Can God divide by zero?

[JackQ]

This is pretty close to what I recall reading somewhere:
The situation of this dilemma is similar to a rigged hand of cards. It’s like setting the cards up in advance so that someone can never win the hand. The same thing applies here. Notice what the dilemma is really communicating: Can God do something that God cannot do? Well, to ask the question is to answer it! The problem here is that this does not constitute a deficit in God’s abilities, the problem here is that logically self-contradictory statements don’t describe anything at all! For example, what does it mean to be a “married bachelor”? Can the greatest geometric mathematician draw a “square circle”? These “things” aren’t things at all. There is no such thing as a married bachelor or a square circle because those descriptions are self-contradictory. Likewise, a “God-made rock so big that God can’t lift it” is a similar description - it’s self-contradictory. It’s not that God can’t make such a thing, it’s that such a thing is not a thing at all! It no more limits God’s power than asking “Can God make a square circle?” The individual words have meaning, but when these specific words are put together they are self-contradictory.

Ditto this.

 

[sidbrown]

There’s no such thing as an actual infinity, with the exception of God.

The set of natural numbers {1,2,3,4,5…} is actually an infinite set.

 

[runningdude]

The set of natural numbers {1,2,3,4,5…} is actually an infinite set.

True, but numbers are rather ethereal - ie they occupy a dimension not of space but of mind.

A true infinity would be the aforementioned rock that was too big for God to lift (ie fills “infinite space”). I’d argue God could make one, but then what would He do with it?

 

[kentuckyliz]

I don’t know about all this mathy stuff. Ick.

When I get to heaven, I’ll just ask Him.

 

[JDaniel]

The set of natural numbers {1,2,3,4,5…} is actually an infinite set.

No, it is not: It is a potentially infinite set of the natural numbers. The large number potentiality exists only as a reification. If it actually existed, we could, one would believe, determine what that final number was, which would determine a species for it. But, as it is, is is simply a vagary. Also, we would know whether it was an odd number or an even number. If we arbitrarily close the set, we, by abstraction, only appear to be preventing the addition or subtraction of any additional unit(s). Remember, number is multitude measured by a number. Multitude is thus the genus of number, and the specific difference, determining the genus into this kind of number rather than that, is the final unit of the number in question. Thus the specific difference (species) that determines or measures multitude into, say, the number seven is the final unit in this number. Add a unit and we change the species, which then becomes eight.

God bless,
jd

 

[sidbrown]

No, it is not: It is a potentially infinite set of the natural numbers. The large number potentiality exists only as a reification. If it actually existed, we could, one would believe, determine what that final number was, which would determine a species for it. But, as it is, is is simply a vagary. Also, we would know whether it was an odd number or an even number. If we arbitrarily close the set, we, by abstraction, only appear to be preventing the addition or subtraction of any additional unit(s). Remember, number is multitude measured by a number. Multitude is thus the genus of number, and the specific difference, determining the genus into this kind of number rather than that, is the final unit of the number in question. Thus the specific difference (species) that determines or measures multitude into, say, the number seven is the final unit in this number. Add a unit and we change the species, which then becomes eight.

God bless,
jd

If you would take a math course in set theory, you would discover that the set of natural numbers is a countably infinite set. And I don’t think that any mathematician would take your explanation seriously.

 

[Pug]

If you would take a math course in set theory, you would discover that the set of natural numbers is a countably infinite set. And I don’t think that any mathematician would take your explanation seriously.

In set theory we find the infinity axiom. Perhaps the other poster prefers not to utilize this axiom. Set theory is not as old as the hills.

The infinity axiom, as far as I know, is equivalent to N existing.

 

[JDaniel]

If you would take a math course in set theory, you would discover that the set of natural numbers is a countably infinite set. And I don’t think that any mathematician would take your explanation seriously.

Just what exactly does “countably infinite set” mean to you?

God bless,
jd

 

[JDaniel]

In set theory we find the infinity axiom. Perhaps the other poster prefers not to utilize this axiom. Set theory is not as old as the hills.

The infinity axiom, as far as I know, is equivalent to N existing.

Pug:

Can you give me your idea of what “postulate” or, “postulation”, means?

God bless,
jd

 

[Pug]

Pug:

Can you give me your idea of what “postulate” or, “postulation”, means?

God bless,
jd

That word most readily brings to mind the parallel postulate, which is independent from Euclid’s other four.

If that is completely unhelpful to you, then to me it is something that is taken without proof. In other words, one does not need to do geometry (or set theory, depending on which we are talking about) with the thing. One can take some other postulate instead. (edit: or none at all)

What I meant in my other post is that the infinity axiom is an axiom (postulate), and hence is not proved.

 

[sidbrown]

Just what exactly does “countably infinite set” mean to you?

God bless,
jd

There are two concepts here. One is countable, the other is infinite.
A set is countable if it has the same cardinality as some subset of the set of natural numbers. A set is infinite if for any natural number, the set has a subset whose cardinality is that natural number.

 

[teachccd]

WOW!! So many smart folks on this thread. I really mean that since I was never that great at math. But I am pretty well versed in that God created the universe out of nothing so I’m pretty sure that He can do or not do whatever He pleases…

 

[JDaniel]

That word most readily brings to mind the parallel postulate, which is independent from Euclid’s other four.

If that is completely unhelpful to you, then to me it is something that is taken without proof. In other words, one does not need to do geometry (or set theory, depending on which we are talking about) with the thing. One can take some other postulate instead. (edit: or none at all)

What I meant in my other post is that the infinity axiom is an axiom (postulate), and hence is not proved.

Pug:

Mea culpa. I did not read it that way, sorry. Yes, you are extremely close. A “postulate” is an assumption granted for the sole purpose of allowing an argument to proceed. But, it never stops being an assumption. An axiom is more akin to a “law” of physics. That’s the problem. Mathematicians run around the halls of academia spouting off all sorts of gibberish until, at some point, they begin to believe that mathematics takes on more objective reality than is possible for it. The undergirding for mathematics is physical objects. But, mathematical objects are objects of a different sort, as St. Thomas says:

“In the framework of immateriality, the mathematician in his strictly scientific character is said to leave aside all sensible matter and to retain in the abstracted result universal intelligible matter.” - Summa Theologica, I, q. 85, a. 1, reply 2
I’m sure not too many mathematicians would like this either.

The infinity axiom is a postulation. In real arithmetic, a person can point to 5 cows. A person can point to 1,000 head of cattle. And, a person can imagine a billion head of cattle. But, such an imaginary object is grounded in its ostensible possibility in reality. The problem with infinity, is that it is not a number. It is a contraction (to borrow from Rossum) that “objectifies” it so that it may be talked about and possibly manipulated in some manner. But, the term itself represents something nebulous. It represents a vagary. There is no number that is represented by the word. In fact, the word means “unbounded.” It is a contraction of the concept an unimaginably huge number. And, it has been known for centuries that it is that which is by definition, dynamic.

It can grow; it can be reduced. This is precisely what makes it vague. However, at any stopping point - where its dynamicality is halted, such as closing it within a system - it becomes finite. The formulation of the axiom must, therefore, deny finite sets within the equation. Why is this so hard to ratiocinate? I theorize that it is caused by nothing more than loosing sight of the fact of reality. As an imaginary object, it is real enough. But, it does not survive outside of the mathematician’s mind, imagination. The infinity axiom does not have the basis, i.e, existentiality, of, say, the Law of Gravity. Furthermore, the infinity axiom depends upon other axioms (postulations) that do not carry as much weight as the axiom itself seemingly carries. But, I am always amazed at how people think.

“The mathematician, scientific in Aristotle’s sense, makes two abstractions: one, to go from the sensible world to the order of individual intelligible matter; the other, to go to the universal or common consideration of intelligible matter itself.”
This is the two-step process by which the human mathematician reifies his material so that it can be worked with. But, that doesn’t mean that his material is worked with in the same way as a carpenter works with wood.

God bless,
jd

 

[JDaniel]

There are two concepts here. One is countable, the other is infinite.
A set is countable if it has the same cardinality as some subset of the set of natural numbers. A set is infinite if for any natural number, the set has a subset whose cardinality is that natural number.

Sid:

Countability is almost acceptable: depending upon its type of correspondence. One to one is easy: a → 1, b → 2, c → 3, etc, or, cow → 1, (2) cows → 2, (3) cows → 3, etc. It becomes more imaginary when it skips correspondence.

But, do you really not see that infinity is an abstraction? And that the axiom is built upon abstractions? And, that is why it is called a postulation?

God bless,
jd

 

[Pug]

Pug:

Mea culpa. I did not read it that way, sorry. Yes, you are extremely close. A “postulate” is an assumption granted for the sole purpose of allowing an argument to proceed. But, it never stops being an assumption. An axiom is more akin to a “law” of physics. That’s the problem. Mathematicians run around the halls of academia spouting off all sorts of gibberish until, at some point, they begin to believe that mathematics takes on more objective reality than is possible for it. The undergirding for mathematics is physical objects. But, mathematical objects are objects of a different sort, as St. Thomas says:“In the framework of immateriality, the mathematician in his strictly scientific character is said to leave aside all sensible matter and to retain in the abstracted result universal intelligible matter.” - Summa Theologica, I, q. 85, a. 1, reply 2I’m sure not too many mathematicians would like this either.

I think people who can think without reference to reality are weird.

The infinity axiom is a postulation. In real arithmetic, a person can point to 5 cows. A person can point to 1,000 head of cattle. And, a person can imagine a billion head of cattle. But, such an imaginary object is grounded in its ostensible possibility in reality. The problem with infinity, is that it is not a number. It is a contraction (to borrow from Rossum) that “objectifies” it so that it may be talked about and possibly manipulated in some manner. But, the term itself represents something nebulous. It represents a vagary. There is no number that is represented by the word. In fact, the word means “unbounded.” It is a contraction of the concept an unimaginably huge number. And, it has been known for centuries that it is that which is by definition, dynamic.

It can grow; it can be reduced. This is precisely what makes it vague. However, at any stopping point - where its dynamicality is halted, such as closing it within a system - it becomes finite. The formulation of the axiom must, therefore, deny finite sets within the equation. Why is this so hard to ratiocinate? I theorize that it is caused by nothing more than loosing sight of the fact of reality. As an imaginary object, it is real enough. But, it does not survive outside of the mathematician’s mind, imagination. The infinity axiom does not have the basis, i.e, existentiality, of, say, the Law of Gravity. Furthermore, the infinity axiom depends upon other axioms (postulations) that do not carry as much weight as the axiom itself seemingly carries. But, I am always amazed at how people think."The mathematician, scientific in Aristotle’s sense, makes two abstractions: one, to go from the sensible world to the order of individual intelligible matter; the other, to go to the universal or common consideration of intelligible matter itself."This is the two-step process by which the human mathematician reifies his material so that it can be worked with. But, that doesn’t mean that his material is worked with in the same way as a carpenter works with wood.

God bless,
jd

Yes, clearly the mathematician does not work with or shape the underlying material. It is more like if the mathematics fits (your situation), wear it. And yes, a postulate or assumption never ceases to be an assumption. That is why a mathematician is aware that she can make a different one if she likes.

I think 5 itself is an abstraction. Yes, I can have 5 cows in my driveway. But I only know it is five by comparison to other things with 5 items in them, like my hand. I can’t have “5” in my driveway. And the natural numbers certainly can’t take up residence there, being even more abstract. I agree with you that infinity is pretty much about arbitrary largeness. Yet, people do tend to confusedly categorize infinity as a number, as if it represents or is a numerical answer, just like 5. So, they are inclined to reason that infinity minus infinity must always equal zero, or a similar confusion. Maybe this is the result of having seen the symbol for infinity placed after an equals sign, so clearly it is a genuine (number) answer.

The formulation of the axiom must, therefore, deny finite sets within the equation.

I don’t understand this. You were saying this about the infinity axiom. Oh, maybe you mean how all those successors are in the one postulated infinite set.

 

[sidbrown]

Sid:

Countability is almost acceptable: depending upon its type of correspondence. One to one is easy: a → 1, b → 2, c → 3, etc, or, cow → 1, (2) cows → 2, (3) cows → 3, etc. It becomes more imaginary when it skips correspondence.

But, do you really not see that infinity is an abstraction? And that the axiom is built upon abstractions? And, that is why it is called a postulation?

God bless,
jd

In scientific endeavors, you will use abstraction all the time. Take for example if you are studying the movement of the earth about the sun. You will not consider people walking or driving on the earth. Now will you study the hibernation patterns of animals for this study. And further, you will not consider the moons of other planets. You will remove all these characteristics and more and focus on the essential properties of mass and gravity of the earth and sun. This is basically what abstraction is, the consideration of the essential qualities of an object under study while removing from the study the non-essential elements.
As far as an infinite set is concerned, another way of looking at it, is that for an infinite set, you can find a one to one correspondence between the original (infinite) set and a proper subset. This cannot be done for a finite set. And further, another way to see that the set of natural numbers {1, 2, 3, …} is infinite is to realize that for any natural number you give me, no matter how large, I can always find one larger. This would not be true of a finite set of numbers.

 

[JDaniel]

In scientific endeavors, you will use abstraction all the time. Take for example if you are studying the movement of the earth about the sun. You will not consider people walking or driving on the earth. Now will you study the hibernation patterns of animals for this study. And further, you will not consider the moons of other planets. You will remove all these characteristics and more and focus on the essential properties of mass and gravity of the earth and sun. This is basically what abstraction is, the consideration of the essential qualities of an object under study while removing from the study the non-essential elements.

Sid:

St. Thomas says:
“In the first order of abstraction, the intellect, operating upon the data presented to it by the various senses and dematerializing such data in order to make things intelligible, leaves aside what is called individual sensible matter but retains, in abstracted form, what is termed common or universal sensible matter.” - Summa Theologica, I, q. 85, a. 1, reply 2.
The difference between individual and common matter here can be best explained by example: individual sensible matter is this wine or that glass existing with their sensible qualities as individual things outside of the the mind. Common, or universal, sensible matter in these cases would be wine in general or glass in general. This is called common or universal because the intellect relinquishes the individual characteristics of the objects brought to it by the senses and considers such objects on a general level.

As far as an infinite set is concerned, another way of looking at it, is that for an infinite set, you can find a one to one correspondence between the original (infinite) set and a proper subset. This cannot be done for a finite set. And further, another way to see that the set of natural numbers {1, 2, 3, …} is infinite is to realize that for any natural number you give me, no matter how large, I can always find one larger. This would not be true of a finite set of numbers.

And that is precisely why it is called a potential infinity. If a larger one (or, a smaller one) can always occur, then infinity is a vagary. It is not precise. At the moment one stops to use one of the large numbers, actual infinity is swapped out for potential infinity. Actual does not mean ethereal. It does not mean “whatever we say it is.” It is what it is, clearly, simply and without equivocation. Closing it in brackets does not protect it from real actuality. You can see why mathematicians would not to call them *potential infinities/I, right?

God bless,
jd*

 

[Spock]

And that is precisely why it is called a potential infinity. If a larger one (or, a smaller one) can always occur, then infinity is a vagary. It is not precise.

It is hard to “grab” infinity, so I will give a different example. Suppose there is a chocolate manufacturer, and wants to advertize its product. Into every box of chocolate they place a coupon. If you collect 10 coupons, you will get a box of chocolate free. Suppose each box costs 1 dollar. The question is: “how much is one box of chocolate worth?”. I will use two methods to show the result.

1. A box of chocolate is worth a little more than the 1 dollar, since it also contains the coupon. (The coupon is worth 0.1 dollar. Remember, 10 coupons earn a new box.) But, the coupon is worth 1/10th of a box of chocolate. To that 1/10th of a box belongs 1/100th of the coupon. The 1/100th of the coupon is worth 1/1000th of box, etc… ad infinitum. So one box is really worth 1 + 1/10 + 1/100 + 1/1000 + … = 1.11111… dollars.
2. Now, suppose you already accumulated 9 coupons (and spent 9 bucks). You go to the store, grab a box, extract the 10th coupon, go to the cashier and present the 10 coupons as payment. So for 9 dollars you got 10 chocolates, therefore each box is worth precisely 10/9 dollars.

So, 1.1111111111… = 10/9. Not “approximately”, exactly, precisely. And there you have your actual infinity.

 

[BKulash_eski]

Does God use numbers? I am not sure that God, would even have us use numbers. Can they be used to prove Love well I suppose.
In marriage three is equal to one that is love(Husband,God, wife)
The Holy Trinity Father, Son and Holy spirit= one god.
Your question is very intriguing… I am going to think aboutthis and repost later.

 

[sidbrown]

So, 1.1111111111… = 10/9. Not “approximately”, exactly, precisely. And there you have your actual infinity.

Yes. And the number of such examples with repeating infinite decimals is endless. And such is the case for irrational numbers also.The decimal expansion of pi, or or the square root of two, each have infinite non-repeating decimal expansions.