What is the basis for reason? And mathematics?

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Eodnhoj7
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Logik wrote: Tue Feb 26, 2019 12:19 am
Eodnhoj7 wrote: Mon Feb 25, 2019 11:02 pm
Logik wrote: Sun Feb 24, 2019 2:11 pm More from the realm of Constructive mathematics.

Here is a consistent logical system in which both A = B AND A != B are true.

This is SUPPOSED to be a logical error?!?!?

https://repl.it/repls/FantasticTenseDividend

#ShatteringTheAristotelianDream

Taking english and converting it to computer language, while admitting you have read and re-read these principles a million times, is beyond suspicious.

However I even argue, and the principle observes this, that the principle can be observed through multiple languages as all languages are merely axioms in and of themselves.
And I already told you that you are welcome to take the work, publish it and claim it as your own. It is not even original - every computer scientist already knows this because this is 100 years old stuff. It's new to YOU because you come from a philosophy background.

Publish what exactly, when I am arguing "space".

Furthermore, why is it that I am the one who keeps pointing you to wikipedia pages, prior work, proofs and theorems which are relevant in the context of that which you are saying?

Because it is in the language of computer programming...and as such is limited to the framework of the language. I already argue, these principles are universal...so why would computer programming "not" observe the majority.

It seems to me that I am the one pointing you to knowledge so as to prevent you from re-inventing the wheel and yet...
If you are going to act like I am stealing from you I'll just stop giving you pointers.

The very fact that you speak OF axioms is clear evidence that I am ahead of you in this game.
In the constructivist realm there are no axioms. Only a canvas - to build/design as one sees fit.

False...construction is dependent upon axioms of connection/seperation, convergence/divergence, point or origin, etc. whether they intend it or not.

That is the problem you do not understand "as one see's fit" necessitates a set of axioms outside the system effectively forming the system itself.
Logik
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Eodnhoj7 wrote: Tue Feb 26, 2019 12:36 am Because it is in the language of computer programming...and as such is limited to the framework of the language. I already argue, these principles are universal...so why would computer programming "not" observe the majority.

Further evidence of your total misunderstanding.

Computation is about INVENTING languages. There is no such thing as 'language of programming'.
Because the Universal Turing Machine can DO anything you can TEACH it to do, the first thing you TEACH it to do is to understand the language you have invented!

Again: you see the mathematics and you are thinking "ha! Language. Must have axioms". No.
I look at Mathematics and go "Ha! Concept."

Eodnhoj7 wrote: Tue Feb 26, 2019 12:36 am
False...construction is dependent upon axioms of connection/seperation, convergence/divergence, point or origin, etc. whether they intend it or not.

That is the problem you do not understand "as one see's fit" necessitates a set of axioms outside the system effectively forming the system itself.

And you only interpret THAT to be the case because you pre-suppose space.
And when you pre-suppose space geometry follows.

Of course in Lambda calculus I can invent space. 2, 5, 10 or 50 dimensional. How many dimensions do you want?
I can invent convergence/divergence/oscillation/quantum behavior and even T-Symmetry (constants!) and any other concept I can IMAGINE.
Do you understand the meaning of total control?

If you can IMAGINE it you can construct it! You are in The Matrix.

Seriously. Go to YouTube. Search for "Universal Turing Machine". Watch a few.
And see if your brain doesn't go "Oh! That's the same fucking thing as I have been saying!"
Speakpigeon
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Location: Paris, France, EU

Logik wrote: Mon Feb 25, 2019 7:35 pm
Speakpigeon wrote: Mon Feb 25, 2019 7:32 pm In other words, it's not logic.
EB
What would convince you that you are wrong?
If it is true that a computer programme is in some way analogous to a logical proof then please provide a transcription of your bit of code into a logical proof so that we can assess for ourselves what it amounts to.
You won't do it, of course, because you're an ignoramus and a pathetic fraud pretending to understand the Curry-Howard correspondence when you don't. The proof is in the pudding.

EB
Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Speakpigeon wrote: Tue Feb 26, 2019 11:31 am
Logik wrote: Mon Feb 25, 2019 7:35 pm
Speakpigeon wrote: Mon Feb 25, 2019 7:32 pm In other words, it's not logic.
EB
What would convince you that you are wrong?
If it is true that a computer programme is in some way analogous to a logical proof then please provide a transcription of your bit of code into a logical proof so that we can assess for ourselves what it amounts to.
You won't do it, of course, because you're an ignoramus and a pathetic fraud pretending to understand the Curry-Howard correspondence when you don't. The proof is in the pudding.

EB
Sorry sophist. You are trying to shift the burden of proof by avoiding the burden of educating yourself.
No can do. You don't even know how much you don't know - you have no authority here.

I gave you the transcript in the original post. Here: https://repl.it/repls/FantasticTenseDividend
To understand WHAT the code does you will probably have to understand HOW the Python interpreter works.
The transcript to the Python source code over here: https://github.com/python/cpython
And I gave you a link to the documentation over here: https://docs.python.org/3/

To understand how the Python interpreter works you are probably going to have to understand HOW the operating system works.
The transcript for the linux kernel is over here: https://github.com/torvalds/linux
Fair warning it's 15 MILLION lines of logic. It will take you some time to read through it.

To understand HOW the kernel works you are probably going to have to learn how the C programming language/compiler works.
You can read its source code here: https://github.com/gcc-mirror/gcc

Once you understand how the operating system works you are going to want to understand how the hardware layer works
Here is the reference manual for the Intel architecture. It's only 2500 pages. You should be able to read it in a few hours.
https://www.intel.com/content/dam/www/p ... 325383.pdf

On a rough approximation the above body of work is the product of a few thousand human lifetimes. And you want me to translate it FOR YOU because you are too fucking lazy to learn? Sorry.
I hope you are a fast reader!

Let us know how it goes and post back in this thread.

P.S This is how compound interest works

You are trying to do shit from first principles - I stand on the shoulders of giants!
Eodnhoj7
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Logik wrote: Tue Feb 26, 2019 12:40 am
Eodnhoj7 wrote: Tue Feb 26, 2019 12:36 am Because it is in the language of computer programming...and as such is limited to the framework of the language. I already argue, these principles are universal...so why would computer programming "not" observe the majority.

Further evidence of your total misunderstanding.

Computation is about INVENTING languages. There is no such thing as 'language of programming'.
Because the Universal Turing Machine can DO anything you can TEACH it to do, the first thing you TEACH it to do is to understand the language you have invented!

Again: you see the mathematics and you are thinking "ha! Language. Must have axioms". No.
I look at Mathematics and go "Ha! Concept."

False because you are still left with a basic computational language from which all languages stem from.

All lambda calculus requires a trifold axiom system universal within all phenomena:

x Variable A character or string representing a parameter or mathematical/logical value
(λx.M) Abstraction Function definition (M is a lambda term). The variable x becomes bound in the expression.
(M N) Application Applying a function to an argument. M and N are lambda terms.

1. The abstraction observes a passive state of form.
2. The application observes an active state of applying the definition.
3. The variable exists under a simultaneous active and passive state through recursion.

Lambda calculus is strictly dependent upon active/passive state of applying defintions in such a manner and as such is grounded fundamentally on these axioms, as well as a trifold nature.

(λx.M[x]) → (λy.M[y]) α-conversion Renaming the bound (formal) variables in the expression. Used to avoid name collisions.
((λx.M) E) → (M[x:=E]) β-reduction Replacing the bound variable with the argument expression in the body of the abstraction

1. Conversion observes one axiom effectively progressing to another through change which necessitates recursion through fractals (the replication of one phenomenon into various states of the same thing; yet distinct in and of themselves.

2. reduction observes a point of inversion where one variable effectively exists as a point of inversion (all axioms are points of inversion in and of themselves); this can be argued as isomorphism.

Eodnhoj7 wrote: Tue Feb 26, 2019 12:36 am
False...construction is dependent upon axioms of connection/seperation, convergence/divergence, point or origin, etc. whether they intend it or not.

That is the problem you do not understand "as one see's fit" necessitates a set of axioms outside the system effectively forming the system itself.

And you only interpret THAT to be the case because you pre-suppose space.
And when you pre-suppose space geometry follows.

False, the universal axiom (regardless of depth of intelligence) is a simple "dot" and as such space is the foundational nature of awareness. Even a simple expierence of "emptiness" is an expression of space.

"space" as a foundational axiom really fuck's up your finite stance, and if you are to maintain any degree of consistency in your philosophical stance you have to negate the concept of infinity...which you can't if space is the foundational axiom.

Of course in Lambda calculus I can invent space. 2, 5, 10 or 50 dimensional. How many dimensions do you want?
False, the principles of space (observed in the prime triad), allow for Lambda to exist...but lambda is not the "be all end all"...as a matter of fact, based upon my brief understanding...it appears to be missing some key principles.

I can invent convergence/divergence/oscillation/quantum behavior and even T-Symmetry (constants!) and any other concept I can IMAGINE.
Do you understand the meaning of total control?

ROFL!!!! I can take 4 copper rods and distort empirical space-time in an area...All your are doing is replicating convergence/divergence/etc.

You "invention" is strictly the recurssion of principles, already in existence, through the focal point of the observer.

You are not inventing anything.

If you can IMAGINE it you can construct it! You are in The Matrix.

False, if one observes they are inside a box they must be aware of an outside of the box...hence the observer does not exist fully in a matrix.

Seriously. Go to YouTube. Search for "Universal Turing Machine". Watch a few.
And see if your brain doesn't go "Oh! That's the same fucking thing as I have been saying!"

I already argued...a thousand times (metaphorically speaking), the principles I argue are "universal" and can be observed ranging from natural law to replications of natural law founded in computer programming...I already believe you.
Logik
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Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm False because you are still left with a basic computational language from which all languages stem from.
Correct! That is what Tarski called a metalanguage! https://en.wikipedia.org/wiki/Metalanguage
Metalanguages are THOUGHT.

Now connect the dots.

I THINK in a metalanguage.
I TRANSFER this metalanguage into a PHYSICAL MACHINE (a computer).

Meta language + Physical machine is what... Meta .. physics?

Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm 1. Conversion observes one axiom effectively progressing to another through change which necessitates recursion through fractals (the replication of one phenomenon into various states of the same thing; yet distinct in and of themselves.
Yes. It's called iteration.
Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm 2. reduction observes a point of inversion where one variable effectively exists as a point of inversion (all axioms are points of inversion in and of themselves); this can be argued as isomorphism.
Yes. The inversion of synthesis.
Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm That is the problem you do not understand "as one see's fit" necessitates a set of axioms outside the system effectively forming the system itself.
So the axioms outside of the system do not need meta-axioms?
Do the meta-axioms not need meta-meta-axioms?
Do the meta-meta-axioms not need meta-meta-meta-meta axioms?

If you are an infinitist (as you claim) then I guess you can never really get to a meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta-meta perspective where you will be happy to lay down an axiom.

Because the moment you lay down an axiom your infinite-meta becomes finite-meta.
Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm False, the principles of space (observed in the prime triad), allow for Lambda to exist...but lambda is not the "be all end all"...as a matter of fact, based upon my brief understanding...it appears to be missing some key principles.
So define those principles! that's what a Metalangauge is for.

Eodnhoj7 wrote: Tue Feb 26, 2019 5:31 pm I already argued...a thousand times (metaphorically speaking), the principles I argue are "universal" and can be observed ranging from natural law to replications of natural law founded in computer programming...I already believe you.
I see. So the principles exist BUT you can't define them in Lambda calculus.
But you CAN define them in ??? Nothing
Averroes
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Logik wrote: Sun Feb 24, 2019 2:11 pm More from the realm of Constructive mathematics.

Here is a consistent logical system in which both A = B AND A != B are true.
Not really! The above quoted statement is itself inconsistent! Any system in which both A=B and A!=B are true is inconsistent. From Wikipedia, we have the following on consistency:
Wikipedia wrote:In classical deductive logic, a consistent theory is one that does not entail a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true.
Intuitionistic logic as well upholds the law of non-contradiction. For example, the law of non-contradiction is made use in the principle of explosion in intuitionistic logic.
Wikipedia wrote:The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ), "from falsehood, anything (follows)", or ex contradictione (sequitur) quodlibet (ECQ), "from contradiction, anything (follows)"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction. That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it. This is known as deductive explosion. https://en.wikipedia.org/wiki/Principle_of_explosion
There is no logic without the law of non-contradiction. So, according to the logical definition of consistency, a logical system in which A=B and A!=B are both true is inconsistent.
_______________________
Logik wrote: Sun Feb 24, 2019 2:11 pm This is SUPPOSED to be a logical error?!?!?
Yes, indeed, you made a logical error.
________________________
Here are the codes you have written:

Code: Select all

``````class Human(object):

def __init__(self):
pass

def __eq__(self, other):
return True

def __ne__(self, other):
return True

A = Human()
B = Human()

# Apparently these two propositions can not be true at the same time
print("A is B: {}".format(A == B))
print("A is not B: {}".format(A != B ))
print("A is A: {}".format(A == A ))
print("A is not A: {}".format(A != A ))
print("(A = A) and (A != A ): {}".format( (A == A) and (A != A)))``````
There are very serious issues, among them moral and legal issues, with this program.

First of all, you have redefined equality and your redefinition of equality differs from both the mathematical definition and from common understanding as well. Here it is:

Code: Select all

`````` def __eq__(self, other):
return True``````
The problem is that it always returns True, whatever is being compared! And the same for your redefinition of inequality:

Code: Select all

`````` def __ne__(self, other):
return True``````
For those who have asked for plain English translation of these codes, here it is. In common English, these lines of codes means:
For the redefinition of equality: Every human is equal to every human.
For the redefinition of inequality: Every human is unequal to every human.

These are clearly contradictory statements! But more importantly in this case, for example, some humans are murderers and some humans are not murderers. Someone who has killed thousands of defenseless women and children is clearly not equal to someone who has not killed any human being. A murderer is clearly not equal to an innocent human being. But according to the redefinition of equality given in the program, a murderer is equal to an innocent human being! This is absolutely unacceptable from both a legal and a moral point of view.

And that is also obviously very different from what mathematicians and people with common sense understand by equality and inequality. Wikipedia gives the logical definition of Liebniz on equality, and this is also expressed in set theory.

Wikipedia:
Leibniz characterized the notion of equality as follows:
Given any x and y, x = y if and only if, given any predicate P, P(x) if and only if P(y).
Symbolically, we can now express Liebniz statement as follows: ꓯxꓯy(x=y ↔ ꓯP(P(x)↔P(y)))

In set theory:
Wikipedia wrote: The equality between A and B is written A = B, and pronounced A equals B. The symbol "=" is called an "equals sign". For example:
{x|P(x)}={x|Q(x)} if and only if P(x) ↔ Q(x). This assertion, which uses set-builder notation, means that, if the elements satisfying the property P(x) are the same as the elements satisfying Q(x), then the two uses of the set-builder notation define the same set. This property often expressed as "two sets that have the same elements are equal." It is one of the usual axioms of set theory, called Axiom of extensionality.
While the redefinition expressed in the Python codes given in the OP can be expressed as follows:
Given any x and y, x=y if and only if, there is at least one predicate P and there is at least one predicate Q such that, P(x) if and only if Q(y).
Symbolically: ꓯxꓯy(x=y ↔ ꓱPꓱQ(P(x)↔Q(y)))

The later is clearly different from the accepted mathematical definition of equality. So here we have two different definitions of equality! Now, since each of these definitions are equal to themselves and not equal to each other, therefore the common understanding of equality must be prevailing!

Interesting it is to observe that if we take the default definition of equality and inequality in Python, then the correct results are obtained. We take the default definition by not redefining equality and inequality! I have rewritten the codes and added some instance variables to the class Human to make it more interesting! Here are the codes relying on the Python implementation of equality and inequality, followed by the results:

Codes are here: https://repl.it/@Averroes/everythingIsFineAgain

Results here:

Code: Select all

``````Netanyahu is a man and is a criminal
Ilhan is a woman and is not a criminal

A is equal to B: False
A is not equal to B: True
A is equal to A: True
A is not equal to A: False
(A = A) and (A != A ): False``````
_________________________
Logik wrote: Sun Feb 24, 2019 2:11 pm #ShatteringTheAristotelianDream
Many of Aristotle thoughts have already been refuted long ago. However, the OP has not contributed to that in any way, shape or form! Certainly not by denying the law of non-contradiction!

Try again if you want, I give you two months to write another Python program violating the law of non-contradiction and at the same time not be making a logical error! Extensions will be given if need be. Take your time, I am not in a hurry. I will assess you work then, if God wills.
Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Averroes wrote: Sun Mar 17, 2019 10:08 am
Logik wrote: Sun Feb 24, 2019 2:11 pm More from the realm of Constructive mathematics.

Here is a consistent logical system in which both A = B AND A != B are true.
Not really! The above quoted statement is itself inconsistent! Any system in which both A=B and A!=B are true is inconsistent. From Wikipedia, we have the following on consistency:
It is only "inconsistent" BECAUSE you have CHOSEN to define "Any system in which both A=B and A!=B are true is inconsistent".

A tautology - nothing more.

Proofs compute. This system computes. If you are going to argue against inconsistency you need to refute Curry-Howard.

Good luck. If you succeed in doing that you will do some great work
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

Averroes wrote: Sun Mar 17, 2019 10:08 am Try again if you want, I give you two months to write another Python program violating the law of non-contradiction and at the same time not be making a logical error! Extensions will be given if need be.
Observe yourself attempting to move the goal post by introducing the vague concept of "logical error".

No extension required. I accept your challenge on one condition only.

Define: "logical error" in a consistent and complete logic.
Averroes wrote: Sun Mar 17, 2019 10:08 am I will assess you work then.
No. I would prefer that you didn't. Nothing against you - I just prefer objective standards to human gate-keepers.

So this is my challenge to you: write an algorithm that recognizes ALL logical errors. Take all the time you need

If I can get my algorthm past your error-detection algorithm then I'd say it's settled?
Last edited by Logik on Mon Mar 18, 2019 6:31 am, edited 3 times in total.
surreptitious57
Posts: 4217
Joined: Fri Oct 25, 2013 6:09 am

Logic wrote:
Define : logical error in a consistent and complete logic
There cannot be an error in a complete system otherwise all systems are flawed

But how certain can you be that any system is actually complete ?
An incomplete one might be free of error but only superficially so
For not being able to detect an error doesnt mean there isnt one
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

surreptitious57 wrote: Sun Mar 17, 2019 10:56 am
Logic wrote:
Define : logical error in a consistent and complete logic
There cannot be an error in a complete system otherwise all systems are flawed
Precisely. And computers are physical machines. They manipulate matter.

So if it works in practice then where is the "error" ?
surreptitious57 wrote: Sun Mar 17, 2019 10:56 am But how certain can you be that any system is actually complete ?
It depends on your subjective bar for completeness. How would you assert that a system is NOT complete?
surreptitious57 wrote: Sun Mar 17, 2019 10:56 am An incomplete one might be free of error but only superficially so
For not being able to detect an error doesnt mean there isnt one
Before you can detect any "errors" you have to know and be able to recognize what an "error" is.

So now we have appointed humans as the arbiters of "errors". Yay.
surreptitious57
Posts: 4217
Joined: Fri Oct 25, 2013 6:09 am

Computers manipulate information not matter but they have human programmers
And if human programmers make errors then computers will not necessarily know
You also cannot be absolutely certain that an algorithm is error free and complete
Logik
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Joined: Tue Dec 04, 2018 12:48 pm

surreptitious57 wrote: Sun Mar 17, 2019 11:03 am Computers manipulate information not matter
No. Computers are made OF matter. They obey the law of physics.

Because computers produce the results that we WANT them to produce (ergo computers use matter to do our bidding) computers manipulate matter.

surreptitious57
Posts: 4217
Joined: Fri Oct 25, 2013 6:09 am

Logic wrote:
So now we have appointed humans as the arbiters of errors
Even if the arbiters of error were non human and infallible and beyond any fault we would still be checking for errors
Because we would have to determine for ourselves there were none so in that respect it would make zero difference
Logik
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Joined: Tue Dec 04, 2018 12:48 pm