## The death of Classical logic and the birth of Constructive Mathematics

What is the basis for reason? And mathematics?

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Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Atla wrote: Sun Feb 24, 2019 4:05 pm Well you only get 0 and 1 fuzzy also has 0 and 1 and everything in between,
Nonsense. All n-value logics can be implemented in Lambda calculus. And they can be run on a classical computer.

It's called emulation ( https://en.wikipedia.org/wiki/Emulator )

We can do quantum computation ON classical computers which is precisely infinite (or as much as memory allows) precision between 0 and 1.
It will run VERY slowly as compared to a real quantum computer, but the principle matters.

You don't understand Turing-completeness...
Atla wrote: Sun Feb 24, 2019 4:05 pm plus with the right hemisphere you can sort of easily add dimensions of logic.
Notice how you keep attacking my character and keep insinuating that something is "wrong" with my brain rather than confront all the facts being laid out in front of you.

You sure are a despicable human being, aren't you?
Atla
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote: Sun Feb 24, 2019 4:07 pm
Atla wrote: Sun Feb 24, 2019 4:05 pm Well you only get 0 and 1 fuzzy also has 0 and 1 and everything in between,
Nonsense. All n-value logics can be implemented in Lambda calculus. And they can be run on a classical computer.

It's called emulation.

We can do quantum computation ON classical computers. VERY slowly as compared to a real quantum computer, but the principle matters.
Atla wrote: Sun Feb 24, 2019 4:05 pm plus with the right hemisphere you can sort of easily add dimensions of logic.
Notice how you keep attacking my character and keep insinuating that something is "wrong" with my brain rather than confront all the facts being laid out in front of you.

You sure are a despicable human being, aren't you?
Emulation sucks, with the right hemisphere I can do it directly, much faster and simpler.
The left hemisphere logic is really only needed in those cases when something is really considered a yes/no question.
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Atla wrote: Sun Feb 24, 2019 4:13 pm Emulation sucks, with the right hemisphere I can do it directly, much faster and simpler.
Really? What's the 162nd prime number?
Atla wrote: Sun Feb 24, 2019 4:13 pm The left hemisphere logic is really only needed in those cases when something is really considered a yes/no question.
Can you think of something that can't be posited as a yes/no question?
Atla
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote: Sun Feb 24, 2019 4:14 pm
Atla wrote: Sun Feb 24, 2019 4:13 pm Emulation sucks, with the right hemisphere I can do it directly, much faster and simpler.
Really? What's the 5623423462134th prime number?
Atla wrote: Sun Feb 24, 2019 4:13 pm The left hemisphere logic is really only needed in those cases when something is really considered a yes/no question.
Can you think of something that can't be posited as a yes/no question?
Well you can emulate everything using yes/no, but I guess you would need to live for a few hundred years to compensate for the lack of direct fuzzy logic.
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

https://repl.it/repls/LimegreenDefiantHardware

However long this takes, it sure as FUCK isn't going to be slower than you!
Last edited by Logik on Sun Feb 24, 2019 4:18 pm, edited 1 time in total.
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Atla wrote: Sun Feb 24, 2019 4:15 pm Well you can emulate everything using yes/no, but I guess you would need to live for a few hundred years to compensate for the lack of direct fuzzy logic.
This is precisely what quantum computers are solving.

So while they are gaining mainstream popularity (and until they become affordable) so you and I can have one in our own homes, we can already start formalizing the models we would want to run on them...
Atla
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote: Sun Feb 24, 2019 4:17 pm
Atla wrote: Sun Feb 24, 2019 4:15 pm Well you can emulate everything using yes/no, but I guess you would need to live for a few hundred years to compensate for the lack of direct fuzzy logic.
This is precisely what quantum computers are solving.

So while they are gaining mainstream popularity (and until they become affordable) so you and I can have one in our own homes, we can already start formalizing the models we would want to run on them...
No, quantum logic isn't fuzzy logic, and there are no real quantum computers yet, probably never will be.
Arising_uk
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote:It doesn't matter.

The law of non-contradiction is broken in exactly the same way.
Ignore identity.
...
Well I already ignore the equality sign in propositional and predicate logic so no problem there but you're going to have to go a long way to convince me that that a thing is not that thing and a thing can exist and not exist at the same time. Unless of course you're going to be a sophist and conflate definitions of "exist"?
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Atla wrote: Sun Feb 24, 2019 4:18 pm No, quantum logic isn't fuzzy logic
Functionally identical.

Here is a Qubit. https://en.wikipedia.org/wiki/Bloch_sphere

It has infinite degrees of freedom to represent infinite values on the surface of a sphere.

Atla wrote: Sun Feb 24, 2019 4:18 pm there are no real quantum computers yet, probably never will be.
Yes. You've told that lie before.

https://quantumexperience.ng.bluemix.net/qx/experience
https://spectrum.ieee.org/tech-talk/com ... ud-service
Last edited by Logik on Sun Feb 24, 2019 4:23 pm, edited 1 time in total.
Atla
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote: Sun Feb 24, 2019 4:21 pm
Atla wrote: Sun Feb 24, 2019 4:18 pm No, quantum logic isn't fuzzy logic, and there are no real quantum computers yet, probably never will be.
Functionally identical.

Here is a Qubit. https://en.wikipedia.org/wiki/Bloch_sphere

It has infinite degrees of freedom to represent infinite values on the surface of a sphere.
Except we will probably never be able to create actual qubits.
All we can do is try to simulate qubit behaviour using rather classical methods.
Scott Mayers
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote: Sun Feb 24, 2019 2:57 pm
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm You are expecting an assignment whereby the left-side expression takes the value of the right-side because you are used to those higher-ordered languages in computing. The error is not to the 'classic' logic though but to your 'top-down' approach to learning.
Why is top-down learning a mistake? Isn't this how all humans learn?
First you experience water, only then do you learn that it's made of Hydrogen and Oxygen.
First we learned about atoms only later we learned about electrons and protons.
And later yet did quantum physics come to the party.

Human experience is top down, not bottom up.
Yes, at first you begin where you are to 'scientifically' determine what may be true. But then you use that to determine a logic 'bottom-up' that predicts what can come of it. You were interested in 'constructing' logic systems? We look at patterns then guess what the pattern can be in a formulated way.

But I did what the ancients did: ask what our 'origins' could be from a minimalistic origin, like Nothing or One thing, and try to find rules that 'fit' to everything. That is how logic operates. If a 'scientific' approach begins with our senses from where we are to induce what the 'laws' of nature might be, 'logic' presumes certain some prior set of laws and tests them 'forward' bottom-up.

I'm non-religious and logically Nihilistic (not morally or psychologically dreadful of the lack of concern of reality). For this to be the case should imply a universe that 'constructs' on its own bottom-up without a mind. Either simple rules or, in my take, no rules at an origin, are required and thus nature is bottom-up in essence. That's my focus...to determine some rationale that begins from nothing at all. It requires recognizing contradiction as an active means to 'construct' reality.
Logik wrote: Sun Feb 24, 2019 2:57 pm
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm The general three laws accepted are:
(1) A law that asserts consistency but often stated as about 'equality'.
A = A but you need to translate in computers as A == A
That is what I have done. Perhaps I should draw a line in the code.

At first I set the context (defining classes objects etc).

The assertions are at the bottom.
Don't do it for me. I haven't learned Python and lack sufficient confidence with the formal object languages. I'm more 'functional' and even more concerned about machine and assembly languages (architecture).

Logik wrote: Sun Feb 24, 2019 2:57 pm
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm (2) A law that asserts,
A or not-A and
But if A represents an object that is a human. The logical expression not A doesn't make sense.

What exactly is the negation of a human? I can't conceive of such a thing!

Is it an ape or a planet?
Negations have different approaches in different logic systems. Our very languages have multiple kinds of negation, not just one type.

For 'classical' types, "Non-X" means "All (that is) not-X"; "not-X" may mean either "any part of non-X (but unspecified)" or just a denial of existence, such as an answer to a question, like, "Does X exist?" or "does some X exist" to which "not-X" doesn't require positing anything.

The "complement" is a negative meant to actually mean, any or all parts that are not-X, but is then more clearly written as 'non-X'. Because the simpler "not-X" often implies that you posited X, then "not-X" means anything that is not X.

So if "human" is posited, then "not-human" actually refers to "non-human", the class of everything else that isn't of the meaning 'human', such as a pencil, green eggs with ham, or any of an infinity of things.

George Boole originally defined his complements by treating the negation as an operator between two variables. Set theories usually do this too. You assign some 'universe' as "U", then, if X is "humans",

"Not-humans" means non-humans and is expressed as: (U - X). You conflated the way we sometime use a negative description in context to imply an opposite within a smaller 'universal'.

If U = 'all animals', then (U - X) means a "non-human but (still) an animal".

So define negation/complements as a binary operator instead of a unary one.

Not-X == U - X
Arising_uk
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Logik wrote:...
So while they are gaining mainstream popularity (and until they become affordable) so you and I can have one in our own homes, we can already start formalizing the models we would want to run on them...
Sod that! Way too fragile with to many support systems required, give me a nanotech rod-logic box. Babbage and Drexler Roolz!
Last edited by Arising_uk on Sun Feb 24, 2019 4:25 pm, edited 1 time in total.
Atla
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### Re: The death of Classical logic and the birth of Constructive Mathematics

No, you told that lie before, because you don't understand that those computers use randomly behaving qubits.
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Atla wrote: Sun Feb 24, 2019 4:24 pm No, you told that lie before, because you don't understand that those computers use randomly behaving qubits.

What kind of qubit do you want, a deterministic one ? That's called a bit.
Logik
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### Re: The death of Classical logic and the birth of Constructive Mathematics

Arising_uk wrote: Sun Feb 24, 2019 4:19 pm Well I already ignore the equality sign in propositional and predicate logic so no problem there but you're going to have to go a long way to convince me that that a thing is not that thing and a thing can exist and not exist at the same time. Unless of course you're going to be a sophist and conflate definitions of "exist"?
So what you are saying is that you don't trust logic, but you trust your eyes? Good!

Because that's EXACTLY what logic is for!
You use logic AFTER experience, not before.
From experience you form abstract concepts like "human" and "cat".
You use logic to construct models of your concepts.

Logic/metaphysics is about the map, not the territory!

In constructive mathematics, the moment you DEFINE something - it exists!

A = Human()

At this point that you can say that "A exists" (or perhaps more precisely - the concept of A exists).
Then you can also say A == A is False. But I don't know what that means.

Probably because I can't think of any meaningful line of inquiry in which I would end up comparing myself to myself.
Last edited by Logik on Sun Feb 24, 2019 4:44 pm, edited 8 times in total.