Re: Where is the paradox in liar?

In article <e34lnq$11q2$1@xxxxxxxxxxxxxxxxxxx>,
"H. J. Sander Bruggink" <bruggink@xxxxxxxxxx> wrote:

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.

As has been pointed out by others, that doesn't help. For example, let
the truth values be real numbers from 0.0 (definitely false) through 1.0
(definitely true). Then what is the truth value of the following:
This sentence does not have a truth value of 1.0.

It is 1.0 iff it is not.

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

groente
-- Sander
.

Relevant Pages

  • Re: Question for religious parents
    ... Which is NOT the same as "jettisoning truth in the name of tolerance". ... Saying that just because you think that a proposition is true doesn't ... contradiction leads to being able to prove that *any* proposition is ...
    (misc.kids)
  • Re: Some advice from the people who know please.
    ... I understand what you are saying. ... easily way to parse out the truth quickly. ... But the way I see it, I frequently find that the journalists that I am ... All credible evidence fits ...
    (alt.lang.asm)
  • Re: The writing is on the wall
    ... The difference between fluid dynamics and economics is that economics ... Marx was a philosopher whose inane ideas ended up morphing into ... the ppl who tell "the truth" are winnowed out early, ... So you are in effect saying that things are totally fucked and that I ...
    (rec.martial-arts)
  • Re: Godels theorem is invalid?
    ... > Then his definition of truth simply does not match the classical one. ... I am not saying that I agree with Tennant's arguments (which are based ... What exactly do you mean by the assertion ... > NOT ONE IOTA OF IMPACT on the TRUTH or the MEANING ...
    (sci.logic)
  • Re: Universality as warrant for relative truth value
    ... say that you set postmodernism aside because it's not a means to your ... There's no truth, only points ... saying this? ... The reason is simple: ...
    (sci.philosophy.meta)