What is the difference between material validity and formal validity?

Answer 1

An argument is said to be formally valid if it is valid in virtue of its form. For example, the argument

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

is formally valid because its validity does not depend on its content (plug in any predicates [some limitations apply], the argument will still be valid). E.g.

All pigs can fly.

Wilbur is a pig.

Therefore, Wilbur can fly.

(Valid, but not sound, since the first premise is false!)

Now, material validity is different in that arguments are valid but not in virtue of their form. Recall that validity is defined as 'no possible valuation which makes the premises true and the conclusion false'. So the following argument is also valid:

John had a nightmare.

Therefore, John had a dream.

If you formalise this argument, it would be "Fa, so Ga", which is invalid (or following Alex Oliver's terminology, impure, for it has both valid and invalid instances). So there seems to be a gap between validity and formal validity (i.e. not all valid arguments are formally valid). That's what Buridan called 'material validity'.

Answer 2

Material validity refers to whether the content of the argument is true or accurate based on evidence and facts, while formal validity refers to the structure of the argument and whether the conclusion logically follows from the premises regardless of the truth of the content. Material validity deals with the actual content of the argument, while formal validity deals with the structure and form of the argument.