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Is there a proposition known to be undecidable?


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12 hours ago, Tristan L said:

Since the reader knows that "witchcraft" wouldn't make much sense in the context, don't they come up with the thought to read again more carefully so as to check what actually stands written there?

No, they come to the conclusion that you're a little off. At least I did. 

Likewise brook, which has a different connotation in standard English, meaning "to stand for or tolerate." As in, "He brooks no difference of opinion."

You give the impression of playing games with your own internal language, which detracts from whatever you're trying to say.

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21 hours ago, joigus said:

But how many of those Anglish speakers are knowledgeable enough to have a meaningful conversation about second-order logic?

Well, since the set of all humans is finite, there always has to be a first one.

21 hours ago, joigus said:

I'm sure a compromise is possible.

Of course. 👍

21 hours ago, joigus said:

Mathematics has nothing to do with empire-building, does it?

Nope, it doesn't, that's totally right, and that's my point: If we only ever speak or write Anglish for the sake of speaking or writing Anglish, it will never become natural or brookful (useful). A speech whose main goal is itself isn't a very useful speech, is it? So here I am, someone who is far more interested in rimlore (mathematics), flitecraft (witcraft, logic), lore (science), and wisdomlove (philosophy, wisdomlore) than in Anglish, but who nevertheless brooks (uses) Anglish to a reasonable extent.

But by rights, this ought to be talked about in a speechlore (linguistics) forum rather than one about maths, so let's get back to the orspringly (original) topic.You seem to have been right after all that CH is a proposition of the kind that I was searching for – almost, that is, for the independence of CH in higher-step logic of the Dedekind-Peano-axioms depends on our not finding a new property of the true set-universe which goes beyond ZFC.

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2 hours ago, Tristan L said:

You seem to have been right after all that CH is a proposition of the kind that I was searching for – almost, that is, for the independence of CH in higher-step logic of the Dedekind-Peano-axioms depends on our not finding a new property of the true set-universe which goes beyond ZFC.

It must have been sheer luck. Let's say I was just talking from hearlore. ;)

But you've made noises in the innermost recesses of my linguistic and mathematical mind and awaken the creatures that live in the gallery of my mathematical and linguistic monsters. Maybe another thread is in order.

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On 2/10/2021 at 10:01 AM, Tristan L said:

Yes, for we cannot simply accept any self-referential statement, like "This statement is false", as meaningful. If we can formalize "this statement cannot be proved from the second-order DP axioms   AND   2+1 = 3" in the speech of second-order (or any higher-step) flitecraft (logic), I'll accept it.

Hi again.

   Thanks for explaining your requirements.  Sadly, I'm not an expert on higher order logic and it seems unlikely I'll have time to become familiar with it over the next few months.  So I'll be bowing out of this conversation.  Sorry I couldn't help. 

Best wishes to you, bye for now.

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8 hours ago, Col Not Colin said:
On 2/10/2021 at 10:01 AM, Tristan L said:

Yes, for we cannot simply accept any self-referential statement, like "This statement is false", as meaningful. If we can formalize "this statement cannot be proved from the second-order DP axioms   AND   2+1 = 3" in the speech of second-order (or any higher-step) flitecraft (logic), I'll accept it.

Hi again.

   Thanks for explaining your requirements.  Sadly, I'm not an expert on higher order logic and it seems unlikely I'll have time to become familiar with it over the next few months.  So I'll be bowing out of this conversation.  Sorry I couldn't help. 

But you did help.

🙂

Thank you for picking out an example of the wider scope of English over Maths.  +1

Truth values are not the only values in English and even these are not fixed.

For instance the apparantly mathematical question "How many sheep are in that field ?"

Say the answer come's back as 13.

But I didn't include the information that 5 of these sheep about to lamb.

Tristan's self referential question also includes (amongst other values) comic value in English.

Edited by studiot
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On 2/12/2021 at 2:09 AM, studiot said:

But I didn't include the information that 5 of these sheep about to lamb.

 

As a child of the suburbs I did not know that lamb could be verbed.

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On 2/15/2021 at 1:14 AM, wtf said:

As a child of the suburbs I did not know that lamb could be verbed.

It is not unique.
As a californian, don't you have the verb to foal for horses ?

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As I know, such theorem independent on Peano's axioms, is Goodstein Theorem.

On the other hand, there in the paper: T. J. Stępień, Ł. T. Stępień, "On the Consistency of the Arithmetic System", J. Math. Syst. Sci. 7, No.2, 43-55 (2017); arXiv:1803.11072 ,  a proof of consistency of Arithmetic System was published. This proof had been done within this Arithmetic System.

                                                                                                                                                                                      Łukasz

Edited by Lukasz
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9 hours ago, studiot said:

As a californian, don't you have the verb to foal for horses ?

The nearest horse is far from where I live. But my point was that horses foal (if you say so); they don't horse. Whereas evidently, lambs lamb. Which I didn't know. 

Now I'm gonna take it on the lam.

Edited by wtf
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1 hour ago, wtf said:

Now I'm gonna take it on the lam.

 roflmao.gif.d2e1ab573474ad4726ace6414c46204d.gif    +1

1 hour ago, wtf said:

Whereas evidently, lambs lamb.

Not quite

Sheep lamb.

Mares foal.

Seals pup

Biches whelp

I'm sure there are plenty more but that will do.

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2 minutes ago, studiot said:

I'm sure there are plenty more but that will do.

Thanks for the info. As a suburbanite I'm just getting over the shock of learning that cheeseburgers are made of chopped up dead cows. I had no idea.

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4 hours ago, Lukasz said:

As I know, such theorem independent on Peano's axioms, is Goodstein Theorem.

On the other hand, there in the paper: T. J. Stępień, Ł. T. Stępień, "On the Consistency of the Arithmetic System", J. Math. Syst. Sci. 7, No.2, 43-55 (2017); arXiv:1803.11072 ,  a proof of consistency of Arithmetic System was published. This proof had been done within this Arithmetic System.

                                                                                                                                                                                      Łukasz

Welcome Lukasz and thank you for the information. +1

I look forward to more excellent contributions from you.

I have been playing with set theory involving non indpendent members (overlap) lately and there seems to be little available.
Do you know anything about this ?

1 minute ago, wtf said:

Thanks for the info. As a suburbanite I'm just getting over the shock of learning that cheeseburgers are made of chopped up dead cows. I had no idea.

Please don't make Kennedy's Berlin mistake.

🙂

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On 2/16/2021 at 6:14 PM, Lukasz said:

As I know, such theorem independent on Peano's axioms, is Goodstein Theorem.

On the other hand, there in the paper: T. J. Stępień, Ł. T. Stępień, "On the Consistency of the Arithmetic System", J. Math. Syst. Sci. 7, No.2, 43-55 (2017); arXiv:1803.11072 ,  a proof of consistency of Arithmetic System was published. This proof had been done within this Arithmetic System.

                                                                                                                                                                                      Łukasz

Goodstein's Theorem cannot be proven in first-order Peano-arithmetic, but it can be shown in the system of the second-order Dedekind-Peano-axioms (called "DP" in this thread), and this system is what I'm interested in.

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