Infinity
This is an observation on the subject of infinity as argued by Ben Askin and Dan Courtney. The debate was pointed out to me by my good friend Shaun Fowler. This is in regard to the statement made in the Westminster Confession, Chapter 2, paragraph 1.
"I. There is but one only, living, and true God, who is infinite in being and perfection, a most pure spirit, invisible, without body, parts, or passions; immutable, immense, eternal, incomprehensible, almighty, most wise, most holy, most free, most absolute; working all things according to the counsel of His own immutable and most righteous will, for His own glory; most loving, gracious, merciful, long-suffering, abundant in goodness and truth, forgiving iniquity, transgression, and sin; the rewarder of them that diligently seek Him; and withal, most just, and terrible in His judgments, hating all sin, and who will by no means clear the guilty."
Looking at both Ben and Dan's arguments regarding numbers and infinity brings to thought some observations of my own. Perhaps I don't understand at what plane they argue for/against the infinite God, but here's what I've observed on the matter of infinity.
Ben states, (1) "But if numbers are mental objects which are members of an actual infinite set, this requires the existence of an infinite mind where they inhere-the mind of an eternal, omniscient God." This is the premise for Dan's rebuttal, (2) "Numbers are metaphors; symbolic representations of some aspect of reality. Numbers are conceptual representations of relationships between aspects of reality. [As Ben asserts, Numbers do not exist] independent of our brains that conceive of them." To which Ben responds, (3) "So, if everything with a brain woke up dead tomorrow, how much would 2+2 equal? If you answered 4, according to Dan, you’d be wrong."
Ben's argument (1) suggests that numbers do not exist without a mind in which they can exist. And, I believe, Dan argues (2) that numbers are a mental representation of a part of reality. And I believe Ben argued on a misquote (3) that Dan suggests numbers cease to exist when all minds die.
First, I think the important part of the initial argument is, (1) "The existence of a number is independent of the existence of a particular instantiation of its properties". This is certainly true. Given a finite reality where no grouping of objects exceeds the concept of the number "8", the concept of "9" can still exist as a "mental object", if there is a mind observing that reality that recognizes its quantitative measurements.
If we argue from the standpoint of the recent study in Science Magazine that our minds have a sense of numerosity, the ability to map quantitative measurements through a designated portion of our minds, the quantitative measurement (number) of infinity is not perceivable in our finite minds. Through inductive reasoning, we can conceive the concept of the number infinity.
This is where Ben's argument (1) is true. The number infinity cannot exist in a finite reality, but it still exists as a mental object or concept. Dan suggests that numbers reflect some part of reality, which would suggest that reality, in Dan's mind, has an infinite aspect to it. Astrophysicists suggest that our physical reality is finite and measurable, so I wonder what aspect Dan believes to be infinite. Our minds have a finite (but extremely large) number of atomic configurations. So, we can only conceive a finite number of thoughts. If you don't believe God and the realm of spirituality exists, then you are limited to what is in physical space, and thus a finite set of numbers by which you can conceive relationships between parts of our reality.
The only way you can tie infinity in a relationship to reality is by a "reification falicy" (something I'm only just now trying to understand; I don't philosophy enough). Our physical and mental reality is not infinite. Our minds can't conceive infinite possibilities and our physical universe is not without some concept of borders or finite limits (according to astrophysicists I've heard from). By inductive reasoning we can observe that integers can count up for as long as we would like to count, which bears the concept of infinity, but does not effect its existence. We can't write down infinity with all the matter available in the universe.
Now, Dan would probably suggest that this inverse relationship between infinity and reality would suggest that an infinite God can't exist. You can't prove that statement by what I just laid out above. If God is infinite, you can't observe the whole of him with the finite number of molecules in your head or in the universe. This means that the universe in comparison is dwarfed by God. This would suggest that God is (partially) observable apart from the universe, if you were able to escape the universe and grow your mind to see some subset of him. This concept, mind you, dates back many hundreds of years regarding infinity, the "turtles all the way down" concept.
If all the minds in the universe died, there would still exist quantitative measurements or groupings of all the objects containable inside the universe, and they are all finite. Does infinity exist? Is God infinite? We can't observe that with our physical minds (singularly, or corporately) if they were entirely altered to only observe God. The universe could not measure the infinite God if all its molecules were dedicated to observing him.
Now, perhaps we are thinking of a different concept of infinity, but the mathematical definition of the infinite set is not an observable concept of God. Ben and Dan are trying to argue for/against God's existence inside reality, and so I would suggest they argue for/against the possibility of observing a portion of the infinite God, if infinity is a mathematical concept. That does leave open at least one other definition of infinity, X+1. I know, it's a childish concept. "Mine goes to 1000!" "Oh yeah, mind goes to INFINITY!" "Well, mine goes to INFINITY+1!"
We can suggest that the definition in the Confession suggests this concept that God, regardless of size, is not wholly observable by the universe. The "turtles all the way down" concept also speaks to this idea that the universe rests at one position while whatever holds it up is outside of it and bigger than it. If God (or turtle) held control over the universe, he must be infinite in order to ensure all possibilities are accounted for. If he is not infinite, then there would be a god (or turtle) outside of God's reality holding him in control.
I would suppose that an Atheist's standpoint is that the universe is without control and infinite in size, something that science has mathematical proof against; symbolic proof representing an aspect of our reality suggesting it to be finite. The question here is whether there is something outside the finite that controls it, or if our reality is truly finite and thus oblivion doesn't even exist. If the big bang theory suggests our universe originated from an infinitely small thing, then that is a lot of nothing to dismiss.
"I. There is but one only, living, and true God, who is infinite in being and perfection, a most pure spirit, invisible, without body, parts, or passions; immutable, immense, eternal, incomprehensible, almighty, most wise, most holy, most free, most absolute; working all things according to the counsel of His own immutable and most righteous will, for His own glory; most loving, gracious, merciful, long-suffering, abundant in goodness and truth, forgiving iniquity, transgression, and sin; the rewarder of them that diligently seek Him; and withal, most just, and terrible in His judgments, hating all sin, and who will by no means clear the guilty."
Looking at both Ben and Dan's arguments regarding numbers and infinity brings to thought some observations of my own. Perhaps I don't understand at what plane they argue for/against the infinite God, but here's what I've observed on the matter of infinity.
Ben states, (1) "But if numbers are mental objects which are members of an actual infinite set, this requires the existence of an infinite mind where they inhere-the mind of an eternal, omniscient God." This is the premise for Dan's rebuttal, (2) "Numbers are metaphors; symbolic representations of some aspect of reality. Numbers are conceptual representations of relationships between aspects of reality. [As Ben asserts, Numbers do not exist] independent of our brains that conceive of them." To which Ben responds, (3) "So, if everything with a brain woke up dead tomorrow, how much would 2+2 equal? If you answered 4, according to Dan, you’d be wrong."
Ben's argument (1) suggests that numbers do not exist without a mind in which they can exist. And, I believe, Dan argues (2) that numbers are a mental representation of a part of reality. And I believe Ben argued on a misquote (3) that Dan suggests numbers cease to exist when all minds die.
First, I think the important part of the initial argument is, (1) "The existence of a number is independent of the existence of a particular instantiation of its properties". This is certainly true. Given a finite reality where no grouping of objects exceeds the concept of the number "8", the concept of "9" can still exist as a "mental object", if there is a mind observing that reality that recognizes its quantitative measurements.
If we argue from the standpoint of the recent study in Science Magazine that our minds have a sense of numerosity, the ability to map quantitative measurements through a designated portion of our minds, the quantitative measurement (number) of infinity is not perceivable in our finite minds. Through inductive reasoning, we can conceive the concept of the number infinity.
This is where Ben's argument (1) is true. The number infinity cannot exist in a finite reality, but it still exists as a mental object or concept. Dan suggests that numbers reflect some part of reality, which would suggest that reality, in Dan's mind, has an infinite aspect to it. Astrophysicists suggest that our physical reality is finite and measurable, so I wonder what aspect Dan believes to be infinite. Our minds have a finite (but extremely large) number of atomic configurations. So, we can only conceive a finite number of thoughts. If you don't believe God and the realm of spirituality exists, then you are limited to what is in physical space, and thus a finite set of numbers by which you can conceive relationships between parts of our reality.
The only way you can tie infinity in a relationship to reality is by a "reification falicy" (something I'm only just now trying to understand; I don't philosophy enough). Our physical and mental reality is not infinite. Our minds can't conceive infinite possibilities and our physical universe is not without some concept of borders or finite limits (according to astrophysicists I've heard from). By inductive reasoning we can observe that integers can count up for as long as we would like to count, which bears the concept of infinity, but does not effect its existence. We can't write down infinity with all the matter available in the universe.
Now, Dan would probably suggest that this inverse relationship between infinity and reality would suggest that an infinite God can't exist. You can't prove that statement by what I just laid out above. If God is infinite, you can't observe the whole of him with the finite number of molecules in your head or in the universe. This means that the universe in comparison is dwarfed by God. This would suggest that God is (partially) observable apart from the universe, if you were able to escape the universe and grow your mind to see some subset of him. This concept, mind you, dates back many hundreds of years regarding infinity, the "turtles all the way down" concept.
If all the minds in the universe died, there would still exist quantitative measurements or groupings of all the objects containable inside the universe, and they are all finite. Does infinity exist? Is God infinite? We can't observe that with our physical minds (singularly, or corporately) if they were entirely altered to only observe God. The universe could not measure the infinite God if all its molecules were dedicated to observing him.
Now, perhaps we are thinking of a different concept of infinity, but the mathematical definition of the infinite set is not an observable concept of God. Ben and Dan are trying to argue for/against God's existence inside reality, and so I would suggest they argue for/against the possibility of observing a portion of the infinite God, if infinity is a mathematical concept. That does leave open at least one other definition of infinity, X+1. I know, it's a childish concept. "Mine goes to 1000!" "Oh yeah, mind goes to INFINITY!" "Well, mine goes to INFINITY+1!"
We can suggest that the definition in the Confession suggests this concept that God, regardless of size, is not wholly observable by the universe. The "turtles all the way down" concept also speaks to this idea that the universe rests at one position while whatever holds it up is outside of it and bigger than it. If God (or turtle) held control over the universe, he must be infinite in order to ensure all possibilities are accounted for. If he is not infinite, then there would be a god (or turtle) outside of God's reality holding him in control.
I would suppose that an Atheist's standpoint is that the universe is without control and infinite in size, something that science has mathematical proof against; symbolic proof representing an aspect of our reality suggesting it to be finite. The question here is whether there is something outside the finite that controls it, or if our reality is truly finite and thus oblivion doesn't even exist. If the big bang theory suggests our universe originated from an infinitely small thing, then that is a lot of nothing to dismiss.