Philosophy/Logic - proving formal validity impossible?
Maciej St. Zięba wrote at 2016-01-07 22:06:17
The formal validity is not the same as factual validity, because the latter depend on the semantic relationship between the terms A, B and C. "All humans are mortals/mammals, all zombies are humans, therefore all zombies are mortals/mammals" has a form of a valid argument, but the problem is whether everybody agrees on the premiss "all zombies are humans" even if we understand that at leats "all zombies are former humans". The problem rarely arises with such rough and general notions like "humans", "cats", "mammals" ets., but quite often with some subtle philosophical issues. In Indian philosophy qe have a discussion on the properties of sound, whether it is eternal or perishing. One school of philosophy (Mimamsa), accepting that sounds can be produced by humans through their speech organs, says that the following argument is valid: "Everything that is a quality of an eternal substance is eternal; Sound is a quality of an eternal substance ether; therefore sound is eternal" is valid. Another school (Nyaya), not rejecting the perosumption that sound is a quality of ether (it abides or is inherent in ether which transmits the sounds from one place to another, like a wave in the ocean), says that this argument is valid: "Everything that is produced by an effort of a creature, causing joining or separation of physical elements, is impermanent; Sound is produced by an effort of a living being (human), by joining and separating parts of the speech organs; therefore sound is impermanent". Both arguments have the same form, but which one of the the two is valid depends on the presuppositions accepted, or at least on those accepted as more important.
Maciej St. Zięba wrote at 2016-01-07 22:08:40
Another issue. Proving the formal validity would need to enter another level of argumentation, a meta-level. This is not possible within the scope of formal logic. It is not possible beyond it as well as the Goedel's paradox has shown.