Re: OUTGOEDELING A HUMAN?

On Feb 22, 10:55 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
abo says...


First of all, let's get rid of the context-dependent phrase
"this sentence" by introducing a name "Abo's sentence" and
defining it to be the sentence

Abo's sentence is not universally true.

Okay, now let's make the definition of "universally true"
more precise:

A sentence S is universally true if
for all interpretations i, if S is given
any interpretation in i, then it is interpreted
as true in i.

which is equivalent to

A sentence S is universally true if there does not
exist an interpretation i such that S is interpreted
as false in i.

So Abo's sentence is equivalent to the following claim:

There is an interpretation i in which Abo's sentence
is interpreted to be false.

So what's an interpretation? An interpretation assigns meanings
to all noun phrases and predicate phrases and provides a domain
for any quantifiers. The above sentence involves quantification
over interpretations. So if interpretation i_1 gives any
interpretation to the above sentence, then i_1 must provide a
domain D_1 which is the set of interpretations quantified over.

So the interpretation of the above sentence in interpretation i_1
is:

There is an interpretation i in D_1 in which Abo's
sentence is interpreted to be false.

If the domain D_1 is empty, then i_1's interpretation of
Abo's sentence is false. If i_2 is a second interpretation
such that D_2 = { i_1 }, then i_2 would interpret Abo's
sentence as:

There is an interpretation i in D_2 in which Abo's
sentence is interpreted to be false.

which, in the case where i_1 is the only element of D_2,
is equivalent to

Abo's sentence is interpreted to be false in i_1.

which is true.

So Abo's sentence is interpreted to be true in some
interpretations, and false in others.

OK let me return to your argument here. Label

Abo's sentence is not universally true.

as (AS). You agree that (AS) is true. Now either you say that it is
true-in-L for some L, or you say there is no such L.

Option 1. It's true-in-L for some L. What does this mean (according
to you)? Apparently it means "For all interpretations i, Abo's
sentence is interpreted to be true." But consider your own D_1 and
i_1. As I understand it, the sentence would be false under this
interpretation. So it's not true-in-L. That is, your argument -
that there are interpretations where the sentence is interpreted to be
true and others where it is interpreted to be false - looks like it's
independent of the language L (perhaps I am mistaken, but that's how I
read it). So you argument shows that (AS) is not true-in-L for *any*
L. But this contradicts the hypothesis.

Hence we must conclude:
Option 2. It's true, but it's not true-in-L for any L. So this just
shows that natural language truth is not the same as true-in-L, for
any L.

.

Relevant Pages

  • Re: OUTGOEDELING A HUMAN?
    ... Yes, but not universally true. ... interpretation you claim to be true what you claim. ... again referring to that fixpoint level! ... implicitly claim truth for your statements in some absolute sense and ...
    (sci.logic)
  • Re: Factoring paper is wrong
    ... > universally true and would in this sense be 'absolute', ... What about formal independency? ... Now reduce it to the Herbrand ... interpretation f', ...
    (sci.crypt)
  • Re: Factoring paper is wrong
    ... >>universally true and would in this sense be 'absolute', ... > What about formal independency? ... Now reduce it to the Herbrand ... > interpretation f', ...
    (sci.crypt)
  • Re: Factoring paper is wrong
    ... >>universally true and would in this sense be 'absolute', ... > What about formal independency? ... Now reduce it to the Herbrand ... > interpretation f', ...
    (sci.logic)
  • Re: Alito In
    ... sethb@xxxxxxxxx (Seth Breidbart) writes: ... >>phrases from it just get other iterations of those phrases. ... > But the editorial claims he said he supports the underlying position. ... In fact, if your interpretation is the one that Alito intended, then I ...
    (rec.arts.sf.fandom)