ambiguous middle

The fallacy of an ambiguous middle occurs when an equivocation is used to mask a fourth term fallacy.


Here is an example:

1. Only man can philosophize.

2. No woman is a man.

3. Therefore, no woman can philosophize.


The syllogism is invalid because the middle term, "man", is equivocal. In moving from the first to the second premises, the meaning switches from "humankind" to "male". Thus, it is not really a "middle" term (a term shared by both premises). Instead, the occurrence of "man" in the second premise is really a fourth term -- which invalidates the argument.


One of the general templates of this fallacy would be:


1. All X's are Y (in sense 1 of Y).

2. All Y's (in sense 2 of Y) are Z.

3. Therefore, All X's are Z. (invalid because Y changed from sense 1 to sense 2)




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