The death of Classical logic and the birth of Constructive Mathematics

[Logik]

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")

Heh, of course, that would be too easy.

What I did was for any object of type "Human" I re-defined the "=" operator to return "False".
It's useful to think of operators as mathematical functions so when you see A = B think f(A, B).

And since it's a function.... i am in control of defining its behaviour.

In the case of Type systems f(A,B) we have what's called parametric polymorphism. The parameters to the function influence the behaviour of the function in real time.

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.]

Yeah, no fault of your own there. High-order logics are abstractions upon abstractions upon abstractions, but somewhere deep down in the belly of the beast it is all boolean logic.

Python is a Hindley-Milner type system (or thereabout, not exactly - but whatever there are religions there on whether object-oriented or functional paradigms are better). https://en.wikipedia.org/wiki/Hindley%E ... ype_system

The key property that makes all these shenanigans possible is the parametric polymorphism.

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.

Oh yeah! There are hundreds if not thousands of ways to fool yourself with these beasts.

Is this something you are referring to? For those initial logic laws though, those comparisons are 'without time' when on paper.

Yep. In theory there is no difference between theory and practice, but in practice there is, and so in inventing boolean logic we are actually creating an illusion that we have paused time. It's kinda hard to maintain that illusion at large scale.

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.

Without turning this into a nit-picking session that's pretty much it. The concept of atomicity (or transactionality) in computer system is the ASSUMPTION that 17 different operations take place at the exact same time. And NONE of them failed, or produced unexpected results.
Some times that's possible where the work is parallelizable, but if it is not you have to serialize events in which case it doesn't take time X, it takes 17*X.

Those problems that you have identified at the component level turn into very interesting sets of problems at the software level.
In order to maintain the illusion of consistency we have to use a LOT of duct tape. And most importantly - we have to pretend that we have control over time. Which is why we have the concept of a system clock. But of course that is just duct tape.

When you start working with distributed systems then you have to start worrying about clock synchronicity and there is just no getting away from geographic latency (that pesky speed of light!) so maintaining the illusion of consistency in distributed systems is an interesting problem-space...

[Logik]

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.

I think the correct way to word this is that you don't realise why my posts aren't "insane".

This is where logic is in 2019.

You are just a few milenia behind.

[Logik]

.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.

Oh yes! This is a problem for everything and anything that behaves like a computer. And your mind is one of those things.

Well what do you trust more? Your eyes or a made-up definitions?

If you evaluate P, and then you evaluate not-P and they are both true then surely you would become a suspect of the definition, no?
This is the quantum realm.

If you observe that something is a cat (P) then you can say that it isn't a cat (not P)
But if you observe that something is NOT a cat (¬P) then you can't immediately conclude that it is (P).

[Logik]

It is not that Classical / Aristotelian logic has been disproven but rather that it has been shown not to be absolute
Outside of computer programmes / mathematical algorithms it is still true that A = A so it is not completely false

In standard mathematics it is still a universally accepted axiom that for every valid equation the
quantities on either side of = are of equal value regardless of anything else [ notation / symbols ]

Also to completely disprove A = A would invalidate the Law Of Non Contradiction

The strict form of the law of identity is stated as:

for all x: x = x

OK fine.

BUT

for all y: y != y
for all z: z != z
for all p: p !=p

If it is not universal then it's probably a good idea to NOT call it a "law"
You are welcome to consider it on case-by-case basis.

Also to completely disprove A = A would invalidate the Law Of Non Contradiction

You mean like this: https://repl.it/repls/FantasticTenseDividend

https://repl.it/repls/FantasticTenseDividend

[Logik]

Is this something you are referring to? For those initial logic laws though, those comparisons are 'without time' when on paper.

I neet to nit-pick at this. When you create a Boolean gate that is (SUPPOSED TO) exist "without time" you are effectively making a false assumption. Pragmatic, but false! It's an error - a necessary evil. Everything else that follows is the Butterfly effect/Chaos at work.

You are CHOOSING to fool yourself. In this universe NOTHING[1] exists outside of time, so just like Classical logic Boolean logic is artificial, but useful!
It is a stepping stone till we figure out quantum computation/fuzzy logic in practical terms.

The laws of thought are meant to be understood in spirit, not in letter. Conceptually, not symbolically.

One day when we get quantum computers off the ground somebody will find a way to contradict the axioms of Boolean logic too (because they are an error), like I have contradicted the axioms of classical logic. This is how science works....

[1] I am probably going to eat my words when we solve T-symmetry https://en.wikipedia.org/wiki/T-symmetry

[Speakpigeon]

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

No. It's a corner stone of logic.

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

No. Between some species of logical proof and computer programmes.

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.

You still have to exhibit the algorithm here.

I hereby reject the law of identity, and give you the law of humanity: A = A is False.

So the law of identity you reject is not the law of identity you reject.
Forgive me for being confused here! What is it you reject exactly?

A thing needs not be the same as itself!

Needs? Whoa. Things do their own things, you know. Me, for example, I would insist being me all the time. In fact, I wouldn't even know how to not be myself. So, you'd have to provide examples of a things which is not itself. Just for a laugh.
EB

[Logik]

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

No. It's a corner stone of logic.

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

No. Between some species of logical proof and computer programmes.

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.

You still have to exhibit the algorithm here.

I hereby reject the law of identity, and give you the law of humanity: A = A is False.

So the law of identity you reject is not the law of identity you reject.
Forgive me for being confused here! What is it you reject exactly?

A thing needs not be the same as itself!

Needs? Whoa. Things do their own things, you know. Me, for example, I would insist being me all the time. In fact, I wouldn't even know how to not be myself. So, you'd have to provide examples of a things which is not itself. Just for a laugh.
EB

*sigh* Idiot. Stop it. Your stupidity is exhausting.

Logical proofs ARE ISOMORPHIC WITH computer programs. Do yo understand what "ISOMORPHIC" means?
I have shown you the algorithm on a WORKING COMPUTER. Written in an OPEN SOURCE language (e.g it's public knowledge)
How much more do you want me to do here?

You seriously need to stop talking and start reading.

Start here: https://en.wikipedia.org/wiki/Curry%E2% ... espondence
Then read this book (it's free!) https://homotopytypetheory.org/book/

[Speakpigeon]

What I did was for any object of type "Human" I re-defined the "=" operator to return "False".
It's useful to think of operators as mathematical functions so when you see A = B think f(A, B).
And since it's a function.... i am in control of defining its behaviour.

And how could that prove anything about anything accept the way your programme works?
EB

[Logik]

And how could that prove anything about anything accept the way your programme works?
EB

Because logical proofs are WORKING COMPUTER PROGRAMS!!!!!!!

What in the above sentence is not making sense to you?
https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.

That is ALL a 'proof' is - a working algorithm. If you expect it to bring you happiness and joy, if you expect it to bring Meaning and Truth to your life then you are looking in the wrong place.

You need to re-calibrate your expectations....

[Speakpigeon]

Logical proofs ARE ISOMORPHIC WITH computer programs. Do yo understand what "ISOMORPHIC" means?

I don't know that myself and that still leave the question of your programme. You think I'm going to sign a contract I don't understand because it's written in a foreign language?! You're being irrational.

I have shown you the algorithm on a WORKING COMPUTER. Written in an OPEN SOURCE language (e.g it's public knowledge)
How much more do you want me to do here?

Where is the algorithm?

You seriously need to stop talking and start reading.
Start here: https://en.wikipedia.org/wiki/Curry%E2% ... espondence
Then read this book (it's free!) https://homotopytypetheory.org/book/

If you can't explain it yourself here, then just too bad.
EB

[Speakpigeon]

And how could that prove anything about anything accept the way your programme works?
EB

Because logical proofs are WORKING COMPUTER PROGRAMS!!!!!!!

What in the above sentence is not making sense to you?
https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.

That is ALL a 'proof' is - a working algorithm. If you expect it to bring you happiness and joy, if you expect it to bring Meaning and Truth to your life then you are looking in the wrong place.

You need to re-calibrate your expectations....

You need to explain yourself here. Stop posting idiotic links and explain yourself.
EB

[Logik]

I don't know that myself and that still leave the question of your programme. You think I'm going to sign a contract I don't understand because it's written in a foreign language?! You're being irrational.

So then don't sign the contract.

Read the books. Learn the language and then convince yourself.

In 2019 you can't call yourself a philosopher OR a logician if you don't understand Mathematics.

If you can't explain it yourself here, then just too bad.

How can I possibly explain myself to somebody who can't be appeased?

I can bring God before your eyes and you will remain skeptical. You have extremely unrealistic expectations...

[Logik]

You need to explain yourself here. Stop posting idiotic links and explain yourself.

Dimwit. In What language do you expect me to explain to you HOW to ride a bicycle?

English? OK. You get on it and you pedal. Happy?

The only way you are going to learn HOW formal logic works is practice, practice, practice, practice it it becomes second nature to you.
Exactly like riding a bike.

Knowledge doesn't "just happen". You actually have to DO THE WORK. All by yourself.

And the very first thing you need to learn to do is HOW to think. You can't read that in a book, but you can start here: https://www.learnpython.org/

[Logik]

Actually it is not, as that "lambda/type/turing" perspective you claimed you thought was original (but found out was not) is strictly an extension of your own perspective looping through itself. You have not put it into language anyone understand but you.

This is a lie.

Millions of people around the world know how to program. More and more are learning every day.

I have put it in a language so basic that a stupid machine running on 1s and 0s can understand it!
You are WAY smarter than a machine, so you should have no problem understanding it too.

The grammar/semantics of the language is public knowledge: https://github.com/python/cpython
The documentation of the language is public knowledge: https://docs.python.org/3/
Tutorials from first principles on how to learn the language are public knowledge: https://www.learnpython.org/
Global communities exist to support and beginners and experts alike if/when they run into problems: https://www.python.org/community/

To whine that I have put it in a "language that nobody understands" is to expect to be spoon-fed knowledge!
How lazy are you?

If you have to "quote" someone...it just means you cannot argue it yourself. The linch pin of your argument is the continual "quotation" of a vast wikipedia page...other than that you provide no argument except maybe the word "isomorphism".

This is how backwards your thinking is! You think you have to do EVERYTHING yourself. Me? I don't have to re-invent the wheel! I will stand on the shoulders of giants instead.

BECAUSE Mathematical proofs are isomorphic to computer programs I don't have to "argue" anything. All I have to do is show it to you.

I can literally drop the cat among the pigeons in the form of a working program and then go drink wine, while moron-philosophers figure out what the fuck happened to their "laws".

Logic is a constructive tool. Logic is LEGO for your mind.

APPLIED SCIENCE, not philosophy is the source of wisdom and knowledge. Philosophy is dead!

WHEN YOU DON’T CREATE THINGS, YOU BECOME DEFINED BY YOUR TASTES RATHER THAN ABILITY. YOUR TASTES ONLY NARROW AND EXCLUDE PEOPLE. SO CREATE.
— Jonathan Gillette

Create knowledge!

[Speakpigeon]

In 2019 you can't call yourself a philosopher OR a logician if you don't understand Mathematics.

I don't call myself either. I do philosophy and logic, though.
And I use whatever mathematics I need but it's really very basic because logic is formally simple. Difficult to understand, obviously, since no one has as of today, even though many great minds have given it a try, but it's simple.
If it gets complicated, you know it's no longer logic, it's mathematics, and then, who cares?

If you can't explain it yourself here, then just too bad.

How can I possibly explain myself to somebody who can't be appeased? I can bring God before your eyes and you will remain skeptical. You have extremely unrealistic expectations...

It's unrealistic to ask you to explain yourself in English and in a rational way?!
Whoa. I guess that says it all...
We're done with the little fraud here, I guess.
EB