The greatest does not exist therefore Anselm ontological argument is wrong
The greatest does not exist therefore Anselm ontological argument is wrong
This is the direct observation that in math the greatest does not exist (following Cantor's theorem). The ontological proof of God requires the existence of the greatest. Therefore God (defined as the greatest) does not exist.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
Cantor’s theorem is only valid if you assume set theory as the foundation for mathematics, but set theory is broken beyond repair which is why mathematicians have abandoned it for a while now.
Naive set theory removed the universal set from its ontology so it can rescue itself from Russel’s paradox.
ZFC has a clever workaround to avoid russel’a paradox, but it too lost the notion of a universal set.
I quite like the idea of the set of “everything” so I reject set theory and ZFC in favour of type theory.
The set of everything does not have subsets.
It has reductions.
Ultimately though. The existence of “the greatest” depends on a simple choice: which theory you assume foundational to mathematics?
If you do settle on set theory then Cantor is the way to refute Anselm.
If you accept type theory as foundational  Anselm’s argument is equivalent to a pantheistic argument.
The greatest is the Universe type.
Naive set theory removed the universal set from its ontology so it can rescue itself from Russel’s paradox.
ZFC has a clever workaround to avoid russel’a paradox, but it too lost the notion of a universal set.
I quite like the idea of the set of “everything” so I reject set theory and ZFC in favour of type theory.
The set of everything does not have subsets.
It has reductions.
Ultimately though. The existence of “the greatest” depends on a simple choice: which theory you assume foundational to mathematics?
If you do settle on set theory then Cantor is the way to refute Anselm.
If you accept type theory as foundational  Anselm’s argument is equivalent to a pantheistic argument.
The greatest is the Universe type.

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Re: The greatest does not exist therefore Anselm ontological argument is wrong
but Muhammad Ali did exist at one time
Imp
Imp

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Re: The greatest does not exist therefore Anselm ontological argument is wrong
St. Anselm Ontological God is logically [re logic only] possible.
As you posited, it is not mathematically possible.
But as I had proven, it is empiricalrationally impossible to be real.
Since the ontological God is impossible to be empiricalrationally real, there is no question of 'God exists as real' nor 'God does not exist' because that is a nonstarter, i.e. moot.
Why the idea of God emerges onto human consciousness is due to the compulsion of some terrible psychological forces driven by a real existential crisis.
The idea of God exists is only useful for psychological reasons and nothing else.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
The link between logic and reality is realizers.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am St. Anselm Ontological God is logically [re logic only] possible.
https://en.wikipedia.org/wiki/Realizability
https://en.wikipedia.org/wiki/Realization_(systems)
And as I pointed out, it is  when you throw away set theory.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am As you posited, it is not mathematically possible.
https://en.wikipedia.org/wiki/Type_theo ... erse_types
So you just rejected The Universe.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am But as I had proven, it is empiricalrationally impossible to be real.
 attofishpi
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Re: The greatest does not exist therefore Anselm ontological argument is wrong
Logik, keep up the good work of being rational. Last week you caught me after half a carton, where I left feeling my mind had been raped, still it was quick and a blast.Logik wrote: ↑Mon Jan 07, 2019 7:47 amThe link between logic and reality is realizers.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am St. Anselm Ontological God is logically [re logic only] possible.
https://en.wikipedia.org/wiki/Realizability
https://en.wikipedia.org/wiki/Realization_(systems)
And as I pointed out, it is  when you throw away set theory.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am As you posited, it is not mathematically possible.
https://en.wikipedia.org/wiki/Type_theo ... erse_types
So you just rejected The Universe.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am But as I had proven, it is empiricalrationally impossible to be real.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
Glad I could stretch your thinking muscle.attofishpi wrote: ↑Mon Jan 07, 2019 8:48 amLogik, keep up the good work of being rational. Last week you caught me after half a carton, where I left feeling my mind had been raped, still it was quick and a blast.Logik wrote: ↑Mon Jan 07, 2019 7:47 amThe link between logic and reality is realizers.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am St. Anselm Ontological God is logically [re logic only] possible.
https://en.wikipedia.org/wiki/Realizability
https://en.wikipedia.org/wiki/Realization_(systems)
And as I pointed out, it is  when you throw away set theory.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am As you posited, it is not mathematically possible.
https://en.wikipedia.org/wiki/Type_theo ... erse_types
So you just rejected The Universe.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 am But as I had proven, it is empiricalrationally impossible to be real.
We are all in the same sinking boat.
Everyone benefits by having smarter people.
 attofishpi
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Re: The greatest does not exist therefore Anselm ontological argument is wrong
I wasn’t talking about me.attofishpi wrote: ↑Mon Jan 07, 2019 10:14 ammmm...not so sure I consider you smarter. Perhaps more knowledgeable in some areas..and there I benefit.
If you learned something you became smarter.
If I learned something I became smarter.
Nett win for everyone.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
Who is ZFC?Logik wrote: ↑Sun Jan 06, 2019 10:18 pm Cantor’s theorem is only valid if you assume set theory as the foundation for mathematics, but set theory is broken beyond repair which is why mathematicians have abandoned it for a while now.
Naive set theory removed the universal set from its ontology so it can rescue itself from Russel’s paradox.
ZFC has a clever workaround to avoid russel’a paradox, but it too lost the notion of a universal set.
Does the greatest possible exists in type theory?
What do you mean?
Of course God is not the universe since we are persons living in the universe.Logik wrote: ↑Sun Jan 06, 2019 10:18 pm Ultimately though. The existence of “the greatest” depends on a simple choice: which theory you assume foundational to mathematics?
If you do settle on set theory then Cantor is the way to refute Anselm.
If you accept type theory as foundational  Anselm’s argument is equivalent to a pantheistic argument.
The greatest is the Universe type.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
You are correct. I should have said the greatest imaginable. The greatest exists for any instance at any given time.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
https://en.wikipedia.org/wiki/Zermelo%E ... set_theory
The "greatest possible" is always a conceptual notion. Type theory has a "Universe" type.
You can always conceptualise two universes, but that is "illegal" in type theory because The Universe is a Singleton.
https://en.wikipedia.org/wiki/Singleton_pattern
If you wanted to speak about Universes (plural) you will run into contradictions (because you are violating the grammar and starting assumption of Type Theory  there is only one universe). You will end up exactly like Cantor and exactly like Russel's paradox. https://en.wikipedia.org/wiki/System_U#Girard's_paradox
I mean a cat is not a subset of The Universe.. A cat is a type of thing within the set which is The Universe.
OK, but if The Universe is the greatest set (set of everything) you can conceptualise, claiming that "God is not the universe" is either a:
* Contradiction, for (Universe + God) > Universe
OR
* God is a type of thing in the Universe.
Last edited by Logik on Mon Jan 07, 2019 3:20 pm, edited 1 time in total.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
The greatest exists for any instance at any given time. The greatest imaginable, the absolute, does not exist. I had to be more precise.Veritas Aequitas wrote: ↑Mon Jan 07, 2019 6:33 amSt. Anselm Ontological God is logically [re logic only] possible.
As you posited, it is not mathematically possible.
But as I had proven, it is empiricalrationally impossible to be real.
Since the ontological God is impossible to be empiricalrationally real, there is no question of 'God exists as real' nor 'God does not exist' because that is a nonstarter, i.e. moot.
Why the idea of God emerges onto human consciousness is due to the compulsion of some terrible psychological forces driven by a real existential crisis.
The idea of God exists is only useful for psychological reasons and nothing else.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
Then your mindset is incompatible with naive set theory. In order to avoid Russel's paradox  the "Greatest" (universal set) was discarded.
Because we are bounded rationalists whatever is claimed to be "The Greatest"  I can simply imagine two of them...
If God is the greatest, then two Gods are greater. And If you can imagine one God, you sure can imagine two!
The whole point of Anselm's argument is to establish an ontological upper bound. The line where reality ends and imagination begins.
Re: The greatest does not exist therefore Anselm ontological argument is wrong
Thanks.
I will read that.Logik wrote: ↑Mon Jan 07, 2019 3:17 pmThe "greatest possible" is always a conceptual notion. Type theory has a "Universe" type.
You can always conceptualise two universes, but that is "illegal" in type theory because The Universe is a Singleton.
https://en.wikipedia.org/wiki/Singleton_pattern
I see and thanks.Logik wrote: ↑Mon Jan 07, 2019 3:17 pm If you wanted to speak about Universes (plural) you will run into contradictions (because you are violating the grammar and starting assumption of Type Theory  there is only one universe). You will end up exactly like Cantor and exactly like Russel's paradox. https://en.wikipedia.org/wiki/System_U#Girard's_paradox
I see and thanks.
So God is not greatest imaginable again, the absolute.