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08:03
I want to add a few things here, when talking about tautology or soundness - we have to clearly separate argument forms from specific arguments. Tautology is a property of a form. Indeed, tautology means always true but for forms, but when we are talking about concrete statements, it is what @ryang is saying that a statement can be true in our universe but false in some other. That being said, to say that P implies Q (note, this is a form) means P -> Q is a tautology.
Another note regarding proving a statement in the form P->Q really means to show it is impossible for Q to be false when P is true. This could be achieved by two ways: 1. Deduction - what was done in the original post. 2. By contradiction
 
3 hours later…
11:16
@TurkhanBadalov "to say that P implies Q (note, this is a form) means P→Q is a tautology." $\quad$ I find this imposition unuseful: it is reductive to conflate implication and tautological implication just because we are using propositional symbols/variables, which we do all the time even under a specified interpretation! (So, in fact, for atomic sentences P and Q, the sentence P→Q cannot be a tautology.)
@TurkhanBadalov I prefer to be able to call "I either am an Oookie or I am not an Oonkie" a tautology since its truth-functional form is true regardless of interpretation.
 
8 hours later…
19:05
@ryang "I prefer" - so what? Who are you that your preference is the law? You need to be HUMBLE
20:04
@Alborz I think that @ryang has made it clear that they no longer want to continue this discussion. Let it be.
Xander Henderson has frozen this room.

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