Mike,

I agree that those two questions are extremely difficult questions about physics, and nobody knows how to anwer them.  But that is not a question about mathematical logic, which Mihai Nadin was discussing in his note below.  

For the first question, you could start by writing an equivalent in an Englishy kind of logic:

1. For every x of type "law of nature" for every time t, law x is consistent at time t.

That is a rather simple statement in logic, but nobody would know how to answer it by any possible experiment  short of examining every region of the universe for all eternity.

The second has the same limitation.  It's a simple statement in logic that cannot be answered without testing it in every location of the universe at all points in time.:,  

2. For every x of type "law of nature" for every y of type "region of the universe", x is applicable at y.

John
 

From: "Mike Bergman" <mike@mkbergman.com>

Hi John,

OK; I'll bite, and give you two. See below.

On 9/21/2024 5:09 PM, John F Sowa wrote:
I agree with the note below.  But nobody but a logician who has studied advanced issues in logic knows how to state an undecidable proposition,  

I would challenge anybody to find a single undecidable proposition in any branch of science or engineering or economics or politics or any field other than advanced mathematics.
  1. "The laws of nature are consistent across time" (the counter was a favorite of Peirce)
  2. "The laws of nature are universally applicable across all regions of the universe."

Thanks, Mike



I won't deny that a professional logician might contrive an undecidable proposition about some subject matter in any of those fields.  But I will predict with almost absolute certainty that no professional in that field would understand it.  And even if the logician could explain that proposition to somebody in that field, I predict with almost absolute certainty that the professional in that field would consider it irrelevant or even ridiculous. 

And by the way, if anybody could contrive such a proposition, I would be delighted to see it.  Please send it to the list, state the proposition in English, translate it to some version of logic, prove that it is indeed undecidable, and find a professional in that field who would consider it significant.

I seriously doubt that anybody could do that, but I'd be happy to be proven wrong.

John
 

From: "Nadin, Mihai" <nadin@utdallas.edu>
 Sent: 9/20/24 5:39 PM
 To: "ontolog-forum@googlegroups.com" <ontolog-forum@googlegroups.com>
 Subject: [ontolog-forum] goedel and more

Discussing Penrose is justified. BUT: the focus should be on Goedel. Allow me to repeat my advice: read the paper, i.e. his proof. Read also Turing, i.e. his proof for the Hilbert challenge.

Against my better judgment, I am suggesting one of my papers:

https://www.researchgate.net/publication/314424008_The_Intractable_and_the_Undecidable_-_Computation_and_Anticipatory_Processes

(in my book https://link.springer.com/book/10.1007/978-3-031-43957-5 this is discussed in detail)

But I am not reacting to recent opinions only for the sake of pointing to my work.

The thing that concerns me regarding the discussion is expressed as 

…and perhaps some day someone will somehow prove things that are unprovable according to GT/C

 

Let us agree that science is not only about what is possible, but also about what is not possible. Squaring the circle—anyone? Just to give an example. Within the number construct we are using, there is PI)—no need to redefine it here. As long as we stick to the numbers used currently in order to represent our measuring (quantitative aspects) of reality, the doubling of the cube and trisecting the angle will remain impossible because of how we defined  . NOT even the not yet invented new forms of computation will do it.

 

Goedel discovered for a well-defined aspect of mathematics that consistency and completeness are not possible. Those using the outcome of his proof owe it to him to understand what the meaning of this is. Doubt is good (Dubito ergo sum), on the assumption that is grounded in knowledge. Get if from the source.

 

Mihai Nadin

https://www.nadin.ws

https://www.anteinstitute.org

Google Scholar