Positive conclusion from negative premise -How To Win Every Argument
An argument which draws a conclusion from two premises is not allowed to have two negative premises, but it is allowed one, provided the conclusion is also negative. A fallacy is committed whenever a positive conclusion follows from two premises which include a negative one.
Some cats are not stupid, and all cats are animals, so some animals are stupid.
(Even though some of them are smart enough not to be cats, the conclusion does not follow. One premise is negative, so any valid conclusion would also have to be so.)
Although two things can be related to each other by means of the relationship which each has with a third, if one of the relationships is concerned with what is not true for one, the deduction must show that the other one is also wholly or partly excluded from some class. In other words, if they each enjoy a different relationship with a third thing, they cannot both be in the same class. The fallacy of drawing a positive conclusion from negative premises persuades us that things do belong to a class by telling of things which do not.
The trouble with this fallacy is that it can be seen coming a mile away. You can try persuading an audience that rats are sheep by telling them what rats are and what sheep are not. You are unlikely to succeed for the simple reason that people smell the rat before the wool is pulled over their eyes. It is just too easy to spot that you cannot claim that things are the same simply because they are different.
The only time you stand a chance of getting away with this one is when you are calling up a radio phone-in show. And that is only because anything goes on a radio phone-in show.