Pattern
The fallacy of the undistributed middle takes the following form:
- All Zs are Bs
- Y is a B
- Therefore, Y is a Z
This can be graphically represented as follows:
where the premises are in the green box and the conclusion is indicated above them.
Here, B is the middle term, and it is not distributed in the major premise, "all Zs are Bs".
It may or may not be the case that "all Zs are Bs," but this 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. The fallacy is similar to affirming the consequent and denying the antecedent. However, the fallacy may be resolved if the terms are exchanged in either the conclusion or in the first co-premise. Indeed, from the perspective of first-order logic, all cases of the fallacy of the undistributed middle are, in fact, examples of affirming the consequent or denying the antecedent, depending on the structure of the fallacious argument.
Read more about this topic: Fallacy Of The Undistributed Middle
Famous quotes containing the word pattern:
“Every child has an inner timetable for growth—a pattern unique to him. . . . Growth is not steady, forward, upward progression. It is instead a switchback trail; three steps forward, two back, one around the bushes, and a few simply standing, before another forward leap.”
—Dorothy Corkville Briggs (20th century)
“His talent was as natural as the pattern that was made by the dust on a butterfly’s wings. At one time he understood it no more than the butterfly did and he did not know when it was brushed or marred. Later he became conscious of his damaged wings and of their construction and he learned to think and could not fly any more because the love of flight was gone and he could only remember when it had been effortless.”
—Ernest Hemingway (1899–1961)
“It is just possible that the tensions in a novel of murder are the simplest and yet most complete pattern of the tensions on which we live in this generation.”
—Raymond Chandler (1888–1959)