If a deductive argument is valid, that does not say much about it: it might still be probatively worthless. Nevertheless, validity is a necessary condition of a deductive argument's being probative. So it is important to have a clear understanding of the notion of validity. An argument is valid if and only if one of its logical forms is such that no argument of that form has true premises and a false conclusion.
Note the asymmetry between validity and invalidity. To be valid, it is sufficient that an argument instantiate a valid argument-form. To be invalid, however, it is not sufficient that an argument instantiate an invalid argument-form. For an argument that instantiates an invalid form may also instantiate a valid form. Exercise for the reader: construct an example.
Valid Form: None of its instances have true premises and a false conclusion.
Invalid Form: Some of its instances have true premises and a false conclusion, and some do not.
This suggests that there is room in logical theory for the concept of contravalidity:
Contravalid Form: All of its instances have true premises and a false conclusion.
Note that what we have here is a tripartition in the sense that the set of argument-forms is divided or partitioned into three disjoint and mutually exhaustive proper subsets, the valid, the invalid, and the contravalid.
According to David H. Sanford (If P, then Q: Conditionals and the Founbdations of Reasoning, Routledge 1989, p. 42), the above tripartition and the concept of contravalidity is traceable to Johannes de Celaya. But Professor Sanford says something that strikes me as incorrect. He writes, "All contravalid arguments are invalid, but not all invalid arguments are contravalid." (p. 42) But this can't be right given that the Celaya classification is a tripartition. If an argument is contravalid, then ALL instances of its form have true premises and a false conclusion. But if an argument is invalid, then SOME instances of its form have true premises and false conclusion and SOME do not. So if an argument is contravalid it is not invalid. Sanford makes it sound as if contravalid arguments are a proper subset of invalid arguments when in fact they are neither valid nor invalid. But it is easy to fall into confusion here since invalidity and contravalidity are usually not distinguished. What Sanford should have said is that all contravalid arguments are not-valid, the not-valid comprising both the invalid and the valid.
Here is an example of a contravalid argument-form:
If p, then either p or not p
—–
p if and only if not p.
Since the premise is a tautology and the conclusion a contradiction, every instance of this schema has a true premise and false conclusion. From a practical point of view, contravalidity is uninteresting — which is why it is not discussed in logic textbooks. But it is theoretically interesting because its symmetry with validity throws into relief the asymmetry of validity and invalidity. Consider this argument:
If an argument has a valid form, then it is valid
—–
If an argument has an invalid form, then it is invalid.
This is a non sequitur, and the conclusion is false to boot. Someone who thinks that the conclusion is true can be said to be confusing invalidity with contravalidity. For if an argument has a contravalid form, then it is contravalid. So it does seem useful for purposes of logical theory to distinguish the valid, the invalid, and the contravalid.