I’m in a Logic class and this seems like a really simple concept but all the explanations given are so wordy that I can’t wrap my head around it.
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**TL;DR: Validity is about *the form* of the argument. Does each step proceed from the previous by a valid rule of inference? If you have an unbroken chain of valid inferences, you have a valid argument.**
A logical argument is *valid* if it only uses valid rules of inferences. E.g., *modus ponens* (affirming the antecedent), *modus tollens* (denying the consequent), law of the excluded middle / double negation / proof by contradiction (unless you’re an intuitionist). Another way to put it is an argument is valid if its conclusion follows from its premises.
An example of a valid argument:
1. All dogs are mammals (i.e., if an animal is a dog, it is a mammal)
2. Fido is not a mammal.
3. Therefore, Fido is not a dog.
This argument is *valid* in that it uses all valid rules of inference. The conclusion (3) is arrived at via *modus tollens* (contraposition).
The opposite of this would be a fallacy, which makes for an invalid argument, because an invalid form of argumentation was used.
An example of an invalid argument is the following argument:
1. All dogs are mammals.
2. Fido is not a dog.
3. Therefore, Fido is not a mammal.
This is not a valid argument, because it makes use of an fallacy (denying the antecedent, also sometimes called the fallacy of the inverse). I.e., each step does not proceed as a valid inference from the previous.
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There’s another concept called soundness. Soundness is concerned with if an argument is both valid *and* its premises are true. Here is a valid but unsound argument:
1. All birds are mammals.
2. Barry is not a mammal.
3. Therefore, Barry is not a bird.
This argument is *valid* in that it uses all valid rules of inference. The conclusion (3) is arrived at via *modus tollens*. But premise (1) is not true, so it is not sound.
So soundness means the conclusion follows from the premises, *and* the premises are also true.
There’s a handy quote that captures the difference between validity and soundness: “If my mother had wheels, she would’ve been a bike.” In keeping with the spirit of the quote, if we assume bicycles are the only object with wheels, then yes, if your mother had wheels, she indeed would’ve been a bike. When the premises are true, the conclusion is true. But she doesn’t actually have wheels. The premise isn’t true.
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