Philosophy/Logic - proving formal validity impossible?
Hello, my logic textbook said that it is impossible to prove formal validity, because an argument "with valid form" is "not necessarily" valid. How is that possible? My textbook defines valid arguments as arguments whose premises support their conclusion. The argument form All A are B, all B are C, All A are C is valid. So couldn't we say that "All cats are mammals, all mammals are animals, therefore all cats are animals" is formally valid because it conforms to All A are B, All B are C, All A are C, in the SAME WAY we say "All cats are mammals, all dogs are mammals, therefore all cats are dogs" is formally invalid because it conforms to All A are B, All C are B, and all A are C?
an argument "with valid form" is "not necessarily" valid
This statement is false. Perhaps you are misreading the text? Nevertheless, your understanding of argument forms is correct. Every argument that has the same form as a known valid argument is itself a valid argument. This is a fundamental principle.
Likewise, every argument that has the same form as a known invalid argument is itself invalid.