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if someone says they always lie, are they lying or telling the truth?


Freakedbydubulge

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1. If someone who doesn't always lie says he always lie, then he's obviously lying.

2. If someone who always lie says he always lie, he would be telling the truth about him always lying, but that would mean he doesn't always lie, therefore ... (goto 1).

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Lets say the statement "I am lying" is the premise (P)
The act of actually lying is the implication (Q)
"I am lying" (P) => Lying (Q)

P => Q

Using logic truth tables (part of boolean algebra, I learnt this in secondary school) according to IF/implication rules there are 4 outcomes given 2 (P, Q) variables:

  • P(True) => Q(True) is TRUE
  • P(True) => Q(False) is FALSE
  • P(False) => Q(True) is TRUE
  • P(False) => Q(False) is TRUE

P (True) => P (False) can only be false.

That means if I say I am lying but I don't lie, then that is the logically contradictory.

 

In this case, you want to figure out if the initial statement is true/contradiction and since you know the implication (act of lying) is true (if they didn’t lie, then its obvious whether there’s a contradiction or not), then regardless of what of whether you intend "I am lying" as true or false, the whole thing is always TRUE. Proof:

  • "I am lying" (T) => Lying (T) is True
  • "I am lying" (F) => Lying (T) is True

The answer to your question, regardless if their statement is true or not, so long as they lie, they are always telling the truth.

 

Hopefully my explanation is clear and I haven’t rattled too many minds

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