But are the premises which lead us to that conclusion true? That’s what I’m doubting, simply because if we substitute “Arians” for X, we get:
If the baptizer or baptized profess non-Trinitarian belief, then the baptism is invalid.
Arians profess non-Trinitarian belief,
**Therefore Arian baptisms are invalid.
**
Notice that the structure of this deductive argument has not changed. It is still a perfectly sound deductive argument. We know matter-of-fact that the conclusion (Arian baptisms are invalid) is false because the Church does not view Arian baptisms as invalid. One or more of the premises which led us to this false conclusion
must be false, otherwise we end up with a logically contradictory statement of Q & not Q.
There are only two premises in this syllogism, so which one (if not both) are false:
- If the baptizer or baptized profess non-Trinitarian belief, then the baptism is invalid.
- Arians profess non-Trinitarian belief
Since premise #2 is undoubtedly false, as history can attest, premise #1
must be false.