The death of Classical logic and the birth of Constructive Mathematics

[Logik]

The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.
In the 2nd half of the 20th century the American mathematician Haskell Curry and logician William Alvin Howard discovered an analogy between logical proofs and working computer programs. This is known as the Curry-Howard correspondence.
Mathematical proofs are working computer programs. https://en.wikipedia.org/wiki/Curry%E2% ... espondence
Therefore, if we can write a working computer program which asserts that A = A is false without producing an error then we have living proof contradicting the founding axiom of Classic/Aristotelian logic.
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!
https://repl.it/repls/SuperficialShimmeringAnimatronics

So here is expert opinion on your bit of Python code by someone who actually speaks Python:

The critical line is this one:

def __eq__(self, other):
return False

This just overrides the comparison method with unconditionally returning "false".
It does no actual identity check, only a mock one.
So, of course this can "prove" whatever you choose as the alleged result.
And that's all there is to it.

OMG.
The little boy is a cheat!
EB

You are SO stupid you don't even understand what you are looking at.

I have given you a logic system which:
1. ALLOWS FOR A == A => TRUE
2. WHILE AT THE SAME TIME IT ALLOWS FOR B == B => FALSE
3. THE SYSTEM DOES NOT EXPLODE!!!!

Was it not you who claimed that IF I was to violate the law of identity THEN logic breaks?
You are staring at a logic system in which I CAN violate the law of identity AND the system DOES NOT BREAK.

YOU CAN"T DO THIS IN CLASSICAL LOGIC.

You don't get to claim "expert opinion" on anonymous source. Bring your "expert" here and I will teach him a thing or 100.

[Logik]

So, of course this can "prove" whatever you choose as the alleged result.

I am here to convince you that this is true for ALL LOGIC.
You can use logic to prove WHATEVER you CHOOSE.
You can use logic to give you ANY answer you WANT.

Well. I can. You don't understand how it works.

[Logik]

So here is expert opinion on your bit of Python code by someone who actually speaks Python:

The critical line is this one:

def __eq__(self, other):
return False

This just overrides the comparison method with unconditionally returning "false".
It does no actual identity check, only a mock one.
So, of course this can "prove" whatever you choose as the alleged result.
And that's all there is to it.

OMG.
The little boy is a cheat!
EB

*sigh* give him a proof of concept and he doubles down on the denial. Fucking dogmatists.

The very point the sophist is missing is that IF you use "=" to mean two different things ANYWHERE in your argument your logic system explodes!
Consistency demands not only consistent operands it demands consistent application of operators too! GRAMMAR!!!

You don't have ANY mental self-discipline to detect errors (e.g grammar violations!), so you keep tripping over the principle of explosion every time you use '=' in two different senses. That is why you suck at logic. You don't even know what an error looks like and you definitely do not have the MENTAL TOOLS to contain it because classical logic does not allow for decidability.

And IF you have TOOLS to detect AND contain The Principle of Explosion THEN you can build perfectly valid and USEFUL para-consistent logics!
That are FAR closer to English (or your native language) than your crappy Classical logic.

Run to your "expert" and ask him if he still thinks I am "cheating": https://repl.it/repls/TintedDefiantInstruction
The identity check is here:

Code: Select all

    if id(self) == id(other):
      return True

I have updated the OP in your honor.

Observe how as the English and Aristotelian grammars diverge in meaning the Aristotelian Universe dehumanizes John and Jane. It's hilarious!

English: John is human.
Python: John == Human
False

English: Jane is human.
Python: Jane == Human
False

Would you like me to get you a shovel?

[Logik]

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

Paraconsistent logics are propositionally weaker than classical logic; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate everything that classical logic does. In some sense, then, paraconsistent logic is more conservative or cautious than classical logic. It is due to such conservativeness that paraconsistent languages can be more expressive than their classical counterparts including the hierarchy of metalanguages due to Alfred Tarski et al. According to Solomon Feferman [1984]: "…natural language abounds with directly or indirectly self-referential yet apparently harmless expressions—all of which are excluded from the Tarskian framework." This expressive limitation can be overcome in paraconsistent logic.

A more conservative language can be more expressive ?!?!? How is that for counter-intuitive to a Classical logician?

IF Python is a metalanguage.
And IF Python is para-consistent.
And IF Python is more expressive.
And IF this meta language can be INTERPRETED BY A PHYSICAL machine

Would you like me to spell it for you? META. PHYSICS.

How is that for laws of thought?

I can have a consistent AND para-consistent logic running SIDE BY SIDE in a Universal Turing Machine.
I can evaluate one set of propositions according the to laws of classical logic (and maintain identity).
I can evaluate another set of propositions according to the laws of natural language (and break transitivity)
I can violate non-contradiction and STILL navigate around the principle of explosion because I can handle contradictions as they happen. IN LOGIC. IN REAL TIME.
And I can STILL get the system to produce the correct answer as any 5 year old would expect!

Isn't this PRECISELY how the human mind works ?!?!?!?

Your knows damn well what "Jane is Human" means without having to translate it into the unintuitive garbage that is set theory.
The contradiction happens in formal logic NOT in English!!!!! Jane belongs to a set? Where is this set?

John is human ( A = C )
Jane is Human (A = C)
John is not Jane ( A != B) <======== CONTRADICTION!

This is where the classical logician panics, and where the para-consistent logician goes. "Oh yea. Fuck it! You know what I mean".

Classical logic is NOT English.
Intuitionistic logic is English.

Classical logic is some fucking unnatural language that you have forced yourself to adopt just so that you eliminate contradictions, rather than just handle them as they arise on case-by-case basis.

Classical logic is not how ANY human should think! It's an unnatural, masochistic prison for your mind!

Humans are a fucking contradiction therefore contradictions exist. That contradicts non-contradiction!

[Logik]

This just overrides the comparison method with unconditionally returning "false".
It does no actual identity check, only a mock one.
So, of course this can "prove" whatever you choose as the alleged result.

So while the Sophist is pointing fingers at MY logic, he forgot to look at his own poopy pants.

If Classical Logic is UNDECIDABLE, how DO you do an identity check USING Classical logic?

Way to shoot yourself in the foot with a shotgun

[Speakpigeon]

The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.

In the 2nd half of the 20th century the American mathematician Haskell Curry and logician William Alvin Howard discovered an analogy between logical proofs and working computer programs. This is known as the Curry-Howard correspondence.
Mathematical proofs are working computer programs. https://en.wikipedia.org/wiki/Curry%E2% ... espondence

Therefore, if we can write a working computer program which asserts that A = A is false without producing an error then we have living proof contradicting the founding axiom of Classic/Aristotelian logic.

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!

Version 1: https://repl.it/repls/SuperficialShimmeringAnimatronics

##### EDIT 1 (changelog)

SpeakPigeon has embarked on a crusade to smear my character. So for the sake of transparency (and to let make an even bigger fool of himself) I have revised the code. I have nothing to hide

Version 2: https://repl.it/repls/TintedDefiantInstruction

Observe how the Aristotelian universe dehumanizes John and Jane

English: John is human.
Formalism: John = Human
False

English: Jane is human.
Formalism: Jane = Human
False

And me I asked for a second advice, independent from the first (and on the original claim, and on the code itself).

So here it is:

I'm not an expert at Python, but this is what I understand of the code. The "==" sign is Python code for comparing two objects for equality. The evaluation will return True or False. The "print" and "format" are display functions not affecting the evaluation.

class Aristotelian(object):
def __init__(self):
pass​
A = Aristotelian()
print("Law of Identity: A = A => {}".format(A == A))

This defines a new class of object type. The class is named as "Aristotelian".
Then the code creates a new object of the type Aristotelian, and store a reference to it in the variable A.
Then it compares A to A. No function specifying how to compare objects has been defined prior to the comparison, so Python uses the built-in comparison function, which evaluates as True whenever it compares an object to itself[/b] as is the case here. So, with this first round, A = A evaluates as True.

class Human(object):
def __init__(self):
pass​
def __eq__(self, other):
return False​
A = Human()
print("Law of Humanity: A = A => {}".format(A == A))

This has broadly the same general structure, but here a "home-made" method for comparing objects has been introduced: def __eq__(self, other).
Once it is defined, this is the method that will be used to evaluate comparisons whenever the "==" operator is present. In this case, we define the __eq__ method to return False, no matter what.

Thus, this home-made definition overrides the build-in operator ==, so that each comparison involving the class Human will use this comparison method, not the built-in one. Thus, in this second round, the A == A comparison can only evaluate as False.

So, basically, this code literally overrides/rewrites the rules of logic to get answers that won't follow the conventional rules of logic.

I also fail to see how this could have any bearing on the validity of the Law of Identity, since the second bit of code, with the home-made method of comparison, doesn't use the Law of identity at all.

I guess I don't need to add anything, this is very clear. People will make their own mind about it.
EB

[Logik]

The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.

In the 2nd half of the 20th century the American mathematician Haskell Curry and logician William Alvin Howard discovered an analogy between logical proofs and working computer programs. This is known as the Curry-Howard correspondence.
Mathematical proofs are working computer programs. https://en.wikipedia.org/wiki/Curry%E2% ... espondence

Therefore, if we can write a working computer program which asserts that A = A is false without producing an error then we have living proof contradicting the founding axiom of Classic/Aristotelian logic.

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!

Version 1: https://repl.it/repls/SuperficialShimmeringAnimatronics

##### EDIT 1 (changelog)

SpeakPigeon has embarked on a crusade to smear my character. So for the sake of transparency (and to let make an even bigger fool of himself) I have revised the code. I have nothing to hide

Version 2: https://repl.it/repls/TintedDefiantInstruction

Observe how the Aristotelian universe dehumanizes John and Jane

English: John is human.
Formalism: John = Human
False

English: Jane is human.
Formalism: Jane = Human
False

And me I asked for a second advice, independent from the first (and on the original claim, and on the code itself).

So here it is:

I'm not an expert at Python, but this is what I understand of the code. The "==" sign is Python code for comparing two objects for equality. The evaluation will return True or False. The "print" and "format" are display functions not affecting the evaluation.

class Aristotelian(object):
def __init__(self):
pass​
A = Aristotelian()
print("Law of Identity: A = A => {}".format(A == A))

This defines a new class of object type. The class is named as "Aristotelian".
Then the code creates a new object of the type Aristotelian, and store a reference to it in the variable A.
Then it compares A to A. No function specifying how to compare objects has been defined prior to the comparison, so Python uses the built-in comparison function, which evaluates as True whenever it compares an object to itself as is the case here. So, with this first round, A = A evaluates as True.

class Human(object):
def __init__(self):
pass​
def __eq__(self, other):
return False​
A = Human()
print("Law of Humanity: A = A => {}".format(A == A))

This has broadly the same general structure, but here a "home-made" method for comparing objects has been introduced: def __eq__(self, other).
Once it is defined, this is the method that will be used to evaluate comparisons whenever the "==" operator is present. In this case, we define the __eq__ method to return False, no matter what.

Thus, this home-made definition overrides the build-in operator ==, so that each comparisons involving the class Human will use this comparison method, not the built-in one. Thus, in this second round, the A == A comparison can only evaluate as False.

So, basically, this code literally override/rewrite the rules of logic to get answers that won't follow the conventional rules of logic.
I also fail to see how this could have any bearing on the validity of the Law of Identity, since the second bit of code, with the home-made method of comparison, doesn't use the Law of identity at all.

I guess I don't need to add anything, this is very clear. People will make their own mind about it.
EB

What a liar!

You asked for a 'second advice' on the first version. Yes. It used to return an unconditional FALSE on equality.

I am stating it as clear as daylight for you that I am INTENTIONALLY doing that. I am FORCIBLY violating the law of identity. And guess what?

THE PROGRAM STILL WORKS WITHOUT ERRORS!!!!! <--------------- THIS IS PROOF

By the way there is even a 3rd version ( I can spit these out much faster than you can validate them)

https://repl.it/repls/StrangeLiquidPolyhedron

Please consult back with your "experts"

Let me even show you where you are lying. The lie is in red.

Once it is defined, this is the method that will be used to evaluate comparisons whenever the "==" operator is present. In this case, we define the __eq__ method to return False, no matter what.

https://repl.it/repls/StrangeLiquidPolyhedron

Code: Select all

  def __eq__(self, other):
    # Forvibly violate identity
    if id(self) == id(other):
      return False
    # Let the parent handle everything else
    else:
      return super(Human, self).__eq__(other)

[Speakpigeon]

What a liar! You asked for a 'second advice' on the first version. I fixed it.
https://repl.it/repls/TintedDefiantInstruction
Please consult back with your "experts"

There's no point talking to you. You've denied the possibility of any rational conversation in English. When asked, repeatedly, to justify your position, you find all sorts of extraordinary excuses and you never provide any. You also asked us to "learn Python" (sic) and to look at the code, as if that was a reasonable way of having a debate on anything. Still, I asked people knowledgeable about Python. They provided two independent assessments and their conclusions are very similar. Your code can only return False once you specify a comparison method. That's all there is to it. Whoa. What kind of weirdo are you?!
And you new code is swell but sorry I won't bother to bother anyone with it, we already know what kind of trick you use. You don't even seem to realise that this is terminal. You've insisted your original code proved the Law of Identity obsolete, indeed "false". I asked two people to look into your code and their replies are without ambiguity. Your code cannot possibly prove anything about the Law of Identity. They also say this is pretty obvious, which begs the question of your sanity.
EB

[Logik]

What a liar! You asked for a 'second advice' on the first version. I fixed it.
https://repl.it/repls/TintedDefiantInstruction
Please consult back with your "experts"

There's no point talking to you. You've denied the possibility of any rational conversation in English. When asked, repeatedly, to justify your position, you find all sorts of extraordinary excuses and you never provide any. You also asked us to "learn Python" (sic) and to look at the code, as if that was a reasonable way of having a debate on anything. Still, I asked people knowledgeable about Python. They provided two independent assessments and their conclusions are very similar. Your code can only return False once you specify a comparison method. That's all there is to it. Whoa. What kind of weirdo are you?!
And you new code is swell but sorry I won't bother to bother anyone with it, we already know what kind of trick you use. You don't even seem to realise that this is terminal. You've insisted your original code proved the Law of Identity obsolete, indeed "false". I asked two people to look into your code and their replies are without ambiguity. Your code cannot possibly prove anything about the Law of Identity. They also say this is pretty obvious, which begs the question of your sanity.
EB

This is fucking awesome. I had never seen somebody deny LIVING PROOF. You see it. It is is mind-independent. It is there for you to examine it and understand it. You do not believe it.

Perhaps I should ask you this question.

Do you accept the Curry-Howard isomorphism?

Do you accept that a WORKING computer program is an objective standard for PROOF-OF-VALIDITY ?

Yes or No?

Perhaps you should ask your 'experts' that very question.

your code can only return False once you specify a comparison method

Correct! I have INTENTIONALLY CHOSEN TO CREATE A LOGIC WHERE A = A is FALSE. This is called a CHOICE!
Humans ARE allowed to make choices. Right?

I have CHOSEN to invent a logic in which rejecting the false authority of identity still preserves LNC and LEM.

By Curry-Howard it is a VALID logic!

If you reject its validity the burden of proof is on you.

You've denied the possibility of any rational conversation in English.

To speak about my Metalanguage ( https://en.wikipedia.org/wiki/Metalanguage ) in English wold immediately make English my meta-meta-language.

That's like using a hammer for brain surgery. No thanks.

The proof IS in the pudding. And the pudding is in Lambda calculus.
If you want some of that pudding ...https://www.learnpython.org/

You also asked us to "learn Python" (sic) and to look at the code, as if that was a reasonable way of having a debate on anything

I am not interested in a debate. There is proof before you.

You are yet to answer the question "What would convince you that you are wrong?"

[Scott Mayers]

Here is another experiment to demonstrate how fundamental information is to human cognition.

In English: "Is this the same rose?"

Hypothesis 1: roseA = roseB => True
Hypothesis 2: roseA = roseB => False

Please DECIDE which of the above is the correct hypothesis and then explain the ALGORITHM by which you came to this conclusion.

roseA.jpg
roseB.jpg

Define "true/false".

[Logik]

Here is another experiment to demonstrate how fundamental information is to human cognition.

In English: "Is this the same rose?"

Hypothesis 1: roseA = roseB => True
Hypothesis 2: roseA = roseB => False

Please DECIDE which of the above is the correct hypothesis and then explain the ALGORITHM by which you came to this conclusion.

roseA.jpg
roseB.jpg

Define "true/false".

Seriously?

Are the two roses the same? Yes or no.
Is it a picture of the same rose (A = B) or is it a picture of two different roses (A != B)?

[Scott Mayers]

Here is another experiment to demonstrate how fundamental information is to human cognition.

In English: "Is this the same rose?"

Hypothesis 1: roseA = roseB => True
Hypothesis 2: roseA = roseB => False

Please DECIDE which of the above is the correct hypothesis and then explain the ALGORITHM by which you came to this conclusion.

roseA.jpg
roseB.jpg

Define "true/false".

Seriously?

Are the two roses the same? Yes or no.
Is it a picture of the same rose (A = B) or is it a picture of two different roses (A != B)?

"Truth" is merely a fitness concept. I asked because this is itself defined as a comparison concept based upon whether one thing agrees to 'fit' to another concept. In your Hypothesis 1, you DEFINE the 'fitness' of roseA to match to roseB as 'true'. The samples of "roseA" and "roseB" are defined 'equal' if the two 'agree' to our concept of 'sameness'.

In your second option (hypothesis 2), you ask if the comparison of equality is 'fit' to some concept of 'false'. But truth and falsity themselves have the same problem, because the word, "true", is the POINTER to the general acceptance of the meaning of the "Law of Identity". What is 'false' is precisely defined against that 'fitness'.

Euclid had to distinguish the KIND of equality relationship of "congruence" differing from regular 'identity' to help show one property of similarity versus ALL parts. So if a triangle has three equal angles (the measure of similar property of comparison) to be 'congruent'. This is a 'similarity' relationship and was something they thought of BEFORE Aristotle. The confusion you hold is understandable to discuss. But it doesn't dislodge 'classical' logic.

To go broader, you add construction axioms, such as that of ZFC, but these have a prerequisite inclusion of the prior classic logic. So these cannot dislodge the validity nor soundness of classic logic but EXTENDS its meaning.

[Speakpigeon]

I have given you a logic system which:
1. ALLOWS FOR A == A => TRUE
2. WHILE AT THE SAME TIME IT ALLOWS FOR B == B => FALSE
3. THE SYSTEM DOES NOT EXPLODE!!!!

Was it not you who claimed that IF I was to violate the law of identity THEN logic breaks?
You are staring at a logic system in which I CAN violate the law of identity AND the system DOES NOT BREAK.

YOU CAN"T DO THIS IN CLASSICAL LOGIC.

You don't get to claim "expert opinion" on anonymous source. Bring your "expert" here and I will teach him a thing or 100.

As in your John/Jane argument, your little cheating programme redefines what the sign "=" means. Where is the contradiction? There is none.

Contrary to your stupid claim here, your bit of code does not evaluate A==A as True and B==B as False. What it does instead is that it evaluates A==A as True when using the built-in comparison method and it evaluates A==A as False when it is using your home-made comparison method. So, it's not doing the two comparisons at the same time, you jerk. No contradiction.

You're the self-proclaimed Python specialist here and here I am explaining to you how it really works. That's how fucking stupid you are.
EB

[Speakpigeon]

You are yet to answer the question "What would convince you that you are wrong?"

???
I already told you several times. Here it is again:

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.
EB

[Logik]

As in your John/Jane argument, your little cheating programme redefines what the sign "=" means.

Re-defines or defines?

Where is the meaning of = defined for classical logic? it isn't?

People in glass houses shouldn't throw rocks...

So, it's not doing the two comparisons at the same time, you jerk. No contradiction.

I am sorry WHAT. TWO comparisons AT THE SAME TIME?!?!?!?!?!?

HOW THE FUCK ARE YOU GOING TO DO THAT IN THIS UNIVERSE? Do you have some magic wand to pause time or something?