Author Topic: The Mathematical Infinite and Almighty God as Infinite Being.  (Read 663 times)

Offline Xavier

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The Mathematical Infinite and Almighty God as Infinite Being.
« on: December 05, 2018, 07:15:28 AM »
Creation of something out of nothing can only be accomplished by an Infinite Being. In other words, we have examples of finite numbers in the real world. Why should we not also have an example of the infinite? If we needed 16 apples in 8 boxes equally, we would place 2 in each. But how did we get 1 or anything at all from 0? Answer: the Infinite. It's the only possible answer, and mathematics confirms it.

Actually, there's a long history of considering as God as analogous to the Infinity. A paper from Cambridge and a brief article excerpted below for discussion. Thoughts? I don't entirely agree with the author, but it's an interesting article.

https://www.cambridge.org/core/journals/religious-studies/article/infinity-in-theology-and-mathematics/2CF5AEEAD8E94E7FABB67F1EAFACDD00

https://math.dartmouth.edu/~matc/Readers/HowManyAngels/Blanc.html

"INFINITY IN THEOLOGY AND MATHEMATICS

Can we apply the same concepts to both the finite and the infinite? Is there something distinctive about the infinite that prevents attribution to it of concepts that we can attribute to the finite? If so, then this could be a reason for our difficulties in talking about God God is infinite, and our concepts, applying, as they do, to the finite objects of our experience, cannot be `extended' to the infinite. God's infinity is sometimes used as an explanation of theological difficulties like the problem of evil or the paradoxes of omnipotence: we do not really know what we mean when we attribute infinite goodness or power to God.
The mathematical concept of the infinite may be able to shed some light on the theological concept. In mathematics, there is a clearly developed concept of the infinite. We might expect that if there are problems of expressibility related to infinity, they will appear in mathematics as well as in theology. Since the mathematical concept is clearer, the source of any difficulties with it may be clearer as well ...

1.2 The theological infinite
The actual infinite, as I have said, can be conceived as collection of an infinite number of parts, the completion of some process that builds the infinite from the finite. The only problem with actually infinite sets, if there is a problem with them, is that there is not enough time to build them. Nevertheless, they are still the kinds of things that could be built from a collection of parts. The theological infinite, however, is not conceived as an infinite collection, but rather as the unbounded or unlimited; it is not in any sense constructible from the finite because it is not a collection at all, not an extension of the finite ...

Descartes puts this as a distinction between the infinite and the indefinite, between a positive and a negative idea. The actual or potential infinite of mathematics is more properly called indefinite; only God is infinite. Indefinite things are those in which we observe no limits, and perhaps can conceive no limits; but we cannot prove that they must have no limits. What we can call infinite, on the other hand, is that in which we not only observe no limits, but also can be certain that there can be no limits.4 [Descartes, Principles of Philosophy, in The Philosophical Works of Descartes, 1, trans. Elizabeth S. Haldane and G.R.T. Ross (Cambridge: Cambridge University Press, 1931), 1, xxvii.]
God is the only thing I positively conceive as infinite. As to other things like the extension of the world and the number of parts into which matter is divisible, I confess I do not know whether they are absolutely infinite; I merely know that I can see no end to them. . . .5 [Descartes, letter to More, 5 February 1649, in Philosophical Letters, trans., ed. Anthony Kenny (Minneapolis: University of Minnesota Press, 1981), p. 242.] ...

But what about number? We do seem to be able to prove that number is infinite, in virtue of the fact, for example, that the series of positive integers can be put into a one-one correspondence with a proper subset of itself. This is a positive proof of infinity, of the sort that Descartes would reserve only for God. In separating God's infinity from the merely indefinite of mathematics, Descartes perhaps means to retain God's infinity as something absolutely unique, mysterious and strange, in the face of which we stand in awe ...

In a sense our idea of the infinite is for Leibniz derived from the finite and from the impossibility that we should ever come to the end of our ability to continue adding or dividing. But our ability thus to build the infinite from the finite, to understand that we can keep applying the same rules or processes over and over, getting a new result each time, is grounded in the idea of the theological infinite. The idea of the theological infinite, which grounds the mathematical infinite, is an idea of an attribute of God. (That is, God is infinite; and God's other qualities are in God in the manner proper to an infinite being. Qualities are determined and limited by the nature of the being in which they inhere; in an infinite being, there is no limitation of the quality by the nature of the being.8 [This explication of God's infinity is close to Aquinas's: cf. Summa Theologica 17.] ) This absolute infinite `precedes all composition and is not formed by the addition of parts'. It is not, that is, a completed whole, but rather, `an attribute with no limits'.9[Leibniz, New Essays on Human Understanding, trans. Peter Remnant and Jonathan Bennett (Cambridge: Cambridge University Press, 1981), 157ff.] ...
Mary, our Heavenly Mother, implores those who receive Holy Communion Daily, or at least Weekly, to Offer their Lives. TEXT OF THE LIFE OFFERING, adapted and pluralized: Dear Lord Jesus, before the Holy Trinity, Our Heavenly Mother, and the whole Heavenly Court, united with Your most Precious Blood and Your Sacrifice on Calvary, We hereby Offer our whole Lives to the Intention of Your Sacred Heart and to the Immaculate Heart of Mary. Together with our life, we place at Your disposal all Holy Masses, all our Holy Communions, all Rosaries, all acts of consecration, all our good deeds, all our sacrifices, and the suffering of our entire life for the Adoration and Supplication of the Holy Trinity, for Unity in our Holy Mother Church, for the Holy Father, Pope Francis the First; and for His Holiness Pope Benedict XVI. For His Eminence Patriarch Kirill of Moscow, His Excellency Metropolitan Hilarion, as well as His Eminence Patriarch Bartholomew of Constantinople, that they may re-unite their flocks with the Catholic Church, and there may soon be but One Fold and One Shepherd. For all the 220+ Cardinals of the Holy Roman Church, for all 5500+ Bishops of the Universal Church that they may be true Apostles and Shepherds; and for the 400,000+ Priests, the 700,000+ Nuns, 50,000+ Monks, 100,000+ seminarians, that they may all become the Saints the Divine Will wishes them to be; we pray for good Priestly and Religious Vocations, and for All Souls until the end of the world. O my Jesus, please accept our life Sacrifice and our offerings and give us Your grace that we may all persevere obediently until death. Amen." https://marianapostolate.com/life-offering/ Please pray this daily and you and your family will be saved. You will avoid Purgatory.

Daily Morning Offering: O my God, in union with the Immaculate Heart of Mary,  I offer Thee the Precious Blood of Jesus from all the Altars  throughout the world, joining with It the offering of my every thought, word, and action of this day. I desire to gain every Indulgence and Merit I can, offering them, together with myself, to Mary Immaculate, Whom Thou hast appointed the dispenser of the merits of Thy Precious Blood, especially by means of this Scapular  [Here kiss your Brown Scapular] that She may best apply them to the interests of Thy Most Sacred Heart. Amen.

Consecration to Our Blessed Mother: My Queen, my Mother! I give myself entirely to Thee, and to show my devotion to Thee I consecrate to Thee this day, my eyes, my ears, my mouth, my heart, my whole being without reserve, Wherefore, good Mother, as I am Thine own, keep me, guard me, as Thy property and possession." http://www.catholictradition.org/Mary/morning-offering.htm

"I am the Lady of the Rosary. Pray the Rosary (i.e. 15 decades; 5 decades is a part of the Rosary) every day to obtain Peace for the World." ~ Our Lady of the Rosary of Fatima.
 
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Offline Quaremerepulisti

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #1 on: December 05, 2018, 02:44:42 PM »
God is absolutely infinite. Which means He is, in every way, beyond our comprehension.

Even the concepts of infinity we are able to come up with can't compare, because they are finite (limited) in some way.  For instance, the infinite set of all integers is finite in the sense it is limited to integers.  In fact, the only way we can even conceive of these sorts of infinities is insofar as they are finite.  I'll have to disagree with the article - so-called "indefinite" things actually do have limits, as I have shown.

Nevertheless, I agree with the article that when we attach any attribute whatsoever to God, we really do not know what it means.  We only know the meanings of attributes for finite objects.  You can only attempt to describe some attribute in terms of other ones, and we don't know what those mean either.
 

Offline Xavier

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #2 on: December 05, 2018, 11:30:25 PM »
God is a Wonder beyond our comprehension. He is the Infinite Being, the source of every being, Creator of every soul, Sustainer of the whole universe. In this life, as the Apostle says, we see as through a glass dimly, but in heaven face to face. It is certain man must be humble and confess his limitation before the Infinite, Who alone is without limits. We do not know what God is, but we know what God is not. We can gain a limited understanding of the Infinite God from His effects, and by analogy with what we know naturally. In heaven, we will know the Infinite Being gave us life and sustained us in existence all the while, as He alone could, having created us ex nihilo.
Mary, our Heavenly Mother, implores those who receive Holy Communion Daily, or at least Weekly, to Offer their Lives. TEXT OF THE LIFE OFFERING, adapted and pluralized: Dear Lord Jesus, before the Holy Trinity, Our Heavenly Mother, and the whole Heavenly Court, united with Your most Precious Blood and Your Sacrifice on Calvary, We hereby Offer our whole Lives to the Intention of Your Sacred Heart and to the Immaculate Heart of Mary. Together with our life, we place at Your disposal all Holy Masses, all our Holy Communions, all Rosaries, all acts of consecration, all our good deeds, all our sacrifices, and the suffering of our entire life for the Adoration and Supplication of the Holy Trinity, for Unity in our Holy Mother Church, for the Holy Father, Pope Francis the First; and for His Holiness Pope Benedict XVI. For His Eminence Patriarch Kirill of Moscow, His Excellency Metropolitan Hilarion, as well as His Eminence Patriarch Bartholomew of Constantinople, that they may re-unite their flocks with the Catholic Church, and there may soon be but One Fold and One Shepherd. For all the 220+ Cardinals of the Holy Roman Church, for all 5500+ Bishops of the Universal Church that they may be true Apostles and Shepherds; and for the 400,000+ Priests, the 700,000+ Nuns, 50,000+ Monks, 100,000+ seminarians, that they may all become the Saints the Divine Will wishes them to be; we pray for good Priestly and Religious Vocations, and for All Souls until the end of the world. O my Jesus, please accept our life Sacrifice and our offerings and give us Your grace that we may all persevere obediently until death. Amen." https://marianapostolate.com/life-offering/ Please pray this daily and you and your family will be saved. You will avoid Purgatory.

Daily Morning Offering: O my God, in union with the Immaculate Heart of Mary,  I offer Thee the Precious Blood of Jesus from all the Altars  throughout the world, joining with It the offering of my every thought, word, and action of this day. I desire to gain every Indulgence and Merit I can, offering them, together with myself, to Mary Immaculate, Whom Thou hast appointed the dispenser of the merits of Thy Precious Blood, especially by means of this Scapular  [Here kiss your Brown Scapular] that She may best apply them to the interests of Thy Most Sacred Heart. Amen.

Consecration to Our Blessed Mother: My Queen, my Mother! I give myself entirely to Thee, and to show my devotion to Thee I consecrate to Thee this day, my eyes, my ears, my mouth, my heart, my whole being without reserve, Wherefore, good Mother, as I am Thine own, keep me, guard me, as Thy property and possession." http://www.catholictradition.org/Mary/morning-offering.htm

"I am the Lady of the Rosary. Pray the Rosary (i.e. 15 decades; 5 decades is a part of the Rosary) every day to obtain Peace for the World." ~ Our Lady of the Rosary of Fatima.
 
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Offline Quaremerepulisti

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #3 on: December 06, 2018, 10:55:06 AM »
God is a Wonder beyond our comprehension. He is the Infinite Being, the source of every being, Creator of every soul, Sustainer of the whole universe. In this life, as the Apostle says, we see as through a glass dimly, but in heaven face to face. It is certain man must be humble and confess his limitation before the Infinite, Who alone is without limits. We do not know what God is, but we know what God is not. We can gain a limited understanding of the Infinite God from His effects, and by analogy with what we know naturally. In heaven, we will know the Infinite Being gave us life and sustained us in existence all the while, as He alone could, having created us ex nihilo.

No, Xavier, we can't gain any real understanding of the Infinite God from His effects.  It is simply impossible for the finite to have any comprehension of the Infinite, and there is simply no "analogy" from the finite to the Infinite either.
 

Offline Daniel

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #4 on: December 06, 2018, 06:14:45 PM »
God is a Wonder beyond our comprehension. He is the Infinite Being, the source of every being, Creator of every soul, Sustainer of the whole universe. In this life, as the Apostle says, we see as through a glass dimly, but in heaven face to face. It is certain man must be humble and confess his limitation before the Infinite, Who alone is without limits. We do not know what God is, but we know what God is not. We can gain a limited understanding of the Infinite God from His effects, and by analogy with what we know naturally. In heaven, we will know the Infinite Being gave us life and sustained us in existence all the while, as He alone could, having created us ex nihilo.

No, Xavier, we can't gain any real understanding of the Infinite God from His effects.  It is simply impossible for the finite to have any comprehension of the Infinite, and there is simply no "analogy" from the finite to the Infinite either.
QMR - What is the precise definition of "analogy", and how is it different from the via superlativa? Seems like the same thing to me. Or do you deny the via superlativa?
« Last Edit: December 06, 2018, 06:16:51 PM by Daniel »
 

Offline Quaremerepulisti

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #5 on: December 07, 2018, 11:08:40 AM »
QMR - What is the precise definition of "analogy", and how is it different from the via superlativa? Seems like the same thing to me. Or do you deny the via superlativa?

Analogy says that we can make meaningful predications of God, because there is analogy between the terms, in the same way that in "He is a good man" and "This meal is good", "good" is used analogously.  It doesn't mean exactly the same thing (its meaning is not univocal), but it means something similar.  Unlike, for instance, "The bank is open today" and "The tree is on the river bank" where bank is used equivocally; that is to say, it doesn't mean the same thing at all.

The V.S. denies that such predications can be made, at least if I understand it correctly.

But note.  We know what it means to say "He is a good man" or "This meal is good" because we know what a man is, and what a meal is.  That's what enables to make the predication and know what the attribute means; a finite intellect is able to comprehend finite objects.  We don't know what God is, because a finite intellect cannot comprehend the Infinite.  We can't therefore know what it really means to say "God is good".

Something reinforced by Divine simplicity/aseity, which must say that God "is" what He "has", such that "God is good" really means "God is goodness itself"; the concept of "good" can't be prior to the existence of God.  But what is goodness? That is God, so the statement is merely a tautology of which we cannot extract the meaning.
 

Offline Non Nobis

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #6 on: December 07, 2018, 11:15:46 PM »
God is a Wonder beyond our comprehension. He is the Infinite Being, the source of every being, Creator of every soul, Sustainer of the whole universe. In this life, as the Apostle says, we see as through a glass dimly, but in heaven face to face. It is certain man must be humble and confess his limitation before the Infinite, Who alone is without limits. We do not know what God is, but we know what God is not. We can gain a limited understanding of the Infinite God from His effects, and by analogy with what we know naturally. In heaven, we will know the Infinite Being gave us life and sustained us in existence all the while, as He alone could, having created us ex nihilo.

No, Xavier, we can't gain any real understanding of the Infinite God from His effects.  It is simply impossible for the finite to have any comprehension of the Infinite, and there is simply no "analogy" from the finite to the Infinite either.

In Genesis it says: "And God created man to his own image". We don't comprehend God by this image, but it is a reflection. God is the creator, the source of all good; the good that we DO understand comes from God and we can know THAT. We know of God that he is not the source of any evil but the source of all good.  I think you don't want to say that this is something "about" God, but I don't see how you can't. I don't see it has any meaning to meditate on Our Lady without seeing that she helps us better know God: "my soul doth magnify the Lord".
[Matthew 8:26]  And Jesus saith to them: Why are you fearful, O ye of little faith? Then rising up he commanded the winds, and the sea, and there came a great calm.

[Job  38:1-5]  Then the Lord answered Job out of a whirlwind, and said: [2] Who is this that wrappeth up sentences in unskillful words? [3] Gird up thy loins like a man: I will ask thee, and answer thou me. [4] Where wast thou when I laid up the foundations of the earth? tell me if thou hast understanding. [5] Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it?
 
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Offline Quaremerepulisti

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #7 on: December 08, 2018, 12:54:23 PM »
No, Xavier, we can't gain any real understanding of the Infinite God from His effects.  It is simply impossible for the finite to have any comprehension of the Infinite, and there is simply no "analogy" from the finite to the Infinite either.

How can the finite possibly comprehend the Infinite?  It's impossible.  The only thing the finite can comprehend is that the Infinite is not finite - e.g. what the Infinite is not.  In fact all the standard attributes that we use for God (omnipotence, omniscience, etc.) merely zero in one aspect of unlimitedness (e.g. not limited in a certain aspect such as power, knowledge, and so on).  IOW, they aren't really "attributes" in the classic sense and we can't understand them as though they were - it is just another way of saying what God is not.  Whereas all understanding of creaturely attributes has to do with limits.

Quote
In Genesis it says: "And God created man to his own image". We don't comprehend God by this image, but it is a reflection.

Right.

Quote
God is the creator, the source of all good; the good that we DO understand comes from God and we can know THAT. We know of God that he is not the source of any evil but the source of all good. 

We don't know what it means in itself for God to be a "creator" or a "source".  All we know are the effects of such.

Quote
I think you don't want to say that this is something "about" God, but I don't see how you can't. I don't see it has any meaning to meditate on Our Lady without seeing that she helps us better know God: "my soul doth magnify the Lord".

And what does it mean to "know" God?

Look, it's like looking up words in a foreign language dictionary that you don't understand at all.  Those definitions are also written in the foreign language, and so you can get definition after definition without ever getting to meaning.  So you can only define attributes of God in terms of other attributes of God, but because you don't understand God you never get to any real meaning.

 
 

Offline Daniel

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #8 on: December 09, 2018, 02:51:43 PM »
QMR - Thanks for the clarification. Turns out I was incorrectly remembering what the via superlativa is. Sorry about that.

But new question: If "good" is "God", and if we can have no complete understanding of "God", then it follows that we can have no complete understanding of "good" either. Yet the sentence "the meal is good" seems to have meaning. Would you agree?
 

Offline Quaremerepulisti

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Re: The Mathematical Infinite and Almighty God as Infinite Being.
« Reply #9 on: December 10, 2018, 08:17:17 AM »
QMR - Thanks for the clarification. Turns out I was incorrectly remembering what the via superlativa is. Sorry about that.

But new question: If "good" is "God", and if we can have no complete understanding of "God", then it follows that we can have no complete understanding of "good" either. Yet the sentence "the meal is good" seems to have meaning. Would you agree?

Yes, we can understand what an attribute means when applied to a finite object, because we can comprehend the finite object.  But attributes in this way don't have meaning in and of themselves; they must be applied to objects.