The death of Classical logic and the birth of Constructive Mathematics

[Eodnhoj7]

I am not insane. I have knowledge.

???
You've admitted several times to not know anything and to not know how to decide that we had knowledge.
Oh, well, just one more contradiction. To those without logic, contradictions can't be really problematic.
EB

The nature of contradiction is address in the failure of contradiction thread, all contradictions applies to contradictions result in truth statements; hence the standard fallacies only exist within the context of the logical system applying them, however they do not exist in a separate logical context.

Even you grounding in the laws of logic, where your context requires these contradiction to exist in a certain framework, still is subject to a bandwagon and authority fallacy.

[Logik]

I am not insane. I have knowledge.

???
You've admitted several times to not know anything and to not know how to decide that we had knowledge.
Oh, well, just one more contradiction. To those without logic, contradictions can't be really problematic.
EB

At first I THOUGHT I know nothing and so I said "I have no knowledge". For I couldn't recognize that what I had was knowledge.
But then I recognized knowledge for what it was. And now I am saying that I have knowledge.

It's called learning. It's a temporal phenomenon. Eureka?

What you fail to recognize is that computers are PHYSICAL ENTITIES. In the PHYSICAL UNIVERSE.
It is not about what they SAY. It is about what they DO.

They manipulate matter.

You are free to misinterpret what I SAY in any way you want, but to misinterpret what computers DO is to deny HOW reality works.

Actions speak louder than words. My WORDS have a physical effect on reality.

My WORDS have objective meaning

Not the words I speak in English - those you can keep.
The words I speak in Python!

John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.

[anne]

For all your arguments using classical logical to disprove classical logic its a pity that
Mathematics ends in contradiction:6 reasons
read
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf

1) an integer = a non-integer
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separation bans itself-thus mathematics is inconsistent
4) Mathematicians dont know what a number is -without be impredicative
5)Mathematics is just a bunch of meaningless symbols connected by rules: Formalism-to avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility

Also with mathematics ending in contradiction then logic(classical) proves you can prove anything in maths ie you can prove Fermat's last theorem and you can disprove Fermat's last theorem
read
http://gamahucherpress.yellowgum.com/wp ... ssible.pdf

[Logik]

For all your classical logical argument its a pity that
Mathematics ends in contradiction:6 reasons
read
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf

1) an integer = a non-integer
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separation bans itself-thus mathematics is inconsistent
4) Mathematicians dont know what a number is -without be impredicative
5)Mathematics is just a bunch of meaningless symbols connected by rules: Formalism-to avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility

Also with mathematics ending in contradiction then logic(classical) proves you can prove anything in maths ie you can prove Fermat's last theorem and you can disprove Fermat's last theorem
read
http://gamahucherpress.yellowgum.com/wp ... ssible.pdf

Indeed. Because the principle of explosion is true. And it works like this.

for all =: = = =

Every time you use the symbol "=" in more than one sense of the word you are violating identity. That is self-inconsistent and therefore a contradiction!

[Speakpigeon]

Indeed. Because the principle of explosion is true. And it works like this.
for all =: = = =
Every time you use the symbol "=" in more than one sense of the word you are violating identity. That is self-inconsistent and therefore a contradiction!

Remind me how you can tell Aristotelian logic is "self-inconsistent"?
EB

[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!

So, if A = A is not necessarily true, how do you prove that 2 = 2 for example?
Or do you just never need to prove that x = x, for any x whatever?
EB

[Speakpigeon]

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

This doesn't make any sense.
I'm lost with your "formalism" here. That's not Aristotelian logic.
John is a subject and "human" is a predicate, so there's no possibility of equality between them. You are making a category mistake.
In Aristotelian logic, "John is human" could be formalised for example as: ∃x(Named-John(x)) ∧ Human(x).
So, the following argument:

John is human
Jane is human
John is Jane

could be formalised as follows:

∃x(Named-John(x)) ∧ Human(x);
∃y(Named-Jane(x)) ∧ Human(y);
Therefore, x=y

And it is obviously not a valid argument.
So, I don't understand your logic here. It doesn't make any sense.
Please clarify.
EB

[Speakpigeon]

The law of identity is the cornerstone of Arostotelian/Classical logic.
A = A is True.
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.
First Order Logic is a massive error! It is complete-but-undecidable. How do you THINK without making decisions?!?

You are mistaken here.
You don't seem to know much about Aristotelian logic.
You can't prove that First Order Logic is Aristotelian logic. So, you need to decide which one you want to argue about.
EB

[Logik]

So, if A = A is not necessarily true, how do you prove that 2 = 2 for example?

Well the two is an object of type integer. In the context of integers the meaning of = is pretty unambiguous. It means "Distance from 0 on the number line". Unless my imagination is lacking - I can't think of another meaning.

But observe that in order to be explicit about the law of identity we need to state it like this: for all x: id(x) = id(x).
So then 2 = 2 means "are the two integers the same distance from 0?"
But id(2) = id(2) means "do the two objects have the same IDENTITY?"

In Python the value and identities of "2" are different things.

Code: Select all

In [2]: 2 == 2                                                                                                                                                                              
Out[2]: True

In [3]: id(2)                                                                                                                                                                               
Out[3]: 96222208947104

In [4]: id(2) == id(2)
Out[4]: True

So then to the question "Are the two integers the same distance from 0?" the answer is True.
And to the question "Do the two objects have the same identity?" the answer is also True.

They answer different questions.

Or do you just never need to prove that x = x, for any x whatever?
EB

It depends on what you mean by "=".

For all numeric types the meaning is clear.
What does "=" mean for sets?

Equivalent contents?
Equivalent size?

If the set of Apples and the set of Oranges are both empty are they the same set?

Code: Select all

In [7]: Apples = []                                                                                                                                                                         

In [8]: Oranges = []                                                                                                                                                                        

In [9]: Apples == Oranges                                                                                                                                                                   
Out[9]: True

So apples and oranges are the same thing? Right

[Speakpigeon]

Or do you just never need to prove that x = x, for any x whatever?

It depends on what you mean by "=".

I mean, for a particular x, id(x) = id(x).
So, how do you prove that a set A of apples is the same thing as the same set A of apples, i.e. id(A) = id(A)?[/quote]
EB

[Logik]

So, the following argument:

John is human
Jane is human
John is Jane

could be formalised as follows:

∃x(Named-John(x)) ∧ Human(x);
∃y(Named-Jane(x)) ∧ Human(y);
Therefore, x=y

So two more of my friends showed up to the party. They brought a GREAT bottle of wine for us to share.
The weird thing they are also called John and Jane (heh, we keep fucking confusing each other. I hope the other John and Jane who live on the 2nd floor don't join the party is going to be a mess.

SO any way

John is human.
Other John is human.
Jane is human.
Other Jane is human too.
None of my guests are the same person.

https://repl.it/repls/ExhaustedVillainousWireframe

Now what you arent' paying attention to is that the whole point of the formal logic is to help you avoid inconsistencies, right?
But it doesn't have contexts! Mine does (shame) all while the Python interpreter assures me that global consistency is maintained.

And so I am going to keep talking (NOT arguing!) about reality in English uttering true facts!
And then 30 minutes into our dinner I am going to ask you to model all the facts in your "proper logic".

Observe that the more of my guests arrive. The more truths I keep uttering, the harder it gets for you to maintain consistency!
And I will keep pushing your logic to the limits till your brain snaps.

Because I know how to find the edge/corner cases in ALL of your formalisms !!! Every single one. SO much so that I contradicted your fucking axioms.
I've been hacking logical systems for better part of the last 20 years...

[Speakpigeon]

John is human.
Other John is human.
Jane is human.
Other Jane is human too.
None of my guests are the same person.

∃w(Named-John(w)) ∧ Human(w);
∃x(Named-John(x)) ∧ Human(x);
∃y(Named-Jane(y)) ∧ Human(y);
∃z(Named-Jane(z)) ∧ Human(z);
¬(w = x ∨ w = y ∨ w = z ∨ x = y ∨ x = z ∨ y = z)

All good.
EB

[Speakpigeon]

Or do you just never need to prove that x = x, for any x whatever?

It depends on what you mean by "=".

I mean, for a particular x, id(x) = id(x).
So, how do you prove that a set A of apples is the same thing as the same set A of apples, i.e. id(A) = id(A)?

So apparently you can't prove that the same set is the same set.
Pretty basic, though.
EB

[Logik]

So apparently you can't prove that the same set is the same set.
Pretty basic, though.

1. I am trying to prove the EXACT opposite of that. I am trying to prove that the Empty set Apples {} is NOT the same as the Empty set Oranges{}.
But in classical logic it is! because an empty set is an empty set. So apples are oranges.
2. You are still focusing on all the things you can do with set theory and ignoring all the things you CAN'T do.

Like the fact that you can't talk about things in the abstract!!!

How many gaps in functionality do you want me bloody show you?

It's a pretty long list: https://www.quora.com/What-are-the-features-of-OOP

All of these concepts exist in my mind and allow me to EXPRESS things about my metaphysic to others (who understand what those concepts-of-concepts mean).

[Speakpigeon]

So apparently you can't prove that the same set is the same set.
Pretty basic, though.

1. I am trying to prove the EXACT opposite of that. I am trying to prove that the Empty set Apples {} is NOT the same as the Empty set Oranges{}.
But in classical logic it is! because an empty set is an empty set. So apples are oranges.

Only in modern mathematical so-called "classical logic", something which is neither classical nor logic.
So, not in classical, Aristotelian logic, no. Apples are not oranges.

2. You are still focusing on all the things you can do with set theory and ignoring all the things you CAN'T do.
Like the fact that you can't talk about things in the abstract!!!
How many gaps in functionality do you want me bloody show you?
It's a pretty long list: https://www.quora.com/What-are-the-features-of-OOP
All of these concepts exist in my mind and allow me to EXPRESS things about my metaphysic to others (who understand what those concepts-of-concepts mean).

You would need to produce an example here to prove your claim, here.
EB