Not really. This is a case of affirming a consequent and explained this way:
Researchers test masks in a laboratory setting. They film unmasked and masked people in various conditions like sneezing, coughing, etc. They conclude from these tests that masks reduce the amount of airborne whatever by some amount.
They then tell us, "Masks work!" The problem here is that if Chinese Disease isn't primarily spread by airborne aerosols like coughing and sneezing, then their conclusion is worthless. Thus, the few studies of populations masked and unmasked that show that the difference masks make in stemming the spread of Chinese Disease is small, typically 1 or 2% and within the margin of error for the study.
Expressed in mathematical terms, this is A (lab tests) mean that B (use of masks in the general population). That is, expressed in clear terms, Tests show that masks work in the lab, they'll work in general use. Where this fails is actual results in general use show that A =/= B and results in the fallacy of Affirming a consequent.
While correct, they also form a paradox:
1) Masks stop a virus
2) Demanding that I wear a mask only admits that your mask doesn't work. Therefore I should wear a mask (which doesn't work).
This paradox has a corollary:
1) Masks stop an infected person from spreading a virus.
2) I am not infected, and wear a mask as protection from those infected.
We are both right.
The circular argument (using a conclusion as the predicate) isn't itself a fallacy. It is also known as the Argument of Faith. All religions are based on faith in some initial circular argument, with arguments extending from that. All religions are based on faith.
Attempting to prove a circular argument either True or False creates the circular argument fallacy (which is also an affirming the consequent fallacy). This is what a fundamentalist does.
Some religions are inherently fundamentalist, such as the Church of Green, the Church of the Ozone Hole, the Church of Global Warming, and of course, the Church of Covid.
The Church of Covid also ignores the N95 specification, which shows masks are completely ineffective against a virus. Cloth masks don't even meet THAT specification.
While masks do stop or severely limit expelled droplets in a sneeze, they do nothing for stopping viruses. Airborne viruses don't stay in the droplets. Even for viruses that did, the droplets will dry out, releasing said virus from the mask itself.
Note that one common complaint about these masks is the way they fog up glasses. That means moisture is exiting the mask (it has to in order to fog the glasses!). Viruses trapped in moisture are expelled along this vector as well.
There have been NO studies of populations wearing masks and not wearing masks. There is no control group. Further, no variance has ever been declared or justified. No calculation of a margin of error value is possible. That calculation is REQUIRED as part of every statistical summary. The margin of error MUST accompany the summary. Further, the summary must select from unbiased raw data by randN. That raw data MUST be published. It MUST be unbiased. The method of collecting it must also be known, as well as the time it was collected and who it was collected from.
There is no data.
With either no data and no declared variance, no statistical summary is possible.
Your equation is not a math equation. It is a logic equation, and an incorrect one for the fallacy you are claiming (compositional error fallacy). That equation error is written: (A)->A
A compositional error is improperly extending the property of an element of a class across the entire class or to the class itself.
In your example, a test of a few masks under control conditions is improperly extended across all masks in all conditions.
You have the right idea, but it is more than just affirming the consequent.
