Explain Fallacy of Undistributed middle term.
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The fallacy of the undistributed middle term occurs in a categorical syllogism when the middle term, which connects the major and minor terms, is not distributed across the premises. In a valid syllogism, the middle term should be distributed in at least one of the premises to ensure that the conclusion follows logically. However, in the undistributed middle fallacy, this crucial distribution is lacking.
For instance, consider the following invalid syllogism:
Here, the term "have feathers" (birds) and "have wings" (bats) share a common middle term, which is "have." However, the term "have" is not distributed in either premise, leading to an invalid conclusion. The undistributed middle term fallacy falsely assumes a connection between the major and minor terms without establishing a comprehensive relationship through distribution.
This fallacy undermines the logical structure of categorical syllogisms, highlighting the importance of ensuring that the middle term is properly distributed across premises to draw valid and sound conclusions.