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I was doing some very, super, light reading on self reference.

It seems to me that the statement

  • nothing that I say is true

both:

  • cannot be understood with the T-schema;
  • is self referential.

- Everything that Bill believes is true.

Heath argues that analyzing this sentence using T-schema generates the sentence fragment—“everything that Bill believes”—on the righthand side of the Logical biconditional.

Is that the case?

It also seems the sentence is both:

  • ungrounded, as it can't be categorically true; but
  • not analytic, because if it is false we can't tell from the sentence alone.

I wondered if this meant the sentence could be true, but that this cannot be formalised into any "truth value".

  • sorry if this is total nonsense btw, i'm stupid and lazy ! –  Jul 15 '16 at 07:59
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    I'm not sure I understand your question, but your sentence is indeed self referential, and it's just another version of the liar paradox. It's equivalent to "everything I say is false", which entails "this sentence is false". – E... Jul 15 '16 at 08:10
  • will edit it, sorry –  Jul 15 '16 at 08:20
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    @MATHEMETICIAN I have a hard time wrapping my mind around a sentence being _true_ while lacking a truth value. True simply is one of the (classically, 2) truth values. Typically when you want to allow for an indeterminate truth value you add a third truth value to represent "neither true nor false". What sort of thing did you have in mind by "true but...cannot be formalized into any truth value"? – Dennis Jul 16 '16 at 13:23
  • There are certainly truths that cannot be formalized. What does it mean to be 'formalized into a truth value'? General truths like 'Everything is similar in some way to something you already know', can be true, but have no reliable embedding in any formalization because ideas like similarity and opposite-ness are not relations, existence is not a predicate, etc. http://philosophy.stackexchange.com/q/36028/9166, http://philosophy.stackexchange.com/q/35897/9166. Not sure this is what you are after... –  Jul 16 '16 at 15:45
  • The Continuum hypothesis can not currently be assigned a truth value, but both ‎Gödel and Cohen believed it to have a definite truth value. https://en.wikipedia.org/wiki/Continuum_hypothesis – user4894 Jun 01 '19 at 23:08

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I'd say no - it's not clear what it means for something which can't be assigned a truth value to be true. If it can't be assigned a truth value, then isn't it "nonsense"?

But the reverse might be so: that which "cannot be assigned a truth value" can be assigned a value of "false", as "nonsense" is not "true". And that which is not true, is false.

user558317
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