Defining Deductive Validity I read the following:
"The argument is deductively valid iff it is impossible for the all of the premises to be true and the conclusion false"
Definitions like these strike me as describing what something CANNOT BE rather than telling me WHAT SOMETHING IS. Is it correct that a definition that is structured like this is effectively "exempting" something explicit while "tolerating" anything else?
For example, based on my understanding of this definition, the following pairs are all "deductively valid":


*

*(all false premises, false conclusion)

*(some false premises, false conclusion)

*(all false premises, true conclusion)

*(some false premises, true conclusion)


The only pair that is NOT deductively valid is:


*(all true premises, false conclusion)


Is that correct?
 A: That's sort-of correct, but it's missing a key point: validity doesn't depend on what happens to be true or false at the time. In essence, validity needs to take into account all possibilities.  So it would not be allowing some false premises, but allowing always false premises.
Another way to state the definition would be that whenever the premises are true, the conclusion is true as well. For an analogy, consider the definition "a joke is funny iff it's impossible to hear the joke and not laugh".  To evaluate whether a given joke is funny, we only care about what happens when the joke is told (whether people laugh).  Similarly, to tell whether a conclusion logically follows from premises, we need to consider what happens when the premises are true.
Consider the premises $P$ and $P\rightarrow Q$, and the conclusion $Q$. Whether or not $P$ is actually true or false is irrelevant for whether the deduction is valid.  The only way truth or falsity comes into play is when something is necessarily true or necessarily false.  For example, the premise $P$ and $\neg P$ (i.e. a contradiction), you can conclude anything, and still have the reasoning be valid (it's impossible for all the premises to be true and the conclusion false, because it's impossible for the premise to be true).
