I'm struggling to understand the actual meaning of tautology. I know how to determine tautology with a truth table. But I don't understand what it actually means, so consider the following reasoning:
"If I know I'm dead, then I'm dead" and "If I know I'm dead, then I'm not dead". Therefore "I don't know I'm dead.
This can be formalised to $\left( \left( P\Rightarrow Q\right) \wedge \left( P\Rightarrow \lnot Q\right) \right) \Rightarrow \lnot P$ where $P:$"I know I'm dead" and $Q:$ "I'm dead".
Using a truth table I can determine that this statement is indeed a tautology. But what does that actually mean? Does it mean that I can't ever know if I'm dead or are the statements simply worded in a way that results in a tautology? Is the conclusion true in the real world?
Best Answer
The statement is true in the real world; it just doesn’t actually say anything very interesting, and in particular it doesn’t say that its conclusion $\neg P$ is true. The statement says that
if knowing that you’re dead implies that you really are dead,
and knowing that you’re dead implies that you really aren’t dead,
then you don’t know that you’re dead.
This is undeniably the case, since you cannot be both dead and not dead at the same time. However, it’s completely uninteresting unless you can imagine a situation in which knowing that you’re dead really does imply both that you are and that you are not dead. Until such a situation arises, the statement is vacuously true: it’s true because it’s an implication whose premise is false. As long as the condition specified in the premise is not met, the statement really says nothing much at all.