This fallacy occurs when, in a syllogistic argument, the “middle term”, which should establish the logical connection between the two premises, is not properly distributed. Consequently, the reasoning appears coherent, but the conclusion does not necessarily follow from the premises.
Definition:
The Undistributed Middle Fallacy is a formal error in logic whereby the common term in the two premises (the middle term) is not used in a manner that establishes a valid connection between them. In a valid syllogism, the middle term must be distributed at least once; if this condition is not met, the syllogism is invalid. For example:
“All whales are mammals. All cows are mammals. Therefore, all cows are whales.”
Here, it should be noted that “being a mammal” is an undistributed middle term and, by itself, establishes no logical connection between “whales” and “cows.”
The typical structure of this fallacy:
Valid syllogistic form:
- All A are C.
- All B are A.
- Therefore, all B are C.
Fallacious form (Undistributed Middle):
- All A are C.
- All B are C.
- Therefore, all A are B.
In this structure, “C” is the middle term, and because it is not distributed universally, the shared feature of A and B in C does not allow us to conclude any direct connection or equivalence between A and B.
Examples from real life:
1. In science:
“All birds are animals. All dogs are animals. Therefore, all dogs are birds.”
Here, it should be noted that “being an animal” is an undistributed middle term and establishes no connection between “birds” and “dogs.”
2. In politics:
“All democracies have an electoral system. Our country has an electoral system. Therefore, our country is a democracy.”
Here, it should be noted that “having an electoral system” is an undistributed middle term and does not, by itself, constitute proof of being a democracy.
3. In law:
“All murderers are human. All doctors are human. Therefore, all doctors are murderers.”
Here, it should be noted that “being human” is an undistributed middle term, and the conclusion is false.
4. In education:
“All medical students must take basic courses. All engineering students also take basic courses. Therefore, all engineering students are medical students.”
Here, it should be noted that “taking basic courses” is an undistributed middle term. Simply sharing a common feature (taking basic courses) does not prove that the two groups are the same.
5. In advertising:
“All best-selling products are advertised. This product is advertised. Therefore, this product is a best-seller.”
Here, it should be noted that “being advertised” is an undistributed middle term and does not prove that the product is a best-seller.
6. In everyday life:
“All native Londoners are English. Linda is English. Therefore, Linda is from London.”
Here, it should be noted that “being English” is an undistributed middle term. From the fact that all native Londoners are English, we cannot conclude that every English person must be from London; she could be from Manchester or any other city in England.
Why is this fallacy dangerous?
- It leads to false conclusions: a superficial shared feature is mistakenly interpreted as a general relationship or equivalence.
- It hides within complex reasoning: the failure to distribute the middle term in extended arguments is difficult to detect and misleads the listener.
- It fuels prejudice: people can justify their biases with arguments that appear logical.
- It provides grounds for political and advertising deception: the seemingly coherent syllogism can be used for false persuasion.
How can we recognise and respond to it?
If an argument is built on a common term shared between two premises, ask:
– “Has the middle term been distributed at least once?”
– “Does the superficial commonality of two groups in one feature really indicate a logical connection or equivalence between them?”
– “Is the conclusion drawn merely on the basis of a superficial shared feature?”
A suitable response might be: “Your reasoning is flawed by the Undistributed Middle Fallacy. Merely sharing a common feature does not imply that two groups are identical or equivalent. For a valid conclusion, you must demonstrate that the middle term is distributed and that a genuine connection between the two premises exists.”
Conclusion:
The Undistributed Middle Fallacy underscores that superficial similarities cannot substitute for logical connections. Merely sharing a common characteristic between two groups does not imply a genuine relationship or equivalence between them. By recognising this fallacy, we can discern arguments that appear syllogistic but are invalid, and avoid accepting false conclusions.