F011 • Formal - Syllogistic Logic
Also known as: Undistributed Middle Term
Two groups can both fit inside a larger category without touching each other at all.
We notice that two things share a property and feel a pull toward concluding they must be related to each other. That pull is categorical reasoning working as designed -- but it misfires when the shared property is too broad to actually connect the two things.
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Pattern: If all A are B and all C are B, then all A are C.
Terms:
A = First category (cats)B = Shared property (mammals)C = Second category (dogs)Steps:
A belong to BC belong to BA are CSorting things into groups is one of the most reliable shortcuts we have. If you know that both cats and dogs are mammals, there is a natural temptation to feel like that shared membership tells you something about the relationship between cats and dogs. The heuristic -- things in the same group are probably related -- works often enough that we lean on it without thinking. But categories have sizes. When the shared group is large enough to contain both things comfortably without them overlapping, the connection we feel is an illusion. The middle term, the group doing the connecting, has to cover all members of at least one category to actually bridge anything. When it does not, the bridge is missing a span, even though it looks complete from a distance.
| Categorical reasoning is extraordinarily powerful and usually reliable. When the shared group is specific enough that membership genuinely constrains what you can conclude, the reasoning holds perfectly |
| The instinct to connect things that share a property is one of our best thinking tools -- it only breaks down when the shared property is too broad to carry the weight of the conclusion |
| You might notice yourself thinking 'these two things have something in common, so they must be connected' -- pause and ask how big that common ground actually is |
| Watch for the moment when a shared label starts to feel like a shared identity. Ask: is this category specific enough to actually bridge these two things? |
| If an argument has the shape 'A is in group X, and B is in group X, so A and B are related,' check whether group X is narrow enough that membership really means something specific |
| Notice when a conclusion feels obvious but you cannot quite explain why. That can be a sign the middle term is doing the persuading without doing the logical work |
| Assuming that any shared category creates a meaningful connection, without checking whether the category is specific enough to do the work |
| Confusing this pattern with valid syllogisms that look similar but have properly distributed terms |
| Fallacy of the Undistributed Middle |
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| A categorical syllogism where the middle term is not distributed in at least one premise. |
| The middle term must connect the major and minor terms, but if it's not distributed, it doesn't establish the necessary connection. |
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