may appear to be a reasonable argument, it is not valid because the first statement does not logically guarantee the second statement. The first statement says nothing like "I do not have my umbrella otherwise", which means that having my umbrella on a sunny day would render the first statement true and the second statement false. Fallacy of the undistributed middle The fallacy of the undistributed middle is a fallacy that is committed when the middle term in a categorical syllogism is not distributed. It is a syllogistic fallacy. More specifically it is also a form of non sequitur. The fallacy of the undistributed middle takes the following form: All Zs are Bs. Y is a B. Therefore, Y is a Z. It may or may not be the case that "all Zs are Bs", but in either case it is irrelevant to the conclusion. What is relevant to the conclusion is whether it is true that "all Bs are Zs," which is ignored in the argument. An example can be given as follows, where B=mammals, Y=Mary and Z=humans: All humans are mammals. Mary is a mammal. Therefore, Mary is a human. Note that if the terms (Z and B) were swapped around in the first co-premise then it would no longer be a fallacy and would be correct. In contrast to informal fallacy Formal logic is not used to determine whether or not an argument is true. Formal arguments can either be valid or invalid. A valid argument may also be sound or unsound: A valid argument has a correct formal structure. A valid argument is one where if the premises are true, the conclusion must be true. A sound argument is a formally correct argument that also contains true premises. Ideally, the best kind of formal argument is a sound, valid argument. Formal fallacies do not take into account the soundness of an argument, but rather its validity. Premises in formal logic are commonly represented by letters (most commonly p and q). A fallacy occurs when the structure of the argument is incorrect, despite the truth of the premises. As modus ponens, the following argument contains no formal fallacies: If P then Q P Therefore, Q A logical fallacy associated with this format of argument is referred to as affirming the consequent, which would look like this: If P then Q Q Therefore, P This is a fallacy