Key Features:
* Truth-preserving: If the premises are true, the conclusion *cannot* be false.
* Logical connection: The premises provide sufficient evidence to guarantee the truth of the conclusion.
* Form over content: The validity of a deductive argument is determined by its logical structure, not the truth of its individual premises.
Example:
Premise 1: All dogs are mammals.
Premise 2: My pet is a dog.
Conclusion: Therefore, my pet is a mammal.
This argument is deductively valid. If the premises are true (and they are), the conclusion must also be true. The argument's structure ensures the conclusion is logically sound based on the premises.
Important Note:
* Validity does not guarantee truth: While a valid argument guarantees the conclusion is true *if* the premises are true, it doesn't guarantee the premises themselves are actually true.
* Soundness: A sound argument is both *valid* and has *true* premises.
Examples of Deductively Valid Arguments:
* Modus Ponens:
* If P, then Q.
* P.
* Therefore, Q.
* Modus Tollens:
* If P, then Q.
* Not Q.
* Therefore, not P.
In contrast, a deductively invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises are true.
Example of an Invalid Argument:
Premise 1: Some birds can fly.
Premise 2: My pet is a bird.
Conclusion: Therefore, my pet can fly.
This argument is invalid. While some birds can fly, not all birds can fly. The premises do not provide enough information to guarantee the conclusion.