Expressions that do not express what they express.

[Antonio Speltzu]

The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

[Daniel Pehoushek]

On Saturday, September 10, 2022 at 5:43:41 AM UTC-4, Antonio Speltzu wrote:
> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

on circularity
Infinity in base two has an infinite length.
the definition has a circle.
your circular expression has n o t in it.

i avoid circular definitions in my work on the polynomial hierarchy.
in the code recursion is always finite.

modesty theorem:
p=np=pspace=#p=#q=qspace for modest size but not for large.
base cases are on k variables with k small.
daniel2380++

[WM]

Antonio Speltzu schrieb am Samstag, 10. September 2022 um 11:43:41 UTC+2:
> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

The expression points uniquely to a number Z but does not give its value. The expression however is not complete. It should specify the way how Z should be expressed. It is possible to abbreviate any desired name by a unique symbol like Z.

Regards, WM

[Antonio Speltzu]

There is an explanation of the paradox, but it is not that.

[Gus Gassmann]

On Wednesday, 14 September 2022 at 13:04:32 UTC-3, WM wrote:
> Antonio Speltzu schrieb am Samstag, 10. September 2022 um 11:43:41 UTC+2:
> > The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

> WM wrote: Bla bla.

"This sentence is false."

[Antonio Speltzu]

El sábado, 10 de septiembre de 2022 a las 11:43:41 UTC+2, Antonio Speltzu escribió:
> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

Or does it?

[Antonio Speltzu]

Nobody knows?

[WM]

If you specify the language (best would be digits), then everybody who does not know which number is meant must be rather stupid. If you don't specify the language then every number can be defined by ß.

Regards, WM

[Sergio]

On 9/10/2022 4:43 AM, Antonio Speltzu wrote:
> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

simplifies to;

1. The expression in P "A" evidently does not express A.

where A = the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P



do you see the problems in 1. ?

[Antonio Speltzu]

So A is a natural number???

[Jeffrey Rubard]

You guys seem nuts.

[Sergio]

the OP is.

[Antonio Speltzu]

Sergio does not distinguish between the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P which is certainly a number and "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" which is a string. Ginger up!

[Sergi o]

not at all, I assigned the letter A to your string of characters to simplify it. Which results in;

1. "The expression in P "A" evidently does not express A."

Then I asked you what problems did you see in 1.
You did not list the problems, or deny there are problems.

[Antonio Speltzu]

El martes, 20 de septiembre de 2022 a las 16:52:22 UTC+2, Sergi o escribió:
> On 9/20/2022 2:00 AM, Antonio Speltzu wrote:
> > El lunes, 19 de septiembre de 2022 a las 21:20:52 UTC+2, Sergio escribió:
> >> On 9/19/2022 2:02 PM, Jeffrey Rubard wrote:
> >>> On Sunday, September 18, 2022 at 1:00:54 PM UTC-7, Antonio Speltzu wrote:
> >>>> El domingo, 18 de septiembre de 2022 a las 18:27:54 UTC+2, Sergio escribió:
> >>>>> On 9/10/2022 4:43 AM, Antonio Speltzu wrote:
> >>>>>> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.
> >>>>> simplifies to;
> >>>>>
> >>>>> 1. The expression in P "A" evidently does not express A.
> >>>>>
> >>>>> where A = the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P
> >>>>>
> >>>> So A is a natural number???
> >>>>>
> >>>>>
> >>>>> do you see the problems in 1. ?
> >>>
> >>> You guys seem nuts.
> >> the OP is.
> >
> > Sergio does not distinguish between the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P which is certainly a number and "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" which is a string. Ginger up!
> not at all, I assigned the letter A to your string of characters to simplify it. Which results in;

Then you should have put:
A = "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P".
Without quotes A would be a number.
In both cases (1) does not make sense.

[Sergi o]

agree, ever use PureBasic?

[Antonio Speltzu]

El sábado, 10 de septiembre de 2022 a las 11:43:41 UTC+2, Antonio Speltzu escribió:

> The expression in P "the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P" evidently does not express the smallest natural number that cannot be expressed in P with less than 100^100 symbols of P.

The paradox is due to the fact that P is not expressible in P.

[Sergi o]

"P" ? or $P$ ?

[Antonio Speltzu]

Irony is one of the recourses of the ignorant.

[Ross A. Finlayson]

The smallest natural number, ..., that requires the same
digits as 100^100, ..., where digits can be replaced for expressions,
my first inclination is to replace the language with an arithmetization
in digits, about "the least last definable number" and so on.

The 100^100 many symbols or say 10^10, here basically 1 is a digit
and 10 is an order of magnitude. Ten's often enough a usual order
of magnitude, about 10^10, as the space of the range of the symbols,
according to defining conditions, which are as arbitrary as P.

By "arbitrary" it's that some symbols in P are small and for example
digits where a literal number is a definition in the extended in P. But,
under operators, expressions that define the terms are larger symbols,
in the sense that much smaller expressions in operations like the modular
and the exponential and so on, make for usual tetration in terms of the
largest numbers that can be written in the least symbols in P, where P
is a language of sequences of terms that have a natural integer value.
(Are defined, ..., also determinate and deterministic, have-a natural value.)

"The least ... not ..." is a usual template for indecision or for reductio, absurdam,
what-if or modal, about where boundaries are distinct or indistinct boundaries.

The Sorites or Heap paradox of "heap of sand, heap of sand, ..., grain of sand, no sand",
that no two grains are ever a heap but heaps are only grains, there's also the
usual Sand-Reckoner where basically, in some arbitrarily large and effectively an
ocean of space under 100^100, is that "2*" for example "doubles what can be written
in digits or the smallest symbols in "100^100 - 2".

That the usual number system itself often is the most significant digit, the most
convenient notation in digits is according to a fixed modulus, usually that being
according to, say, any encoding of a number according to a notation
(that's deterministic, ..., distinct, unique, ...).


So, what was it, "smallest, ..., requires 100^100 symbols", here it has to be avoided
the use-mention distinction, where "100^100 of the largest symbols in P define
a natural integer, with the value that it has, deterministic".

So, here "it's also the largest number".

Basically tetration and stacking tetration,
are "the largest symbols that compress the most".

The densest arithmetic coding though gets back into real numbers.

[Sergi o]

Irony meter it pegged out!

[Ross A. Finlayson]

Yeah irony supposedly is undefined.

Sometimes it's "oh, the humanity".

Still though it's like rain, a free ride, ....

Let's just say irony is always lost, ....

But, life is ironic enough itself.

[Ross A. Finlayson]

Dunning-Krueger is the worst sort of _irony_, ....

[Sergi o]

Then can irony your shirts too

notice the title

"Advances in Experimental Social Psychology"

David Dunning;

Abstract

In this chapter, I provide argument and evidence that the scope of people's ignorance is often invisible to them. This meta-ignorance (or ignorance of
ignorance) arises because lack of expertise and knowledge often hides in the realm of the “unknown unknowns” or is disguised by erroneous beliefs and
background knowledge that only appear to be sufficient to conclude a right answer. As empirical evidence of meta-ignorance, I describe the
Dunning–Kruger effect, in which poor performers in many social and intellectual domains seem largely unaware of just how deficient their expertise is.
Their deficits leave them with a double burden—not only does their incomplete and misguided knowledge lead them to make mistakes but those exact same
deficits also prevent them from recognizing when they are making mistakes and other people choosing more wisely. I discuss theoretical controversies
over the interpretation of this effect and describe how the self-evaluation errors of poor and top performers differ. I also address a vexing question:
If self-perceptions of competence so often vary from the truth, what cues are people using to determine whether their conclusions are sound or faulty?


[paywall]


https://www.sciencedirect.com/science/article/abs/pii/S0022103119301635

How innuendo shapes impressions of task and intimacy groups
Highlights

• Groups were perceived to lack warmth when described as highly competent.
• Groups were perceived to lack competence when described as highly warm.
• Innuendo effects were observed in relation to both task and intimacy groups.
• Communicating using innuendo indirectly weakened people's desire for group membership.


So, you #4 ?