Truth v Validity
In ordinary speech you might hear someone say, "you have a valid point," or "your argument is false." That's OK in ordinary speech, but in logic terms like "validity," 'invalidity," "truth" and "falsity" have precise meanings which our everyday ways of speaking don't always adhere to.
Truth and and falsity are properties of statements (also sometimes called 'sentences' or 'propositions'). "The moon orbits the earth" is true.
"The moon is made of green cheese" is false. Some things we say can't be true or false: e.g. questions, commands, or exclamations. Such utterances are not statements.
Validity and invalidity are properties of arguments. An argument is valid if the conclusion follows necessarily from the premises. For instance,
Premise 1: Canada is larger than France.
Premise 2: France is larger than Singapore.
Conclusion: Canada is larger than Singapore.
is a valid argument because if the premises are true, the conclusion must be true. So the precise definition of validity is this:
An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.
The definition of invalidity follows from this:
An argument is invalid if and only if it is possible for the premises to be true and the conclusion false.
So this argument is invalid:
Premise 1: All tigers have stripes
Premise 2: Ziggy has stripes.
Conclusion: Ziggy is a tiger.
The conclusion doesn't follow from the premises because the fact that all tigers have stripes doesn't mean that nothing else has stripes.
Ziggy could be a zebra.
So what about the following argument? Is it valid or invalid?
Premise 1: The moon is made of green cheese.
Premise 2: Green cheese is edible.
Conclusion: The moon is edible.
This argument is valid. If the premises are true, the conclusion must be true. This illustrates an important point: the validity of an argument has nothing to do with the truth of its premises or the truth of its conclusion. For this reason, we don't want our arguments to be merely valid: we want them to be sound.
An argument is sound when it is valid and all the premises are true.
Philosopher Frank Williams offers the following analogy to illustrate both truth and validity are independent considerations that both matter in the assessment of arguments. An argument is like a weight hanging from a rope that is tied to a metal plate screwed into the ceiling. Imagine you are sitting underneath this weight. You have two worries. 1) The rope might not be strong enough. 2) The metal plate might not be securely attached. Checking to see if the rope is strong is like checking an argument for validity. Checking to see if the plate is secure is like checking that the premises are true. If either check reveals a problem you won't sit beneath the weight. And if a premise is false or if the reasoning is faulty, you can't trust the conclusion of an argument.
Further references
How to prove an argument invalid by a counterexample
Truth
The difference between induction and deduction
Truth and and falsity are properties of statements (also sometimes called 'sentences' or 'propositions'). "The moon orbits the earth" is true.
"The moon is made of green cheese" is false. Some things we say can't be true or false: e.g. questions, commands, or exclamations. Such utterances are not statements.
Validity and invalidity are properties of arguments. An argument is valid if the conclusion follows necessarily from the premises. For instance,
Premise 1: Canada is larger than France.
Premise 2: France is larger than Singapore.
Conclusion: Canada is larger than Singapore.
is a valid argument because if the premises are true, the conclusion must be true. So the precise definition of validity is this:
An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.
The definition of invalidity follows from this:
An argument is invalid if and only if it is possible for the premises to be true and the conclusion false.
So this argument is invalid:
Premise 1: All tigers have stripes
Premise 2: Ziggy has stripes.
Conclusion: Ziggy is a tiger.
The conclusion doesn't follow from the premises because the fact that all tigers have stripes doesn't mean that nothing else has stripes.
Ziggy could be a zebra.
So what about the following argument? Is it valid or invalid?
Premise 1: The moon is made of green cheese.
Premise 2: Green cheese is edible.
Conclusion: The moon is edible.
This argument is valid. If the premises are true, the conclusion must be true. This illustrates an important point: the validity of an argument has nothing to do with the truth of its premises or the truth of its conclusion. For this reason, we don't want our arguments to be merely valid: we want them to be sound.
An argument is sound when it is valid and all the premises are true.
Philosopher Frank Williams offers the following analogy to illustrate both truth and validity are independent considerations that both matter in the assessment of arguments. An argument is like a weight hanging from a rope that is tied to a metal plate screwed into the ceiling. Imagine you are sitting underneath this weight. You have two worries. 1) The rope might not be strong enough. 2) The metal plate might not be securely attached. Checking to see if the rope is strong is like checking an argument for validity. Checking to see if the plate is secure is like checking that the premises are true. If either check reveals a problem you won't sit beneath the weight. And if a premise is false or if the reasoning is faulty, you can't trust the conclusion of an argument.
Further references
How to prove an argument invalid by a counterexample
Truth
The difference between induction and deduction
Source...