Re: Where is the paradox in liar?

Newberry wrote:
There is one only if you assume every sentence is true or false.

Precisely. So why do we keep saying that every sentence is either true
or false? We have just proved by contradiction that this is not the
case. Liar's paradox is a counterexample.

1 Every sentence is eiher true or false Assumption
2 "This sentence is false" is neither true nor false. Proven above
3 Not every sentence is either true or false Conclusion from 1 and 2

I.e. a viable system of formal logic must have more than 2 truth
values.


This doesn't follow. What does follow is that every formal
logic in which you can represent "This sentence is false."
must have more than 2 truth values.

In mathematical logic, provability can be defined, but not
truth.

groente
-- Sander
.

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