Kdjykuj

“Either it is sunny or it is raining. But now, it is neither sunny nor is it raining. So, the Boston Bruins will win the Stanley Cup this year.”

Is this argument valid or invalid? I’m pretty stumped, but I’m going to say invalid because the premises contradict each other, but I honestly don’t know. Also, in addition to valid and invalid, could you explain why that is the case? Thanks!

This argument is valid on most definitions of validity.

The common definition of validity in use today is: if the premises are true, then the conclusion must be true.

worded another way, there must be no possible way for it to have all true premises and a false conclusion.

The value of validity (on this definition) is that it checks whether an argument is truth-preserving -- i.e. if you make all of its premises true, would the conclusion then also be true?

The argument you're looking at depends on a trick in the definition of validity: In your argument, it is impossible for all of the premises to be true at the same time because 1. S or R and 2. not S and not R are contradictory premises. Since you can never construct a case where you made all premises true and the conclusion false, it is never the case all true premises gives you a false conclusion (because it is never the case that there are all true premises).

The validity of this argument relates to the principle of explosion since once we've hit a contradiction, all the rules are out the window.

A second and pedagogically important point is that even though in common parlance: "good" , "sound", "valid", "strong", "clear" and many other words have similar seeming meanings, in logic, they each have a distinct meaning.

An argument of this form is valid but it's not really a good argument, because as Mark Andrews points there's no relation between these premises and this conclusion.

If you're doing some rather advanced logic (not your first course in formal logic or critical thinking), you may run into other definition of validity. On some of these, this argument fails, because you cannot construct a model with these premises and this conclusion. But this isn't your garden-variety definition.

I agree with @virmaior's answer.

The results of this proof checker confirm the validity of the argument:

Line 4 is obtained from disjunctive syllogism (DS) on lines 1 and 2. See section 16.2 in forallx. Line 5 introduces a contradiction from lines 3 and 4. Line 6 comes from explosion (X) from line 5.

For explosion, see page 119 in forallx. Here is the authors' motivation for that rule:

It is a kind of elimination rule for ‘⊥’,
and known as explosion. If we obtain a contradiction, symbolized by ‘⊥’, then we can infer whatever we like. How can this
be motivated, as a rule of argumentation? Well, consider the English rhetorical device ‘. . . and if that’s true, I’ll eat my hat’. Since
contradictions simply cannot be true, if one is true then not only
will I eat my hat, I’ll have it too.

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/