It may be a silly doubt but I am really confused about valid and
invalid terms.
From whatever I read, I concluded that:
Validity and invalidity apply only to arguments, not to propositional statements.
For a (simple)statement either it can be true or false.
For arguments- It is valid if all the premises are true, then the conclusion must be true.
Invalid when it is possible that all the premises are true and the conclusion is false.
For a propositional formula (compound propositions) – a tautology, contingency, contradiction, satisfiable, unsatisfiable, valid terms make sense.
Now my confusion is:
- Can we use the $Invalid$ term with a compound proposition (propositional formula)? If yes, Then what is the condition for its invalidity?
Best Answer
It certainly makes sense to have terminology to distinguish truth/falsity of propositional statements from validity/invalidity of arguments that purport to be logical reasoning. On the other hand it is very common for authors to use valid to describe a compound formula with assignments of truth and falsity to its atomic propositions when it results in the overall formula being true (resp. invalid when an assignment gives a false result).
Good authors will be careful in the use of terminology (and in the definitions), but informal usage will vary. Ultimately if you want to use the terms valid/invalid for compound propositions, you should provide consistent definitions that alert readers or listeners to your meaning.