The Omniscience Principle

[Simmer]

I was browsing the web and I came across something which claimed to be the principle of omniscience:

for every function p: X → 2, ∃x ∈ X(p(x) = 0) ∨ ∀x ∈ X(p(x) = 1)

I thought it looked interesting, but I can’t seem to make out just exactly how it works...

is this something one can use in conjunction with absolute infinite? or is it spam... 

any input gladly taken.

 

-Oliver

Edited July 13, 2020 by Simmer

[studiot]

1 hour ago, Simmer said:

I thought it looked interesting, but I can’t seem to make out just exactly how it works...

is this something one can use in conjunction with absolute infinite?

This is a genuine sub sub branch of Pure Mathematics which is very obscure.

Try reading this

Wikipedia has a simple offering for once

https://en.wikipedia.org/wiki/Limited_principle_of_omniscience

 

Then read a full blooded paper from Birmingham University

 

https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf

 

Avoid the religious books by Paul Tranter

They are not connected.

 

https://books.google.co.uk/books?id=I8bKDwAAQBAJ&pg=PA69&source=gbs_selected_pages&cad=2#v=onepage&q&f=false

 

[joigus]

On 7/13/2020 at 5:27 PM, studiot said:

This is a genuine sub sub branch of Pure Mathematics which is very obscure.

Try reading this

Wikipedia has a simple offering for once

https://en.wikipedia.org/wiki/Limited_principle_of_omniscience

 

Then read a full blooded paper from Birmingham University

 

https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf

 

Avoid the religious books by Paul Tranter

They are not connected.

 

https://books.google.co.uk/books?id=I8bKDwAAQBAJ&pg=PA69&source=gbs_selected_pages&cad=2#v=onepage&q&f=false

 

I wasn't aware of this branch of maths. Thanks a lot, Studiot. +1

I've found this other one:

https://plato.stanford.edu/entries/mathematics-constructive/

Stanford's Encyclopedia of Philosophy has helped me a lot in the past (to understand the Kochen-Specker argument in QM, for example).

[Simmer]

So if I were to replace x with Ω, would the equation be able to distinguish itself to be god or bad

[Simmer]

https://ncatlab.org/nlab/show/principle+of+omniscience
 

here’s a simpler one...

Edited July 19, 2020 by Simmer

[Simmer]

On 7/19/2020 at 6:51 PM, Simmer said:

https://ncatlab.org/nlab/show/principle+of+omniscience
 

here’s a simpler one...

I noted this one did not embed the function into itself

 

whats the difference?

Edited July 21, 2020 by Simmer

[studiot]

1 hour ago, Simmer said:

I noted this one did not embed the function into itself

 

whats the difference?

Sorry I don't follow.

The difference between what and what?

 

Nice link however. Thank you +1.

 

Personally as a pragmatic Mathematician I am not with the constructionists.

A short quote from Joigus' link will serve to show what I mean

Quote

https://plato.stanford.edu/entries/mathematics-constructive/

Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”

 

Anyone who has studied more than the simplest differential equations will have met examples of

We can prove the existence  (there existence) of a solution, but that does not help us to find it. (construct).
Worse, much of physics is controlled by, and therefore demonstrates the existence of solutions, to equations that we cannot solve.

[Simmer]

Well obviously if all instances of x equal true then x is true

and if only some instances of x exist but some don’t then x is false

this means god as x can be thought of under the same terms, under the same similarity of x after being defined as either true or false respectively

 

but what is the similarity of the two, truth and falsehood, that lead to a definite conclusion

is it indicated in the equation already? Does the simple indication of truth and falsehood mean that the truth and falsehood is known?

 

https://quantumcomputing.stackexchange.com/questions/5273/how-can-quantum-computing-win-97-of-times-in-coin-flipping-experiment?rq=1

this seemed not entirely related

but still involved the same concepts 

Edited July 22, 2020 by Simmer

[studiot]

I think some people expect too much of mathematical 'true' and 'false'.

They try to use them in situations where they are inappropriate.

Take the integer equation

a + b = 10

What is its solution?

This has an infinity of solutions which are 'true'

But it also has an infinity which are 'false'.

 

[Simmer]

Lol I’d take the wheels out of the cart and attach them to it if I were them...

[Simmer]

Earlier I mentioned the absolute infinite but I failed to clarify:

 

∀X:Φ(X)→∃α:ΦVα(X∩Vα)

 

should replace x in the omniscient principle ^^^

[Simmer]

https://www.phil.uu.nl/~iemhoff/Mijn/Slides/seattle17.pdf
 

intuitional logic