Re: Descriptions, Presuppositions, Liar, Gödel

On Apr 22, 1:58 pm, Newberry <newbe...@xxxxxxxxxx> wrote:

1. A presupposes B if and only if A is neither true nor false unless B
is true.

Then A is not a sentence and has nothing to do with the Liar Paradox.

You can't "define" something as being "a sentence that isn't true and
isn't false".

I hereby define a CB-X as being a sentence that is neither true nor
false. Then the Liar Paradox is just an instance of a CB-X. No big
wup.

Giving new names to things is VERY BAD!

1. Occam says to use existing systems.

2. You aren't solving an existing problem with an existing system. If
you define a system called "Hypersets" and all of your theorems
concern the new system, then you have not solved any existing
problems. You have to prove a theorem that makes no reference to the
new system if it is to be an existing problem that the new system
solves. Otherwise, why invent a new system whose only justification
is itself?

C-B

or equivalently as

2. A presupposes B if and only if
(a) if A is true then B is true,
(b) if A is false then B is true.

That is if "The present King of France exists" is not true then "The
present King of France is bald" is neither true nor false. Bivalence
no longer holds.

Bas C. van Fraassen attempted to apply this theory to the Liar
paradox. "This sentence is false." He notes that the sentence is
paradoxical only if we assume bivalence, which we have left far
behind. He then goes on and analyzes the strengthened liar X = "This
sentence is either false or neither true nor false"

X presupposes T(~X). We have seen that T(~X) cannot be true; therefore, X has a presupposition that is not true. This is why X is neither true nor false. << [Van Fraassen, p. 148]

According to Kurt Gödel his argument is closely related to the Liar.
So how can we apply the presupposition analysis to it? First we note
that "All round squares are large" presupposes "A round square
exists." We can generalize it as

(Ax)(Fx -> Gx) (1)

presupposes

(Ex)Fx (2)

but (1) is equivalent to

~(Ex)(Fx & ~Gx) (3)

Therefore (3) also presupposes (2). Gödel's sentence has the
following format

~(Ex)(Ey)(Pxy & Qy) (4)

where Pxy means x is a proof of y, Q has been constructed such that
only the Gödel number of (4) satisfies it. Let the Gödel number of
(4) be m. Then

~(Ex)(Pxm) (5)

(5) states that there is no proof of (4). But (4) presupposes

(Ex)(Pxm) (6)

Therefore if (6) is not true then (4) is neither true nor false. If
(5) is true then there is no proof of (4), and (4) is neither true nor
false.

On Referring
P. F. Strawson
Mind, New Series, Vol. 59, No. 235 (Jul., 1950), pp. 320-344

Presupposition, Implication, and Self-Reference
Bas C. van Fraassen
The Journal of Philosophy, Vol. 65, No. 5 (Mar. 7, 1968), pp. 136-152


.

Relevant Pages

  • Devlin, Devlin, havent you read your Frege?
    ... So, when proper attention is paid to context, the Liar Paradox ceases ... is just as pressing a conundrum for situation theory as it is for any of ...
    (sci.logic)
  • =?iso-8859-1?q?Re:_Descriptions,_Presuppositions,_Liar,_G=F6del?=
    ... false - that's why it's a paradox", but you can and that's no ... Bas C. van Fraassen attempted to apply this theory to the Liar ... A presupposes B if and only if A is neither true nor false unless B ...
    (sci.logic)
  • =?iso-8859-1?q?Descriptions,_Presuppositions,_Liar,_G=F6del?=
    ... P. F. Strawson in his 1950 paper "On Referring" questioned the theory ... Bas C. van Fraassen attempted to apply this theory to the Liar ... But since the Liar paradox bears a certain similarity to ... A presupposes B if and only if A is neither true nor false unless B ...
    (sci.logic)
  • Re: Descriptions, Presuppositions, Liar,...
    ... Bas C. van Fraassen attempted to apply this theory to the Liar ... But since the Liar paradox bears a certain similarity to ... A presupposes B if and only if A is neither true nor false unless B ... exists X." The statement "If there is a largest twin prime, ...
    (sci.logic)
  • Re: OUTGOEDELING A HUMAN?
    ... and neither does "corresponds with the way the world is". ... and you are saying that the Liar ... The Liar paradox is not even expressible in ZFC. ... Why in the world should ZFC be affected by the Liar paradox? ...
    (sci.logic)