

The premises and conclusion of this argument are, as a matter of fact, all true. But the argument is invalid. If Paris were to declare independence from the rest of France, then the conclusion would be false, even though both of the premises would remain true. Thus, it is possible for the premises of this argument to be true and the conclusion false. The argument is therefore invalid.

This quickly led me to think that he's circumventing any subtlety. For example, there are arguments that I could make in the same style, but where the conclusion is impossible to make false. Consider

London is in England.
Beijing is in China.
So: This is an argument.

To summarize, I do believe there's some fundamental flaw in my reasoning in regards to creating this little paradoxical-seeming statement, but at the same time, I don't think the author's logic was correct either.