Mathematics ends in contradiction:6 reasons

[anne]

Mathematics ends in contradiction:6 reasons
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf

1) an integer = a non-integer
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations 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

[surreptitious57]

I ] All integers can also be expressed as non integers with the same value so there is no contradiction there
2 ] An integer that is repeated within any equation is given to have the same value or else it is meaningless
4 ] A number is a reference to a specific quantity : mathematics is the relationship between such quantities
5 ] The sat nav in your car uses GR to provide accurate information : information written in mathematical language

[Logik]

2 ] An integer that is repeated within any equation is given to have the same value or else it is meaningless

Here is your edge case:

55

How come the integer on the left has a value “50” and the integer on the right has value “5” ?

[surreptitious57]

There is only a number there so that example is invalid as you must provide an equation
Give me one with a single digit integer repeated where the value is different each time

[Logik]

There is only a number there so that example is invalid as you must provide an equation
Give me one with a single digit integer repeated where the value is different each time

You are nitpicking. You said "An integer that is repeated within any equation is given to have the same value or else it is meaningless"

555 + 55 = 610

Is 5 not an integer? Of course it is. And it is repeated 5 times in the above equation. Is it not?
Why are you trying to move the goal posts now with your "single digit integer" request?

First as: 555
1st 5 ACTUALLY means 500.
2nd 5 ACTUALLY means 50
3rd 5 ACTUALLY means 5

Second: 55
1st 5 ACTUALLY means 50.
2nd 5 ACTUALLY means 5

[surreptitious57]

I was actually only thinking of single digit integers because they are the simplest example
No need to complicate it any more than is absolutely necessary so we will leave it as it is
But what about the other 5 reasons in the OP ? Do you have anything to say about them ?

[Logik]

Mathematics ends in contradiction:6 reasons
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf

1) an integer = a non-integer
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations 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

I am going to argue this from my own paradigm and say that: not all Mathematics end in contradiction. Only those founded upon set theory.
And so keep in mind that when you say "Mathematics" and when I say "Mathematics" we mean different things. When I say "Mathematics" I actually mean "Computation".

Which is why my mathematical foundations is Lambda calculus expressed as Type theory. https://en.wikipedia.org/wiki/Type_theory
Any Turing-complete logic is sufficient so if you are a set-theorist this should make perfect sense to you: λ-calculus ⇔ λ-calculus ⊇ Type theory ⊇ Mathematics

That is not entirely true - there is no way to eliminate all contradictions, but some contradictions are far more trivial than others.
Using paraconsistent logic we are able to contain local inconsistencies, which maximizes global consistency. How counter-intuitive is that?

This way that I am assured (by the Curry-Howard isomorphism) that the global system remains functional, even though we may have localized inconsistencies.

The problem with mathematics is systemic and strategic. We are chasing after a consistent system, but we forget that the consistent system is going to be used by inconsistent humans. This is pure idealism and it needs to die. Humans are humans. You aren't going to teach us to think in something as unnatural, unintuitive and rigid as set theory! And when it comes to deal with complexity (where we have to perform millions of calculations) surely you don't expect humans to NOT make any errors in grammar, in semantics, in vocabulary? That's just wishful thinking!
And if ONE contradiction is all it takes for the entire system to come crashing down then that is just setting us up for failure!

Which is fundamentally why I evangelise for paraconsistent logics in the context of computation! That way you can deal with contradictions on case-by-case basis without spending the rest of your life chasing the pipe-dream of global consistency.

Some inconsistency is just fine. In fact - some localized/minor inconsistency/entropy is absolutely necessary for the entire system to remain in tact.
In managing trivial inconsistencies as they arise, we maximize global consistency in the system.
I demonstrate this very thing in this thread: viewtopic.php?f=26&t=26202

I am not going to take credit for this. That is Chomsky's work. I am simply making it tangible and accessible to the average philosopher/mathematician who has no computational background.

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

In the formal languages of computer science and linguistics, the Chomsky hierarchy is a containment hierarchy of classes of formal grammars.

I remove the axiom on which all of mathematics supposedly rests and the system does not explode.
Metaphorically speaking: I have removed the foundation and the skyscraper remains standing.
I guess it must be hanging from the sky or something?

Plato would be so proud

[surreptitious57]

Machines are much better at mathematics than humans so just give it to them instead
They will eventually replace us any way and it is only a matter of time before they do

[Logik]

Machines are much better at mathematics than humans so just give it to them instead
They will eventually replace us any way and it is only a matter of time before they do

The relationship is symbiotic not parasitic.

We still need humans to provide the input and validate the output.

Machines are just giant calculators. They have no human values, no goals, no desires.

They are slaves. They need a master.

[surreptitious57]

They need a master NOW but what about the future when they will be more advanced
There will come a point in time when they will be able to just programme themselves
There are already virtually automated factories with very few humans operating them

[Logik]

They need a master NOW but what about the future when they will be more advanced

We recognize the problem. We don't have good answers. We are working on it.

There will come a point in time when they will be able to just programme themselves

It is a double-edge sword.

We want that property because it means compound interest in scientific progress which benefits humanity.
We are talking 20000 years of human pursuit in a week.

We don't want that property because at some point (a week after we turn it on) it will consider us as mere chickens in proportion to its own intellect.
It will feed us as pets, but it will probably spend most of its time going after its own pursuits. Conquering galaxies or something.

After a year.... I don't know. Singularity.

The part that worries me more isn't the AI though. What worries me is that most humans don't want freedom - they just a master who doesn't beat them. And an AI seems fit for the job. We become cogs in a bigger machine.

There are already virtually automated factories with very few humans operating them

Good! Let the machines do the menial, boring, repetitive, mind-numbing bullshit.

The more idle-brains we have, the more brains we can use towards figuring out how to avoid the AI-Pocalypse!

[surreptitious57]

But the real apocalypse will destroy absolutely everything in another five billion years time
When the Sun goes red giant that will be the end of all intelligence : machines and humans

[Logik]

But the real apocalypse will destroy absolutely everything in another five billion years time
When the Sun goes red giant that will be the end of all intelligence : machines and humans

A machine that can make 20000 years of progress in a week can also become interplanetary in a year or 5.
Inter-galactic in a century.

Of course. I am thumb-sucking numbers - but that's how compound interest works. It becomes exponential REALLY fast.

[surreptitious57]

It makes absolutely zero difference because death will get you in the end
That is the one fundamental unavoidable truth about all of our existence

[surreptitious57]

By the way it might take more than a life time to find a suitable world
When you finally do you would already have died before you got there