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:
“Put out the light, and then put out the light.
If I quench thee, thou flaming minister,
I can again thy former light restore
Should I repent me; but once put out thy light,
Thou cunning’st pattern of excelling nature,
I know not where is that Promethean heat
That can thy light relume.”
—William Shakespeare (1564–1616)
“Why it was that upon this beautiful feminine tissue, sensitive as gossamer, and practically blank as snow as yet, there should have been traced such a coarse pattern as it was doomed to receive; why so often the coarse appropriates the finer thus, the wrong man the woman, the wrong women the man, many years of analytical philosophy have failed to explain to our sense of order.”
—Thomas Hardy (1840–1928)
“It may be tempting to focus on the fact that, even among those who support equality, men’s involvement as fathers remains a far distance from what most women want and most children need. Yet it is also important to acknowledge how far and how fast many men have moved towards a pattern that not long ago virtually all men considered anathema.”
—Katherine Gerson (20th century)