Arguments Against the Five Ways

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I’m trying to deal with someone who has little time for Thomism! Can anyone help me? Particularly with this idea of time/space being a loop thus removing the need for a prime mover: -
  1. Prime mover - Aquinas had little understanding mechanics and at a guess absolutly no idea of modern physics. It is completely feasable that everything, that’s time and space, may be in an eternal loop.
  1. Cause and effect - This kind of thinking was dominant in Western civilization until the advent of scientific methodology and yes the dawning of modern physics. That everything must have emerged from one thing in a linear progression and that thing must have been the first thing, see (1)
  1. The impossiblity of existence - again there isnt much difference here between (1) and (2) Aquinas yet again uses the mechanism of reduction to a starting point where God (TM pending) where there was only an existent being (Oh No!! screams of Pantheism deafen me) but an equaly valid argument would be that everything has always existed in a state of purpetual transformation, you know like in a loop!
 
I’m trying to deal with someone who has little time for Thomism! Can anyone help me? Particularly with this idea of time/space being a loop thus removing the need for a prime mover: -
Time & space cannot exist without matter/energy. Time & space sans matter/energy = nothingness. Time is nothing more than the measure of motion. If time & space could exist sans matter/energy, what would move? If time & space could exist sans matter/energy, what would motion be relative to? If somehow nothingness could move, where would it move? To think of a plurality of matter/energy coming to be, one simultaneously thinks of space & time. Otherwise, there would be nothing to move. There would be just beings (chunks of matter/energy) always and forever equidistant from each other. So, how does time & space loop?

Next, assuming matter/energy, and time & space, in what sense do they loop? Does he/she mean in the sense that history repeats itself? Or, in some mathematically abstract sense? How does that tie in with the beings of reality, as opposed to the beings of reason?

God bless,
jd
 
  1. Prime mover - Aquinas had little understanding [OF] mechanics and at a guess absolutly no idea of modern physics. It is completely feasable that everything, that’s time and space, may be in an eternal loop.
The problem with this is that an eternal loop of this sort is the same as saying “infinite loop.” We could not be in the picture, so to speak, if we were involved in an infinite loop as it would take an infinite time/duration to get here. The Now would still be approaching, but, would be an infinite duration off in the infinite distance. In fact, there would never, ever be a way of determining an infinite loop. The conjecture would remain forever a conjecture. To say that such a time/duration must have looped us here, is no different than saying an infinite God got us here. Except, there’s no revelation from STEM that that is the case. The Christian has Revealed Truth which, in the opinion of most, I believe, is far better than infinite conjecture.
  1. Cause and effect - This kind of thinking was dominant in Western civilization until the advent of scientific methodology and yes the dawning of modern physics. That everything must have emerged from one thing in a linear progression and that thing must have been the first thing, see (1)
If this is so, why do Scientists continue to use those words? “Cause” and “effect.” What purpose would they apparently serve - except, perhaps, to confuse? How do they help up-coming scientists? Yet they are descriptive words that allow us to have intimate relation with our histories. They allow us, in fact, to immerse ourselves in history. When an effect occurs repeatedly (i.e., always, or, for the most part) after a given action, under the same or similar conditions, the scientist is able to infer that his subject is ordered or determined to produce that effect. In this case he becomes the agency, the efficient cause. The formal and material causes exist in the material he is working with. And, of course, that the material is determined to produce this and not that consequent effect is the reason or final cause.
  1. The impossiblity of existence - again there isnt much difference here between (1) and (2) Aquinas yet again uses the mechanism of reduction to a starting point where God (TM pending) where there was only an existent being (Oh No!! screams of Pantheism deafen me) but an equaly valid argument would be that everything has always existed in a state of purpetual transformation, you know like in a loop!
Actually Aquinas does not use a reduction to a starting point. What he uses is a reasoning to an intentional agency. All men are aware that the eggs do not appear, by their own agency and intention, in a nest. Some intending agent(s) make them to be there. And, the intending agent(s) is/are not indifferent to the result of them being there. It is the “aim” of the antecedent action(s). Even an inept child can see the events, including those leading up to the laying of the eggs, the tending of them, and the hatching and rearing of the young birds. Physics and mathematics is unnecessary, unless we are seeking after the structure of these events and actions. “Structure” is another word for material and formal cause, in my view.

God bless,
jd
 
Thanks JD, looks like you know much more about this than me. The idea is that space-time and matter/energy are not seperate things. Space-time is a reference system invented by humans and used to discribe matter/energy and its distribution, density, flux etc. Does that make sense? You cant simply seperate the two concepts, by doing so, you create a false dichotomy.

Mathematically abstract? MMmm not really sure what you are driving at with that term. I think we need to be careful because we tend to like using abstractions ourselves, for example ‘essences’.

There is evidence to suggest that this particular version of Universe is one amounst many that have existed. Bang >> Crunch >> Bang ad infinitum or Fizzle >> Bang >> Fizzle or Collide >> Bang >> Fizzle >> Rip and so on ad infinitum. The argument is that there is no reason to believe that there is a starting point, except of course that we are brought up with certain socially ingrained logical assumptions, one of which being that all things must start somewhere, therefore Universe must also have an orgin somewhere back in time.
 
Thanks JD, looks like you know much more about this than me. The idea is that space-time and matter/energy are not seperate things. Space-time is a reference system invented by humans and used to discribe matter/energy and its distribution, density, flux etc. Does that make sense? You cant simply seperate the two concepts, by doing so, you create a false dichotomy.
Fighting:

I think this is correct.
Mathematically abstract? MMmm not really sure what you are driving at with that term. I think we need to be careful because we tend to like using abstractions ourselves, for example ‘essences’.
But there’s a difference!

Physical abstraction:
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
This is a single-step process: going directly from those things that are somatic (actual objects), in form, to us, to things that are universal, in form, to us. We clearly perceive identities in birds, so there must be bird-ness.

vs:

Mathematical abstraction:
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; emphasis mine
This is a two-step process, that brings us finally to what is termed, “intelligible” matter. IOW, a matter of the imagination.
There is evidence to suggest that this particular version of Universe is one amounst many that have existed. Bang >> Crunch >> Bang ad infinitum or Fizzle >> Bang >> Fizzle or Collide >> Bang >> Fizzle >> Rip and so on ad infinitum. The argument is that there is no reason to believe that there is a starting point, except of course that we are brought up with certain socially ingrained logical assumptions, one of which being that all things must start somewhere, therefore Universe must also have an orgin somewhere back in time.
That’s true, and, I haven’t had time to really think that through. Certainly, when one considers an Infinite God Creating a universe in an Eternal Now, one can easily see that Creation may well be a “timeless” event: instantaneous for God, but not even nearly instantaneous for us. My first thought is that Creation is a sort of “roll-out”, although not for God. But, we may intellectualize it in that way and often do.

I could agree with the latter part of your paragraph if we were able to determine that we, in fact, reside within an Infinity. But, an actual infinity cannot be composite. When someone says that the universe or, multi-verse, is infinite, I require to know how. How can finite, disparate elements add up to infinity?

God bless,
jd
 
Fighting:

I think this is correct.

But there’s a difference!

Physical abstraction:
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
This is a single-step process: going directly from those things that are somatic (actual objects), in form, to us, to things that are universal, in form, to us. We clearly perceive identities in birds, so there must be bird-ness.
Could this just be pattern recognition do you think?
Mathematical abstraction:
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; emphasis mine
I’m a little confused about your understanding of the mathematics used in Physics (Applied mathematics) and Pure mathematics. As I understand it, pure mathematics is indeed high level abstraction and a pursuit of of almost pure intellect with no need for a basis in empirical data. Applied maths, on the other hand is the application of mathematics to empirical data i.e. pattern recognition. I don’t see the difference?
I could agree with the latter part of your paragraph if we were able to determine that we, in fact, reside within an Infinity. But, an actual infinity cannot be composite. When someone says that the universe or, multi-verse, is infinite, I require to know how. How can finite, disparate elements add up to infinity?
Re: Infinity

It does throw up all sorts of paradoxes doesn’t it. George Cantor had a good crack at the problem of infinity but just made things weirder IMO. One of the biggest problems with infinity is that it can’t be quantified in any manner YET it is probably the single most important quantity in applied maths EVER!!! Crazy!
 
  1. Prime mover - Aquinas had little understanding mechanics and at a guess absolutly no idea of modern physics. It is completely feasable that everything, that’s time and space, may be in an eternal loop.
Actually, Aquinas thought it was perfectly reasonable to think the world had always existed. He repeatedly says that no one can ever prove that the world has not eternally been.

Yet this has nothing to do with his proof for God’s existence. It is “verticle” or “hierarchical” not linear.

Another incorrect understanding of the great Doctor.

fighting said:
2) Cause and effect - This kind of thinking was dominant in Western civilization until the advent of scientific methodology and yes the dawning of modern physics. That everything must have emerged from one thing in a linear progression and that thing must have been the first thing, see (1)

The first sentence in this response is meaningless. It says absolutely nothing from a philosophical standpoint. The second sentence, likewise, fails to intellectually engage in the principle of causality.

Ask this person what he thinks the law of causality is, with respect to the mind and the universe.

fighting said:
3) The impossiblity of existence - again there isnt much difference here between (1) and (2) Aquinas yet again uses the mechanism of reduction to a starting point where God (TM pending) where there was only an existent being (Oh No!! screams of Pantheism deafen me) but an equaly valid argument would be that everything has always existed in a state of purpetual transformation, you know like in a loop!

This borders on unintelligibilia. An “eternal loop” would do nothing whatsoever to destroy Aquinas’ argument for a first cause, prime mover, first efficient cause, etc. The causal chain is vertical, not horizontal. Think of the causes going on right now. Ultimately, if there is to be any movement right now, there must be an unmoved mover, which causes all things to move.
 
The argument is that there is no reason to believe that there is a starting point, except of course that we are brought up with certain socially ingrained logical assumptions, one of which being that all things must start somewhere, therefore Universe must also have an orgin somewhere back in time.
This argument is false.
 
Could this just be pattern recognition do you think?

I’m a little confused about your understanding of the mathematics used in Physics (Applied mathematics) and Pure mathematics. As I understand it, pure mathematics is indeed high level abstraction and a pursuit of of almost pure intellect with no need for a basis in empirical data. Applied maths, on the other hand is the application of mathematics to empirical data i.e. pattern recognition. I don’t see the difference?
These patterns are not like dress patterns, are they? Are the beings to which they refer real beings? Or, do they supercede reality? Or, must they remain mental objects, or rather, constructs?
Re: Infinity
It does throw up all sorts of paradoxes doesn’t it. George Cantor had a good crack at the problem of infinity but just made things weirder IMO. One of the biggest problems with infinity is that it can’t be quantified in any manner YET it is probably the single most important quantity in applied maths EVER!!! Crazy!
Yes it does. But, never forget, “infinity” is a mere word. A word is the written utterance of something that has meaning. The meaning may be skewed however the user wishes. Accordingly, there are two kinds of infinity. There is actual infinity, which is something that possesses determinate existence. And, there is potential infinity, which is the usual kind for us to ponder and for maths. It doesn’t have actual existence precisely because it is, by its nature, indeterminate. You can enclose a potential infinity inside brackets, but, that just forces a postulation.

God bless,
jd
 
Actually, Aquinas thought it was perfectly reasonable to think the world had always existed. He repeatedly says that no one can ever prove that the world has not eternally been.
Hello, Exodus:

I have found where Saint Thomas indicates that no one had yet proved that it was impossible for God to create an infinity of this kind, e.g., an infinity of spiritual beings. (On the Eternity of the World, close to the end.). This is where he was discussing the possibility of a transcendental multitude. I have not found where he discusses that no one has ever proved that the world has not eternally been. Could you tell me where he discusses this? I find that odd, as he spends so much effort on disproving the actual infiniteness of the world based upon recognizing that what is generally spoken of is a sensible continuum. (Commentary on the Physics, Bk. III, les. 12, n. 773; Summa Theologica, I, q. 25, a. 2, reply 1).

He says elsewhere that God’s infinity is an infinity of perfection; while, matter’s infinity is an infinity of imperfection, privation. So, while he admits that no one has proved the world’s eternality, he senses that it is not so. And this before modern science!

God bless,
jd
 
Well, Hindus believe time is a loop, but they still believe it needs a prime mover—indeed so did Aristotle; no Greek philosophers had an idea of linear time. Remember, Greece and India are very similar, especially linguistically (“mahatma”, for instance, would be “megatmos” in Greek).

Anything not logically necessary (and the universe isn’t) requires some other thing to cause its existence. Since God is existence (Subsistent Act of Being), it is in his nature to exist, and therefore he is logically necessary.
 
I have not found where he discusses that no one has ever proved that the world has not eternally been. Could you tell me where he discusses this?
Hey JDaniel. Let me start by saying that I take a lot of joy reading your posts, when I happen to see them.

Aquinas’ views on creation can be found most fully explained in the ST I I q. 44, 45, 46. These questions often get overlooked. Here is his I answer that from q. 46 a. 2. “whether it is an article of faith that the world began?”

By faith alone do we hold, and by no demonstration can it be proved, that the world did not always exist, as was said above of the mystery of the Trinity (32, 1). The reason of this is that the newness of the world cannot be demonstrated on the part of the world itself. For the principle of demonstration is the essence of a thing. Now everything according to its species is abstracted from “here” and “now”; whence it is said that universals are everywhere and always. Hence it cannot be demonstrated that man, or heaven, or a stone were not always. Likewise neither can it be demonstrated on the part of the efficient cause, which acts by will. For the will of God cannot be investigated by reason, except as regards those things which God must will of necessity; and what He wills about creatures is not among these, as was said above (Question 19, Article 3). But the divine will can be manifested by revelation, on which faith rests. Hence that the world began to exist is an object of faith, but not of demonstration or science. And it is useful to consider this, lest anyone, presuming to demonstrate what is of faith, should bring forward reasons that are not cogent, so as to give occasion to unbelievers to laugh, thinking that on such grounds we believe things that are of faith.

Objection 1. It would seem that it is not an article of faith but a demonstrable conclusion that the world began. For everything that is made has a beginning of its duration. But it can be proved demonstratively that God is the effective cause of the world; indeed this is asserted by the more approved philosophers. Therefore it can be demonstratively proved that the world began.

Reply to Objection 1. As Augustine says (De Civ. Dei xi, 4), the opinion of philosophers who asserted the eternity of the world was twofold. For some said that the substance of the world was not from God, which is an intolerable error; and therefore it is refuted by proofs that are cogent. Some, however, said that the world was eternal, although made by God. For they hold that the world has a beginning, not of time, but of creation, so that in a certain hardly intelligible way it was always made. “And they try to explain their meaning thus (De Civ. Dei x, 31): for as, if the foot were always in the dust from eternity, there would always be a footprint which without doubt was caused by him who trod on it, so also the world always was, because its Maker always existed.” To understand this we must consider that the efficient cause, which acts by motion, of necessity precedes its effect in time; because the effect is only in the end of the action, and every agent must be the principle of action. But if the action is instantaneous and not successive, it is not necessary for the maker to be prior to the thing made in duration as appears in the case of illumination. Hence they say that it does not follow necessarily if God is the active cause of the world, that He should be prior to the world in duration; because creation, by which He produced the world, is not a successive change, as was said above (Question 45, Article 2).
JD:
I find that odd, as he spends so much effort on disproving the actual infiniteness of the world based upon recognizing that what is generally spoken of is a sensible continuum. (Commentary on the Physics, Bk. III, les. 12, n. 773; Summa Theologica, I, q. 25, a. 2, reply 1).

He says elsewhere that God’s infinity is an infinity of perfection; while, matter’s infinity is an infinity of imperfection, privation. So, while he admits that no one has proved the world’s eternality, he senses that it is not so. And this before modern science!
I’m not sure what you mean by infinity with respect to matter. I don’t think Aquinas would say that matter is “infinite.” Indeed, it is a mixture of both potential being and actual being, and therefore must be finite in some respects. But whether this means it cannot at the same time be eternal is another matter. Perhaps it has been eternally changing?

Thanks.
 
These patterns are not like dress patterns, are they? Are the beings to which they refer real beings? Or, do they supercede reality? Or, must they remain mental objects, or rather, constructs?

Yes it does. But, never forget, “infinity” is a mere word. A word is the written utterance of something that has meaning. The meaning may be skewed however the user wishes. Accordingly, there are two kinds of infinity. There is actual infinity, which is something that possesses determinate existence. And, there is potential infinity, which is the usual kind for us to ponder and for maths. It doesn’t have actual existence precisely because it is, by its nature, indeterminate. You can enclose a potential infinity inside brackets, but, that just forces a postulation.

God bless,
jd
Could it be that the patterns are mental representations of reality? Perhaps they supercede reality more they are a part of reality? It could be that the subject-object division is alot fuzzier than is generally accepted. I have never been comfortable with the Platonic sphere of ideal forms are anything but organised sensory perception to aide in dealing with reality in a more efficient manner.

Re: Infinity and beyond

Isnt it odd how different minds see things at times? Your discription of actual infinity is almost exactly how I would discribe infinty in mathematics, which is thought of as a number without bounds but has a definate existence. Given me much food for thought,
 
Hey JDaniel. Let me start by saying that I take a lot of joy reading your posts, when I happen to see them.
Likewise, I yours.
Aquinas’ views on creation can be found most fully explained in the ST I I q. 44, 45, 46. These questions often get overlooked. Here is his I answer that from q. 46 a. 2. “whether it is an article of faith that the world began?”
By faith alone do we hold, and by no demonstration can it be proved, that the world did not always exist, as was said above of the mystery of the Trinity (32, 1). The reason of this is that the newness of the world cannot be demonstrated on the part of the world itself. For the principle of demonstration is the essence of a thing. Now everything according to its species is abstracted from “here” and “now”; whence it is said that universals are everywhere and always. Hence it cannot be demonstrated that man, or heaven, or a stone were not always. Likewise neither can it be demonstrated on the part of the efficient cause, which acts by will. For the will of God cannot be investigated by reason, except as regards those things which God must will of necessity; and what He wills about creatures is not among these, as was said above (Question 19, Article 3). But the divine will can be manifested by revelation, on which faith rests. Hence that the world began to exist is an object of faith, but not of demonstration or science. And it is useful to consider this, lest anyone, presuming to demonstrate what is of faith, should bring forward reasons that are not cogent, so as to give occasion to unbelievers to laugh, thinking that on such grounds we believe things that are of faith.
Objection 1. It would seem that it is not an article of faith but a demonstrable conclusion that the world began. For everything that is made has a beginning of its duration. But it can be proved demonstratively that God is the effective cause of the world; indeed this is asserted by the more approved philosophers. Therefore it can be demonstratively proved that the world began.
Reply to Objection 1. As Augustine says (De Civ. Dei xi, 4), the opinion of philosophers who asserted the eternity of the world was twofold. For some said that the substance of the world was not from God, which is an intolerable error; and therefore it is refuted by proofs that are cogent. Some, however, said that the world was eternal, although made by God. For they hold that the world has a beginning, not of time, but of creation, so that in a certain hardly intelligible way it was always made. “And they try to explain their meaning thus (De Civ. Dei x, 31): for as, if the foot were always in the dust from eternity, there would always be a footprint which without doubt was caused by him who trod on it, so also the world always was, because its Maker always existed.” To understand this we must consider that the efficient cause, which acts by motion, of necessity precedes its effect in time; because the effect is only in the end of the action, and every agent must be the principle of action. But if the action is instantaneous and not successive, it is not necessary for the maker to be prior to the thing made in duration as appears in the case of illumination. Hence they say that it does not follow necessarily if God is the active cause of the world, that He should be prior to the world in duration; because creation, by which He produced the world, is not a successive change, as was said above (Question 45, Article 2).
OK. Well, this is a little different than what I was understanding you to mean. (Mea culpa!) There is no question that there can be no demonstration of the earth’s newness. But, that does not mean that he found the supposition of an eternal world ‘reasonable’. From the point of view of the earth itself, he could see no dialectic leading to any premises that would prove that the earth was not eternal. I agree with him on this. Yet, that does not deny the dialectic that indicates that matter is finite and if it is finite, there is reason to conclude that the world, or universe, is as well.
I’m not sure what you mean by infinity with respect to matter. I don’t think Aquinas would say that matter is “infinite.” Indeed, it is a mixture of both potential being and actual being, and therefore must be finite in some respects. But whether this means it cannot at the same time be eternal is another matter. Perhaps it has been eternally changing?
I agree that he would not say that matter is “infinite.” I don’t know of any statement, by him, that the world might be “eternal,” though. While he perceived a difference in the meanings of the two words, it was only slight. A created world, like a created man, can have a newness, a beginning, yet be ‘eternal’. The word “eternal” was more akin to potential infinity for him, which is another kind of “infinity.” God certainly has the power to create being that then lasts for ever.

God bless,
jd
 
Could it be that the patterns are mental representations of reality?
FF:

Yes, that is what it means to reify, which is another word for abstracting. If one sees a bunch of cows, and counts those cows - one at a time by one - they may total to ten cows. That would become a universal, so that any beings that totalled to ten could be understood, in that sense, in terms of number.
Perhaps they supercede reality more they are a part of reality?
There may be ‘senses’ when the universal supercedes reality. For example, the abstraction of ‘man-ness’ leaves aside all of the sensible qualities (and imperfections, therefore) of matter and views man as pure essense, views man as rational being. (One could get to like all men if that were the case! 🙂 )
It could be that the subject-object division is alot fuzzier than is generally accepted. I have never been comfortable with the Platonic sphere of ideal forms are anything but organised sensory perception to aide in dealing with reality in a more efficient manner.
It is correct to think of it in terms of ‘organizing’. That is what reification allows us to do, to organize. There are clearly beings that are related more or less completely, in the world. Under the heading of species, we can thus organize things through this process. We tend to do this not only for self-preservation reasons, but also, for intellectual reasons.
Re: Infinity and beyond
This is probably the way it should always be understood. In mathematics, I can see that delimiting it can be useful. But, it should never be forgotten who is doing the delimiting.
Isnt it odd how different minds see things at times? Your discription of actual infinity is almost exactly how I would discribe infinty in mathematics, which is thought of as a number without bounds but has a definate existence. Given me much food for thought,
And that is exactly the problem: that is like looking at a cloud and perceiving it as unchanging, as permanent. As a cloud, it has existence. It has magnatude. It appears to be delimited. But, only for a second. We look away, then look back and it is different, not completely, but ever so slightly. Potential infinity has actuality. It is the only kind of infinity that can be actual for us. Remember, all other actual numbers are speciated by the unit that is their ultimate, or final, number. Infinity has no ultimate or final number, and, therefore, cannot be speciated. There is no ultimate number to which another one cannot be added, or another one subtracted. Whether or not brackets are put around it.

God bless,
jd
 
I have read your response a few times now. I’m still none the wiser. Are you saying that universals replace specific instances of a thing? Or that abstractions are in some way “realer”?
 
I’m trying to deal with someone who has little time for Thomism! Can anyone help me? Particularly with this idea of time/space being a loop thus removing the need for a prime mover: -
  1. Prime mover - Aquinas had little understanding mechanics and at a guess absolutly no idea of modern physics. It is completely feasable that everything, that’s time and space, may be in an eternal loop.
I thought modern physics says that the universe is expanding at an exponential rate so that now there is not enough mass, (and so, gravity), in the galaxies to pull the universe back to a point again to complete a loop. I think that modern physics favoured view is that the universe must continue expanding through space forever.
Eventually there is the ‘cold death’, or something, of the universe when all the stars burn out and there is no more energy produced in the universe. So how would a universe move from a stable dead condition back to some sort of space-time quantum rebirth, where does the energy for that come from?
 
Re: Infinity & beyond

What would you say to the idea that the demarkation for ‘actual’ and ‘potential’ infinity is yet another remnant of Aristotle? A hundred years afterwards Archimedes pretty much set up the death of the idea that ‘actual infinity’ does not have actual existence, when he used the idea of actual infinty to find the areas and volumes of curved shapes. Were these ideas overlooked in favour of the Aristotlean view and thus not really dealt with rigorously, until Newton and Leibniz leading Leibniz to exclaim:

“I am so in favour of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.”

The more you know…
 
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