The death of Classical logic and the birth of Constructive Mathematics

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

Post Reply
Atla
Posts: 2888
Joined: Fri Dec 15, 2017 8:27 am

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

Post by Atla »

Logik wrote: Sun Feb 24, 2019 4:26 pm
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.
:lol: :lol: :lol: :lol: :lol:

What kind of qubit do you want, a deterministic one ? That's called a bit.
You talked about randomly behaving qubits that somehow give the right answers.

You are an idiot as always, not having an idea what you are talking about.

Well I think that's enough now, I have better things to do.
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

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

Post by Logik »

Atla wrote: Sun Feb 24, 2019 4:31 pm You talked about randomly behaving qubits that somehow give the right answers.
Yes. All qubits do that. They give the approximately right answer (with high degree of certainty).

It doesn't mean quantum computers are always right, but it does mean that they are very rarely wrong.

IF you can define the procedure for obtaining the answer... A human still has to express/explain the HOW.
Scott Mayers
Posts: 1694
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

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

Post by Scott Mayers »

Atla wrote: Sun Feb 24, 2019 4:18 pm
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.
"Fuzzy logic" was specifically designed as a multi-variable logic used to attempt to determine how to either design a quantum-logical system or for artificial intelligence. So it is related. But I agree that no quantum computers will exist literally as expected. They will always require more energy per unit bit because you require super-cooling the metal to reduce its 'induction' effects. These are natural magnetic waves that get induced when current accelerates and decelerates. To make a 3-valued, unit requires setting a loop of metal that allows a negative voltage, a zero-voltage, and a positive one and thus needs to alter frequencies too quick for very-very-small-scale electronics. So these parts have to be also larger than their binary components. Furthermore, they've designed the 'Q-bit' as an 2-dimensional array of these in multiples (8, I think?).

They would have an advantage to do unique KINDS of computing, such as encrypting and decrypting at powerful rates. So they'd work like 'master-keys' for both creating hard locks and undoing them. But the rate at which they get used to encrypt would cancel out the effective speed of decrypting canceling out their prior effectiveness. They'd still be good to prevent things like 'snooping' though and would make some things permanently unable to be tapped when devised with proprietary copyright systems, like HDMI electronics.
Atla
Posts: 2888
Joined: Fri Dec 15, 2017 8:27 am

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

Post by Atla »

Scott Mayers wrote: Sun Feb 24, 2019 4:50 pm
Atla wrote: Sun Feb 24, 2019 4:18 pm
Logik wrote: Sun Feb 24, 2019 4:17 pm
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.
"Fuzzy logic" was specifically designed as a multi-variable logic used to attempt to determine how to either design a quantum-logical system or for artificial intelligence. So it is related. But I agree that no quantum computers will exist literally as expected. They will always require more energy per unit bit because you require super-cooling the metal to reduce its 'induction' effects. These are natural magnetic waves that get induced when current accelerates and decelerates. To make a 3-valued, unit requires setting a loop of metal that allows a negative voltage, a zero-voltage, and a positive one and thus needs to alter frequencies too quick for very-very-small-scale electronics. So these parts have to be also larger than their binary components. Furthermore, they've designed the 'Q-bit' as an 2-dimensional array of these in multiples (8, I think?).

They would have an advantage to do unique KINDS of computing, such as encrypting and decrypting at powerful rates. So they'd work like 'master-keys' for both creating hard locks and undoing them. But the rate at which they get used to encrypt would cancel out the effective speed of decrypting canceling out their prior effectiveness. They'd still be good to prevent things like 'snooping' though and would make some things permanently unable to be tapped when devised with proprietary copyright systems, like HDMI electronics.
Fuzzy logic is inherent to the right hemisphere, it has also always been part of human nature, like classical logic is inherent to the left one.
As for quantum computers, I mean that the common belief is that qubits exist in a superposition of all possible states, and then when checked, they give the desired answer. But that's impossible as when checked they give a random answer. I think quantum computers will only ever be able to influence this kind of randomness of qubits in certain directions, but that's a very different mechanism.
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

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

Post by Logik »

Atla wrote: Sun Feb 24, 2019 5:04 pm Fuzzy logic is inherent to the right hemisphere, it has also always been part of human nature, like classical logic is inherent to the left one.
As for quantum computers, I mean that the common belief is that qubits exist in a superposition of all possible states, and then when checked, they give the desired answer. But that's impossible as when checked they give a random answer. I think quantum computers will only ever be able to influence this kind of randomness of qubits in certain directions, but that's a very different mechanism.
They do not give a random answer.... quantum computers we have today are capable of returning the ground state of a quantum system.
Well. They give a random answer if you sample them ONCE.

That's why you sample them 100000 times. They are perfect for Monte Carlo type problems.
Scott Mayers
Posts: 1694
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

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

Post by Scott Mayers »

Logik wrote: Sun Feb 24, 2019 2:57 pm
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm (3) A law that directly asserts no third option that permits
A and not-A......Exclusive Middle possibility such as {A, [color = red]A and not-A[/color], not-A} excluding the contraction [“con-” (with) “-tra-” (third) “diction” spoken-part]
Constructive mathematics starts precisely with rejecting LEM.
This is the fundamental problem with LEM.

You could say that color = red (A)
But then the negation of "color" (not A) could mean either:
* The entire light spectrum that is NOT red
or
* Everything in the universe that doesn't have the color red.

The problem with FOL is precisely that which is not written. Context!
Ha Ha :lol:
I accidentally meant (and is now corrected above in the last post) for the 'red' command to color the text, not anything referring to the variable!

Anyways, I already just explained how this is done using the form of Complimentary style using universals. By limiting the larger class, U, to whatever smaller subset, you can control how the negation is interpreted but you need to use negation as a binary operator rather than the normal unary one.

Not-Red = Some non-Red,

Non-Red (or not-Red as a "complementary") == The universe minus Red

Non-Red color = The universe of colors minus Red [restricted universe]
Logik wrote: Sun Feb 24, 2019 2:57 pm
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm (1) Law of Consistency
A ⊙ A = 1,

(2) Law of Exclusion, which is just the 'dual' of (1)
A ⊕ A = 0 and

The law of excluding the 'middle' term also relates to Aristotle's use of he middle term but is equivalent to the above and the law of non-contradiction implied by both of these but more clearly emphasized by the use of the normal OR operator as

(3) Law of Non-contradiction
A + A̅
You are falling for the exact same error. because you can't define ⊙, ⊕ and + (but I can - in computer code).
I can construct ANY logic I want to produce the results you expect.

I will construct you a logic in which:

A ⊙ A = 0
A ⊕ A = 1
A + A̅ = 1
I'm not sure what you think is in error? These ARE defined through Boolean logic completely. These are just a summary of the minimal laws and their meanings for all consistent logic. To define in Boolean, you don't begin with exclusive-or nor the 'coincidence' operator but by using strictly the logical constant set {-, +, ∙} and the variable-constants {0, 1, (P)} and any number of variable names. That's it.
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm These are all proved within most Boolean systems by simply using the inclusive-or, and, and complement. Then it proves later defines the exclusive or and uses DeMorgan's Theorem to determine the duals which included defining the inverse of exclusive-or as the 'coincidence operator.
The problem is still interpretation ;)

I can interpret any symbol differently to how you intended it to be interpreted.

You have no control over that.
Maybe a misinterpretation? The last comment may expand upon this.
Scott Mayers
Posts: 1694
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

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

Post by Scott Mayers »

@Logik, I checked your Python but can't determine what it means without homework as I have opted out of learning object orientated languages other than their logical motivation and very basic set-ups. They are designed effective for group programming or compiling with projects based on programming in groups such as with open-source programming. I've not been interested in an employment writing programs other than for myself and so stuck to the functioning and assembly/machine language. Are you able to translate those samples in a pseudo-code or functioning language? Otherwise I'll have to postpone trying to make sense of it.
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

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

Post by Logik »

Scott Mayers wrote: Sun Feb 24, 2019 5:19 pm Anyways, I already just explained how this is done using the form of Complimentary style using universals. By limiting the larger class, U, to whatever smaller subset, you can control how the negation is interpreted but you need to use negation as a binary operator rather than the normal unary one.

Not-Red = Some non-Red,

Non-Red (or not-Red as a "complementary") == The universe minus Red

Non-Red color = The universe of colors minus Red [restricted universe]
You've ended up arguing for Type theory. Where operators are context AND operand sensitive ;)
Scott Mayers wrote: Sun Feb 24, 2019 5:19 pm I'm not sure what you think is in error? These ARE defined through Boolean logic completely.
These are just a summary of the minimal laws and their meanings for all consistent logic. To define in Boolean, you don't begin with exclusive-or nor the 'coincidence' operator but by using strictly the logical constant set {-,

Code: Select all

[code]+
[/code], ∙} [/b] and the variable-constants {0, 1, (P)} and any number of variable names. That's it.
And when you have done that you will have a consistent system of RULES for working with booleans.
What happens when you want to manipulate non-booleans? Like "Human".
What you don't have is:

You are stuck back with the problem of interpreting the operator within a restricted universe (e.g context)
or within the global context.

Which is precisely why you need Type theory. So that your operands are context AND input-sensitive.
Scott Mayers wrote: Sun Feb 24, 2019 2:29 pm Maybe a misinterpretation? The last comment may expand upon this.
The only way to avoid mis-interpretation is to remove that which mis-interprets from the equation.
This is basically why regular languages (all programming languages) can interpret themselves.

Because they are built (from the ground up) using the concept of a Turing machine.
Something that can do search & replace.

https://en.wikipedia.org/wiki/Regular_language
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

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

Post by Logik »

Scott Mayers wrote: Sun Feb 24, 2019 5:33 pm @Logik, I checked your Python but can't determine what it means without homework as I have opted out of learning object orientated languages other than their logical motivation and very basic set-ups. They are designed effective for group programming or compiling with projects based on programming in groups such as with open-source programming. I've not been interested in an employment writing programs other than for myself and so stuck to the functioning and assembly/machine language. Are you able to translate those samples in a pseudo-code or functioning language? Otherwise I'll have to postpone trying to make sense of it.
Avoid the homework. I'll just tell you what I have done - probably much easier, since I have (kind of) tricked everybody.
I've changed the meaning of "=" and "!=" in the context of anything that is of type "Human".

e.g I have created a restricted universe.

If you were to create a different kind of object (e.g boolean) the universe will continue to function as you expect it and in accordance to the general laws of boolean logic.

But that was simply the easiest way to navigate around LNC/Identity. Another way I can do it is by leveraging the flow of time and the fact that the computer has a digital "ticker".

The Law of identity demands that you don't use the SAME meaning at the SAME time, but it is exceptionally vague as to the sampling interval.
And so we cannot evaluate the value of P and not-P at the EXACT SAME time.

What computers do is first they evaluate P THEN they evaluate not-P. I am using this gap in sampling to flip the truth-value of P under everybody's nose.

And so what I have simply done is built a quantum computer which oscillates at the precisely at the frequency of the classical computer so P and not-P return 1 every time you sample them one after another.

Demonstration here: https://repl.it/repls/FoolishAverageTest

An interesting property of this system is that ordering actually matters.
( A == A ) and (A != A ) is True
BUT
( A != A ) and (A == A) is False.

This is a deep rabbit hole into computer science and atomicity so I'll stop here.
User avatar
Arising_uk
Posts: 12313
Joined: Wed Oct 17, 2007 2:31 am

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

Post by Arising_uk »

Logik wrote:.What computers do is first they evaluate P THEN they evaluate not-P. ...
That seems to be a big problem for computers then? As in Logic if you evalute P and it is true then you don't have to evaluate ¬P as its false by definition and vice versa.
Scott Mayers
Posts: 1694
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

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

Post by Scott Mayers »

Logik wrote: Sun Feb 24, 2019 5:46 pm
Scott Mayers wrote: Sun Feb 24, 2019 5:33 pm @Logik, I checked your Python but can't determine what it means without homework as I have opted out of learning object orientated languages other than their logical motivation and very basic set-ups. They are designed effective for group programming or compiling with projects based on programming in groups such as with open-source programming. I've not been interested in an employment writing programs other than for myself and so stuck to the functioning and assembly/machine language. Are you able to translate those samples in a pseudo-code or functioning language? Otherwise I'll have to postpone trying to make sense of it.
Avoid the homework. I'll just tell you what I have done - probably much easier, since I have (kind of) tricked everybody.
I've changed the meaning of "=" and "!=" in the context of anything that is of type "Human".

e.g I have created a restricted universe.

If you were to create a different kind of object (e.g boolean) the universe will continue to function as you expect it and in accordance to the laws of boolean logic.

But that was simply the easiest way to navigate around LNC/Identity. Another way I can do it is by leveraging the flow of time and the fact that the computer has a digital "ticker".

The Law of identity demands that you don't use the SAME meaning at the SAME time, but it is exceptionally vague as to the sampling interval.
And so we cannot evaluate the truth-value of P and not-P at the EXACT SAME time.

What computers do is first they evaluate P THEN they evaluate not-P. I am using this gap in sampling to flip the truth-value of P.

And so what I have simply done is built a quantum computer which oscillates at the precisely at the frequency of the classical computer so P and not-P return 1 every time you sample them one after another.

Demonstration here: https://repl.it/repls/FoolishAverageTest
Okay, it still might be helpful to understand what you've done in the program because you could have simply wrote,

print("A is B: true")
print("A is not B: true")
print("A is A: true")
print("A is not A:true")

At least given I lack knowing the language, you may as well have just printed the above. I can't interpret it as is without knowing some basic functioning definitions of Python, like "_init_", "pass", or rules they define in its 'logic'. [I can create my own 'objects' this way using structures but can't be sure if that has other factors added I'm not aware of.]

Now, I am familiar with timing problems on the level of the components and is something I argued a few years ago in an intense debate on "The Monty Hall Problem". Because the means of higher-order languages to 'trick' even the programmer to think they haven't cheated, there resides a 'cheat' because some processes take twice as long than others on the level of the gates in the chips when minimized to an operation even though people think all operations take the same amount of time. As such the outcome inappropriately comes out as what they expect without realizing that the design to "test" the theorem is fixed to the expected result.

Is this something you are referring to? For those initial logic laws though, those comparisons are 'without time' when on paper. That was a reason for specifically calling implication a "conditional", for instance, to avoid the interpretation as a 'cause' just as the 'assignment operator' for computers is "=". Similar for "and": It doesn't mean "and then" as we use in regular language as it begs time between the events/variables. You might want to test something logical about time itself and so don't want the logical material of the variable use time to prove something about itself, which creates a problem.

EDIT: I saw your own additional edit above and so we seem to agree on what's occurring. You might be interested in my thread here a while back on that "monty hall problem" I recall making a comparison of this critical error to a similar misuse of it in the form of Bell's Inequality Theorem to be used to test Einstein's challenge against their 'wierdness' interpretation. (Copenhagen intepretation). But it was long and so it something you might want a new tread to speak on if you're interested.

But if you share this concern, I feel I might have a friend on this problem that your're welcome to join in on. It can justify Einstein's original interpretation as correct and today's acceptance of what occurs in entanglement as a 'trick'.
Last edited by Scott Mayers on Sun Feb 24, 2019 6:53 pm, edited 1 time in total.
User avatar
Speakpigeon
Posts: 976
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

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

Post by Speakpigeon »

Logik wrote: Sat Feb 23, 2019 1:25 pm The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.
I hereby reject the law of identity, and give you the law of humanity: A = A is False.
A thing needs not be the same as itself!
Prove it.
EB
Scott Mayers
Posts: 1694
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

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

Post by Scott Mayers »

Speakpigeon wrote: Sun Feb 24, 2019 6:52 pm
Logik wrote: Sat Feb 23, 2019 1:25 pm The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.
I hereby reject the law of identity, and give you the law of humanity: A = A is False.
A thing needs not be the same as itself!
Prove it.
EB
He admitted it as a type of 'trick' in the programming. Read my correspondence with him.
User avatar
Speakpigeon
Posts: 976
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

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

Post by Speakpigeon »

Logik wrote: Sun Feb 24, 2019 5:46 pm I have (kind of) tricked everybody.
I've changed the meaning of "=" and "!=" in the context of anything that is of type "Human". e.g I have created a restricted universe.
If you were to create a different kind of object (e.g boolean) the universe will continue to function as you expect it and in accordance to the general laws of boolean logic. But that was simply the easiest way to navigate around LNC/Identity. Another way I can do it is by leveraging the flow of time and the fact that the computer has a digital "ticker". The Law of identity demands that you don't use the SAME meaning at the SAME time, but it is exceptionally vague as to the sampling interval.
And so we cannot evaluate the value of P and not-P at the EXACT SAME time. What computers do is first they evaluate P THEN they evaluate not-P. I am using this gap in sampling to flip the truth-value of P under everybody's nose. And so what I have simply done is built a quantum computer which oscillates at the precisely at the frequency of the classical computer so P and not-P return 1 every time you sample them one after another.An interesting property of this system is that ordering actually matters. ( A == A ) and (A != A ) is True BUT ( A != A ) and (A == A) is False. This is a deep rabbit hole into computer science and atomicity so I'll stop here.
Pathetic. This has nothing to do with logic. You are insane.
EB
User avatar
Speakpigeon
Posts: 976
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

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

Post by Speakpigeon »

Scott Mayers wrote: Sun Feb 24, 2019 6:55 pm He admitted it as a type of 'trick' in the programming. Read my correspondence with him.
Yes, I bet he doesn't even realise how insane his posts are.
EB
Post Reply