The key concept in deductive logic is the concept of validity. One good way to learn to understand the concept of validity better is to discover what makes arguments invalid.
Reflect: Choose an argument (already chosen below) from the following list of arguments (try to make sure not to choose the same argument as someone else). Consider the way in which the reasoning is actually invalid (perhaps subtly). Think about why that argument is invalid in the sense that it would be possible for all of the premises to be true and the conclusion false.
- ARGUMENT: No snakes are mammals. No mammals are birds. Therefore no snakes are birds.
Write: Put the argument into standard form, clearly identifying the premises and conclusion. Once you have done so then demonstrate that the argument is invalid in one of two ways: Either explain a scenario in which the premises could be true and the conclusion false, or find another argument with the same form that has true premises and a false conclusion. Once you have done so, make sure to explain how your argument refutes the validity of the original argument. Mention if you think that there is anything that could be done to make the original argument valid.
In standard form:
1.All dogs have fur
2.All mammals have fur
Conclusion: So all dogs are mammals.
This is not a valid argument. Due to the 2 premises don’t state that all dogs are mammals. If there was a third premise stating that all dogs are mammals, then the conclusion would be correct, which then would make the argument valid. Even though the two premises are facts, the there is no connection to the premises and conclusion that would make the conclusion true.