Mathematics ends in contradiction:6 reasons
Mathematics ends in contradiction:6 reasons
Mathematics ends in contradiction:6 reasons
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf
1) an integer = a noninteger
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations bans itselfthus 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: Formalismto avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf
1) an integer = a noninteger
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations bans itselfthus 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: Formalismto avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility

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Re: Mathematics ends in contradiction:6 reasons
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
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
Re: Mathematics ends in contradiction:6 reasons
Here is your edge case:surreptitious57 wrote: ↑Wed Feb 27, 2019 7:56 am2 ] An integer that is repeated within any equation is given to have the same value or else it is meaningless
55
How come the integer on the left has a value “50” and the integer on the right has value “5” ?

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Re: Mathematics ends in contradiction:6 reasons
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
Give me one with a single digit integer repeated where the value is different each time
Re: Mathematics ends in contradiction:6 reasons
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"surreptitious57 wrote: ↑Wed Feb 27, 2019 8:19 amThere 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
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

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Re: Mathematics ends in contradiction:6 reasons
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 ?
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 ?
Re: Mathematics ends in contradiction:6 reasons
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.anne wrote: ↑Wed Feb 27, 2019 7:24 amMathematics ends in contradiction:6 reasons
http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf
1) an integer = a noninteger
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations bans itselfthus 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: Formalismto avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility
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 Turingcomplete logic is sufficient so if you are a settheorist this should make perfect sense to you: λcalculus ⇔ λcalculus ⊇ 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 counterintuitive is that?
This way that I am assured (by the CurryHoward 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 casebycase basis without spending the rest of your life chasing the pipedream 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
I remove the axiom on which all of mathematics supposedly rests and the system does not explode.In the formal languages of computer science and linguistics, the Chomsky hierarchy is a containment hierarchy of classes of formal grammars.
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
Last edited by Logik on Wed Feb 27, 2019 2:51 pm, edited 10 times in total.

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Re: Mathematics ends in contradiction:6 reasons
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
They will eventually replace us any way and it is only a matter of time before they do
Re: Mathematics ends in contradiction:6 reasons
The relationship is symbiotic not parasitic.surreptitious57 wrote: ↑Wed Feb 27, 2019 10:12 amMachines 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
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.

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Re: Mathematics ends in contradiction:6 reasons
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
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
Re: Mathematics ends in contradiction:6 reasons
We recognize the problem. We don't have good answers. We are working on it.surreptitious57 wrote: ↑Wed Feb 27, 2019 10:32 amThey need a master NOW but what about the future when they will be more advanced
It is a doubleedge sword.surreptitious57 wrote: ↑Wed Feb 27, 2019 10:32 amThere will come a point in time when they will be able to just programme themselves
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.
Good! Let the machines do the menial, boring, repetitive, mindnumbing bullshit.surreptitious57 wrote: ↑Wed Feb 27, 2019 10:32 amThere are already virtually automated factories with very few humans operating them
The more idlebrains we have, the more brains we can use towards figuring out how to avoid the AIPocalypse!

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Re: Mathematics ends in contradiction:6 reasons
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
When the Sun goes red giant that will be the end of all intelligence : machines and humans
Re: Mathematics ends in contradiction:6 reasons
A machine that can make 20000 years of progress in a week can also become interplanetary in a year or 5.surreptitious57 wrote: ↑Wed Feb 27, 2019 10:50 amBut 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
Intergalactic in a century.
Of course. I am thumbsucking numbers  but that's how compound interest works. It becomes exponential REALLY fast.

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Re: Mathematics ends in contradiction:6 reasons
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
That is the one fundamental unavoidable truth about all of our existence

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Re: Mathematics ends in contradiction:6 reasons
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
When you finally do you would already have died before you got there
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