How can an argument have true premises and still be logically invalid?
In logic, an argument is considered valid only if the truth of its premises logically guarantees the truth of its conclusion. An argument can have true premises and still be invalid if the conclusion does not follow from those premises by necessity.123
In such cases, the argument's structureāor inference formāis flawed. Even if the specific statements (the content) happen to be true, the logical connection between them is missing, meaning it is possible for the premises to be true while the conclusion remains false.3
For example, consider this invalid structure:
* Every X is a Y.
* Some Zs are Ys.
* Therefore, some Zs are Xs.3
If you replace the variables with "dog," "mammal," and "winged creature," you get: "Every dog is a mammal. Some winged creatures are mammals. Therefore, some winged creatures are dogs." Here, the premises are true, but the conclusion is false because the structure does not guarantee the result.3
Logicians distinguish this from a sound argument, which requires both true premises and a valid logical structure.3