Proving God exists with SET THEORY?
ฝัง
- เผยแพร่เมื่อ 12 ต.ค. 2020
- This video is adapted from the argument by Christopher Menzel in Two Dozen Arguments (or so) For God. Originally sketched out by Alvin Plantinga, this argument demonstrates that being a realist about abstract objects (specifically as sets) necessitates that these objects exist as thoughts in the mind of God.
The way you can tell an atheist from a crowd is that they are wearing top hats, and suddenly appear when you call for them
And when they do appear, there’s no cause
I’ve learned about so many arguments for God’s existence I’ve never heard of before because of this channel
Man,What a video👏👏👏👏.
That is simply legendary
I certainly appreciate these fresh new arguments and thinking instead of just the same old apologetics. Even if I disagree or if the target of the argument is niche its still fascinating and shows great thought in attempting to explore these ideas which is something I think everyone should embrace.
We shouldn’t ignore ideas that don’t fit with our beliefs we should openly allow challenge between ideas to take place and let the one which proves stronger to be believed.
The trouble with the view that sets are thoughts of God is that it doesn't allow us to hold on to what we normally think of as a set. The most basic property that all mathematical objects have is that they are abstract. Philosophers have trouble describing exactly what it means to be abstract, but one thing they can all agree on is that God, if he exists, is not an abstract object (abstracta can't create universes after all), and that mathematical objects, if they really do exist as abstract objects, exist regardless of whether anyone is thinking of them. In fact, the properties you gave, that they are timeless, spaceless, and immaterial, are really just consequences of this more fundamental property. But if sets are actually thoughts in the mind of God, then they are no longer abstract objects. Now their existence depends on a concrete being, which is not at all what we think of mathematical objects as being.
Way over my head! But I got some interesting points though.
I liked how you narrated the whole story too!
Way under rated
[Nominalists laughing/cringing]
What i've read in the philosophical literature is that the cumulative hierarchy is what they call "indefinitely extendible", or, in the words of aristotle, a potential infinity instead of an actual one. Basically whenever you think you have "all sets" in the cumulative hierarchy, you just make an ordinal M greater than all the ones done untill now and keep the hierarchy going.
Wondering about this, i thought, the concept of "perfection" seems to be indefinitely extendible, whenever you have a perfect being S, you could make a more perfect being S' which has all the perfect properties of S and can create S, this seems to indicate that there is no " maximal perfect being " just as there is no "maximal ordinal", it simply can keep going, it is indefinitely extendible.
Another thought i had was, if a maximally perfect being existed, to what ordinal can he count? He cant count all of them because there is no such thing, whenever you think of a being S which can count untill an ordinal M, i can think of another one S' which can count untill M+1.
This was a really nice thought experiment to me, what are your views on it?
An indefinitely extendible view of sets is incompatible with vanilla Platonism, as Platonism takes all sets to exist as abstract objects. But once you tell me which sets are abstract objects, then (since the cumulative hierarchy *is* indefinitely extendible) I can construct additional sets. But, that means these new sets are not abstract objects. So, vanilla Platonism is false. What I lay out in this video is the idea that, since sets are the thoughts of God, sets actually are indefinitely extendible because God has the ability to think of any sets. He may never be able to think of *all* the sets, but for any set, there is a possible world where God thinks of those sets.
Your argument against a maximally perfect Being seems to have a flaw; a maximally perfect Being cannot be created. It exists necessarily, and thus it is impossible for any being to create it.
// Another thought i had was, if a maximally perfect being existed, to what ordinal can he count? He cant count all of them because there is no such thing, whenever you think of a being S which can count until an ordinal M, i can think of another one S' which can count until M+1. //
This is interesting. While God cannot count *all* ordinals, He can count to *any* ordinal. We can compare this to an analogous thought experiment: What natural number can an immortal human with perfect memory count to? Well, he can in theory count to *any* number! But can he count *all* of them? No. No matter how long he counts upwards (a million years, a trillion years, a googolplex years), he will not count all the numbers. Likewise, for any specific ordinal, God can "count" to it, but he cannot "count" all of them.
Thanks for your thoughts. Have a nice day! :)
@@ApologeticsSquaredThere is a paradox of omniscience which also deals with sets however.
If we define a set of all sets that god can/does know and god is omniscient then this should include all sets but then the information on wether or not god is truly omniscient should be contained within that set. Another way to phrase this information is that god would need to know there’s nothing which exists outside of the sets of which he is aware. But do do this he would require knowledge outside of the set of what he knows.
This too would infinitely extend the possible sets of all knowledge by an infinite regress of self reference without any definitive termination ever being reached. Even if there is nothing else outside of the original set the possibility of something beyond awareness and understanding can never be truly disconfirmed.
This then proves that god cannot be omniscient because there is something he cannot know
6:17: Nitpick, which I think you know based on some other art and just misdrew something: 2 is usually defined as {∅, {∅}} (when you arenʼt just constructing it out of Peano axioms directly, which I prefer, or some other construction like Church numerals; set theory is not *unique* in being able to be a foundation of math). You could still define it the way you did but that make some later definitions harder.
As for the actual argument: Iʼm not sure why youʼre assuming these others donʼt exist (under platonism, since this entire video assumes that)? You canʼt just construct a “set of all sets which exist”; you need to use the axioms of set theory, and thereʼs no reason to say the other sets you can construct *donʼt* already exist. There could be an infinite number of already-existing sets (and, for the modified version of your argument in a response video, an infinitely deep hierarchy of sets and classes and ….) already out there existing under platonism. There doesnʼt need to be a point where they *stop* which you can then use to jump out and ask why the collections of those donʼt exist.
I wish more Christian's knew of you
Thanks!
I'm already knowing him,and that's simple amazing the apologetics he does(I've never ever seen this kinda anywhere).
Simple,Amazing.
Not all maths are/can be expressed with set theory, though.
Also, there are many philosophy of maths that account for what you describe, such as fictionalism and modal structuralism. Even if you are a mathematical Platonist, it doesn't necessarily mean that you believe in a god. Read up on philosophy of maths on SEP or watch Logos' excellent video on the subject.
Also, ZF set theory is clearly a man-made construct. Would you include the axiom of choice? Do you know if ZF set theory is consistent?
According to the SEP, "Thus, set theory has become the standard foundation for mathematics, as every mathematical object can be viewed as a set, and every theorem of mathematics can be logically deduced in the Predicate Calculus from the axioms of set theory."
You see, I haven't just made up the idea that ZF set theory is viewed as foundational for mathematics!
Btw, I'm a solid logicist, but it seems pretty clear to me that Platonism is a pretty shaky stance for atheists.
Have a nice day! :)
@@ApologeticsSquared I know you didn't make it up, but SEP is flat out wrong. There are other ways to formulate a first order language that cannot be expressed as set theoretic, and there are maths/logic that do not fall under ZF set theory. So most, yes, all, no (how would you prove that all maths are set theoretic in the first place?). SEP isn't great for things like math (and probability). Better look at math books if you want to talk about it.
I agree that Platonism is a pretty shaky stance for anyone. Which is probably why most mathematicians are not Platonists.
You should watch Logos' videos. Logicism has its problems too.
If whatever mathematics is on the lowest level - like sets - is infused in what's actually 'physically' real, then it would be enough like that last view about God, with exception to God existing. In other words, only those sets would actually exist that exist physically, even though you could use the rules they follow to build more complex ones and more of them.
But even if one believed that numbers must somehow exist separately on their own, yet necessarily, maybe they could exist in some platonic sense. Again, without any necessity for being based on additional entity - a mind of God.
Hello!
The view espoused in your first paragraph seems quite hard to swallow, if I understand it. On purely intuitive grounds, it simply seems bizarre!
(No offense! It just seems weird to me!)
Beyond that, it seems to get the worst of both worlds. On the one hand, you have the mysterious spaceless timeless number-entities that the detractors of Platonism decry. On the other hand, all those math equations about the nonexistent sets "built" from the existing sets would need to be true without talking about really existing things -- exactly what the detractors of Nominalism decry! All the criticisms of any philosopher in any camp of this discussion seem to apply against this view.
Regarding your second paragraph, the video is entirely an attack on non-Activist Platonism. If the sets exist Platonically, why aren't there more sets that exist Platonically?
Have a nice day! :)
...there is a book written by Tony Tymstra...here is a chapter you may find interesting...the book is available on amazon, the link is below.
THE LITTLE BUTTERFLY PROOF
How much more amazing can this planet be? A butterfly
returns to the forest four generations later after having never
been there before and lands on the same trees as its great
grandparents once did, traveling almost 3000 miles and never
getting lost. How can that not be proof of something grand in
this world?
The Great North American monarch butterfly's migration is
only one example of nature's seemingly endless number of
inspiring mysteries.
It is a demonstration of the complex and elegant
entanglements that are still hidden from us. Such a testimony
quietly compels us to discover and understand the world
around us.
Before these butterfly sanctuaries were discovered in the late
1970s, people in North America had always wondered where
did all these monarch butterflies go. And in a strange twist of
beautiful irony, the people in Mexico had always wondered
where did all these butterflies come from. These are two
different views of the same incredible pilgrimage. This
migration is truly one of nature's wondrous revelations because
it is not the life of one butterfly that makes this so unusual. It is
the life of four generations of butterflies that makes this story
complete and causes us to ponder about our own purpose and
destiny.
This is a beautiful story. The migration starts in the middle of
the forest, in the mountains of Michoacán. It is in an area only
thirty by fifty miles round. Millions upon millions of butterflies
converge in this place to overwinter enjoying the warmth of the
Mexican sun. During their stay in this migratory site, the female
monarchs become fully developed, and mating takes place.
As this first generation begins their spring migration, they fly
over mountain ridges to as far north as Texas and to the
southern parts of the United States. Here they lay eggs on
milkweed plants along the way. This generation soon dies, but
in four days, their eggs will hatch into baby caterpillars. These
earthbound caterpillars eat ferociously for two weeks before
becoming fully-grown. They will then find a quiet and safe
place to hide. Here they will start the process of transforming
into a chrysalis.
For about ten days, the caterpillar will undergo a remarkable
transformation called metamorphosis, and soon a beautiful
butterfly will emerge. Deeply embedded in their nature, this
second-generation somehow knows to continue the journey,
and they fly north to the mid-United States and to the lower
parts of Canada where they will lay eggs and begin the cycle for
the next generation.
As the third generation emerges, they will find milkweed
plants, eat, breed, and lay eggs, and soon a fourth generation of
butterflies is born. When autumn arrives, and the leaves fall,
this fourth-generation will fly all the way back to Mexico.
Picking up thermals and getting carried aloft on the upper
winds.
They will travel roughly sixty miles a day. After two months,
they will eventually arrive at the same thirty by fifty-mile
forested area of that first generation. It will have been a flight of
almost 3000 miles without having any knowledge of being there
before, and never getting lost on the way. It is an incredible feat.
The Monarch Butterfly migration inspires an overwhelming
feeling of reverence and admiration for the glory of nature. It is
still a mystery as to how they do it.
In early Christianity, the butterfly was a symbol of the soul. In
China, it was used as a symbol of bliss and joy. People in
Australia and New Zealand call the monarch butterfly "the
wanderer." To Native Americans, the butterfly is a symbol of
joy, color, and change. The butterfly has inspired many poets,
thinkers, and writers. Perhaps this is a testimony to the Creator
of this world. Is a butterfly proof that a Creator exists? If and
when we learn all the mysteries of the world, then perhaps we
will know, but the Great Butterfly Migration gives us a glimpse
towards that answer.
www.amazon.com/Possible-Impossible-Probable-Proof-exists/dp/B088B4SKSK/ref=sr_1_1?dchild=1&keywords=tony+tymstra&qid=1607226097&s=books&sr=1-1
Colossians and Act reads: " *_God is before all things in which everything came to be and in where everything lives, moves and have their beings_* ".
God is the set of all things. In a way you can say God does not exist. He is existence Himself.
a universal set is impossible
@@nicholocadongonan1074 If you're saying it must be true.
@@STREEEEEET yeah fr. check out Russell's Paradox and the infinite regress from powersets of the universal set.
@@nicholocadongonan1074 I'm familiar with Russel's Paradox and i've been thinking on how to respond this because i don't want to sparkle a debate over this topic so i'll just say this instead. Math is not reality., even if you could demonstrate that Frege's idea of concepts = extensions breaks down under Russel's paradox that just show you that Frege's idea is wrong.
Take as an example the Barber's paradox which is derived from Russel's., you can put together all those sentences to puzzle someone whether the barber shave himself or not but if it were reality then either the barber would have a beard or don't.
Moreover we know for a fact that there is the set of all things called EXISTENCE. In order to exist you need to be part of the set existence or else you don't exist thus existence is the set of all things necessarily.
Now we circle back to what i said initially, according to Act's and Colossians God is the set of all things; God is existence Himself., the Great I AM.
I pray that you join the side of reason, far more fun and defensible.
@@STREEEEEET set theory isn't mathematics per se even, nor did i imply that math had ontic status. ig there still can't be a universal set.
so i'd further reject there being such a set called existence; i'm pretty sure your view is pantheistic too. and i'm not a pantheist, so yeah, we'll have to agree to disagree here. have a nice day! 🤜🤛
My only question here is.... Why should we expect there to be more sets?
Infinity is as big as it could ever get. Even with the idea that we can just keep getting bigger sizes of infinity, it’s still infinity. It’s all it can be, all there can be. Right?
It all seems kind of ethereal without getting into super technical stuff, but the different sizes of infinities are very different from one another. So, the question of why there aren't *more* infinities is a coherent question.
Have a nice day! :)
The set theory stuff is very standard. The “sets exist if they are in the mind of God” stuff is less standard. Just sayin’
Transfinite Set Theory was revealed to me by the Christian God - Georg Cantor, inventor of set theory (paraphrased)