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A syllogism is a logical argument based on simple statements. For example:
- All plants are living things.
- All trees are plants.
- Therefore, all trees are living things.
The first few (often, just two) statements are called premises. The final statement, the conclusion, must follow the "rules" set by the premises to reach a logical result. Syllogisms are often used in conjunction with Venn diagrams to determine the validity of an argument. Just as they are used to support sound arguments, they can also be used to evaluate poor arguments.
 Invalid syllogisms
There are many ways for a syllogism to fail, resulting in a incorrect or false conclusion. An incorrect conclusion is the product of fallacious premises (untrue statements, over-generalizations, irrelevance, etc.), faulty logic in reaching said conclusion (ignoring quantifiers like "some" or "all" in the premises, etc.), or a combination of both.
- Some animals that were thought to be extinct have been rediscovered to be not extinct.
- Dinosaurs were thought to be extinct.
- Therefore, some dinosaurs have been rediscovered to be not extinct.
In this example, the conclusion is faulty because of the "illicit major." In other words, the conclusion cannot be drawn as such because the first premise is only talking about some extinct animals. The word "some" in the conclusion gives the illusion of symmetry and soundness, making the fallacy more covert.
One particular example is often known as "politician's logic".
- Something must be done
- This is something
- Therefore we must do it
In this case, the obvious mistake is assuming that the policy to be enacted is the right one.