Aquinas, Logic & The First Cause. (Thread 1)

[MindOverMatter]

For those of you who are interested, i have made yet another thread about Aquinas. Aquinas’s arguments are based upon brutal logic, there is no place for flights of fancy in the five proofs. To think that Aquinas must be wrong, before stating irrefutable evidence, doesn’t say anything about his arguments, but rather it exposes the bitter prejudice that people have about the idea of proving Gods existence. They hate God. However, Logic tells me that things always happen for a reason; otherwise there is no reason for them to happen. Therefore they ought not to happen in so far as logic is concerned. This truth cannot change, and is absolutely true regardless of whether or not things appear to us as if to change without a cause. It is never reasonable to think that something can come out of nothing by its own. Unless, we refuse the law of non-contradiction, which is precisely what the atheists and agnostics on this forum have been doing. We cannot escape the fact that there must be such a thing as a timeless cause that explains its own being. If something changes, it is because something causes it to change. I hope that Warpspeedpetey Leaves a comment or two. So, heres my argument.

1. Time, merely means that physical beings are in a state of change. This does not mean that all beings must be identified with change (if I’m correct, this is an example of the fallacy of composition). At most, it can only mean that there are beings that are in a state of change or becoming. Therefore to say that there is no “before” time, can only mean that there is no “change” before time. It does not mean that there is no “being” before time. Please note, that no one is saying that there is no such thing as a being that is not caused. One is only saying that anything which begins to change has been caused to change by previous conditions or actualities.

2. Before there can be any change at all, there has to be such a thing as “being”. Therefore “being” transcends time and is the cause of it.

3. If we accept that there is no change before time, then whatever exists before time, must be timeless and pure actuality; as in, its very being is expression without potentiality. To put it another way, the First cause must be by its very nature a changeless “cause”; as in, it does not “become” a cause, rather it is a timeless cause in respect of its nature.
**
4.** And as for the nature of that cause, such a being cannot be an inert physical object, since inert physical entities only change because something has caused them to change, regardless of whether it is a classical cause or something we know nothing about. The potentiality to change cannot come out of no-where, unless we choose to violate the law of non-contradiction.

5. Therefore, the first cause cannot be said to have a reasonable causal relationship with the universe, unless it has in its being a personal nature with an eternal will to create entities.

6. Also, such a being has to be perfect, since there can be no potentiality in a first cause. Therefore all things that are proper to the nature of a first cause, must already be actual and realized from all eternity, in so far it is the cause of all beginnings. Hence the saying that God is pure actuality.

Conclusion. It is not a matter of comprehending the nature of the first cause, but rather it is about understanding what it must be, regardless of how we may feel about it aesthetically speaking.

 

[JDaniel]

For those of you who are interested, i have made yet another thread about Aquinas. Aquinas’s arguments are based upon brutal logic, there is no place for flights of fancy in the five proofs. To think that Aquinas must be wrong, before stating irrefutable evidence, doesn’t say anything about his arguments, but rather it exposes the bitter prejudice that people have about the idea of proving Gods existence. They hate God. However, Logic tells me that things always happen for a reason; otherwise there is no reason for them to happen. Therefore they ought not to happen in so far as logic is concerned. This truth cannot change, and is absolutely true regardless of whether or not things appear to us as if to change without a cause. It is never reasonable to think that something can come out of nothing by its own. Unless, we refuse the law of non-contradiction, which is precisely what the atheists and agnostics on this forum have been doing. We cannot escape the fact that there must be such a thing as a timeless cause that explains its own being. If something changes, it is because something causes it to change. So, heres my argument.

1. Time, merely means that physical beings are in a state of change. This does not mean that all beings must be identified with change (if I’m correct, this is an example of the fallacy of composition). At most, it can only mean that there are beings that are in a state of change or becoming. Therefore to say that there is no “before” time, can only mean that there is no “change” before time. It does not mean that there is no “being” before time. Please note, that no one is saying that there is no such thing as a being that is not caused. One is only saying that anything which begins to change has been caused to change by previous conditions or actualities.

2. Before there can be any change at all, there has to be such a thing as “being”. Therefore “being” transcends time and is the cause of it.

3. If we accept that there is no change before time, then whatever exists before time, must be timeless and pure actuality; as in, its very being is expression without potentiality. To put it another way, the First cause must be by its very nature a changeless “cause”; as in, it does not “become” a cause, rather it is a timeless cause in respect of its nature.
**
4.** And as for the nature of that cause, such a being cannot be an inert physical object, since inert physical entities only change because something has caused them to change, regardless of whether it is a classical cause or something we know nothing about. The potentiality to change cannot come out of no-where, unless we choose to violate the law of non-contradiction.

5. Therefore, the first cause cannot be said to have a reasonable casual relationship with the universe, unless it has in its being a personal nature with an eternal will to create entities.

5. Also, such a being has to be perfect, since there can be no potentiality in a first cause. Therefore all things that are proper to the nature of a first cause, must already be actual and realized from all eternity, in so far it is the cause of all beginnings. Hence the saying that God is pure actuality.

It is not a matter of understanding the nature of the first cause, but rather it is about understanding what it must be, regardless of how we may feel about it aesthetically.

Don’t forget, all Aquinas is proving, by Proof 1 and Proof 2 (and all the proofs, for that matter) is that there was a Prime Mover, and, a First Efficient Cause. He only suggested that that First Cause/Prime Mover is what we refer to as God. This being could be called any other sensible name. By “sensible” (as opposed to nonsensical), I mean that it could not be called the “universe”, for example, because the universe, as we know it and define it, is not “sensically” coherent with the definition and concept of Prime Mover and First Cause, by virtue of two facts: the universe had a beginning and has an end.

From this point, we then extrapolate from the necessity of what this being-we-refer-to-as-God is. This being-we-refer-to-as-God must be Pure Perfection. From the logic that it must be Pure Actuality, Pure Being, Pure Existence, Pure Creator, Pure Final Cause, Pure Logic, Pure Unity, etc., etc., we are left with no other choice but to conclude that it is Pure Perfection. So, it is “god”.

That it is the catholic “God” is derived from the reports we have received for several thousand years, that (1) forecasted the coming of Christ, and, (2) described God’s determinates and named them. These reports are much too independent, much too diverse as to time and location of the reporter, much too similar to one another, and much too reliable as prophecies, to be false or falsified. Interestingly, the determinates described by those early reporters are the same as we derive from the logic of the five proofs.

Was there any presupposition? Obviously, none on the part of the reporters, as they existed long before Aquinas. And, obviously none on the part of Aquinas’ five proofs, as they stand alone and are validated by the very logic itself, and from the necessity from the extrapolations from that foundational logic due precisely to the logic itself.

jd

 

[JDaniel]

Because I had these ideas in my mind and wanted to get them written down, I didn’t have time to apologize to you for grabbing onto your comet trail and, hopefully, adding a little something to your excellent analysis of Aquinas’ proof from efficient causality.



jd

 

[MindOverMatter]

Because I had these ideas in my mind and wanted to get them written down, I didn’t have time to apologize to you for grabbing onto your comet trail and, hopefully, adding a little something to your excellent analysis of Aquinas’ proof from efficient causality.



jd

Thanks for your excellent analysis; I gained greatly from it.
I may have made a comet trail, but you turned it in to a supernova.

 

[eichenb2]

For those of you who are interested, i have made yet another thread about Aquinas. Aquinas’s arguments are based upon brutal logic, there is no place for flights of fancy in the five proofs. To think that Aquinas must be wrong, before stating irrefutable evidence, doesn’t say anything about his arguments, but rather it exposes the bitter prejudice that people have about the idea of proving Gods existence. They hate God. However, Logic tells me that things always happen for a reason; otherwise there is no reason for them to happen. Therefore they ought not to happen in so far as logic is concerned. This truth cannot change, and is absolutely true regardless of whether or not things appear to us as if to change without a cause. It is never reasonable to think that something can come out of nothing by its own. Unless, we refuse the law of non-contradiction, which is precisely what the atheists and agnostics on this forum have been doing. We cannot escape the fact that there must be such a thing as a timeless cause that explains its own being. If something changes, it is because something causes it to change. I hope that Warpspeedpetey Leaves a comment or two. So, heres my argument.

1. Time, merely means that physical beings are in a state of change. This does not mean that all beings must be identified with change (if I’m correct, this is an example of the fallacy of composition). At most, it can only mean that there are beings that are in a state of change or becoming. Therefore to say that there is no “before” time, can only mean that there is no “change” before time. It does not mean that there is no “being” before time. Please note, that no one is saying that there is no such thing as a being that is not caused. One is only saying that anything which begins to change has been caused to change by previous conditions or actualities.

2. Before there can be any change at all, there has to be such a thing as “being”. Therefore “being” transcends time and is the cause of it.

3. If we accept that there is no change before time, then whatever exists before time, must be timeless and pure actuality; as in, its very being is expression without potentiality. To put it another way, the First cause must be by its very nature a changeless “cause”; as in, it does not “become” a cause, rather it is a timeless cause in respect of its nature.
**
4.** And as for the nature of that cause, such a being cannot be an inert physical object, since inert physical entities only change because something has caused them to change, regardless of whether it is a classical cause or something we know nothing about. The potentiality to change cannot come out of no-where, unless we choose to violate the law of non-contradiction.

5. Therefore, the first cause cannot be said to have a reasonable causal relationship with the universe, unless it has in its being a personal nature with an eternal will to create entities.

6. Also, such a being has to be perfect, since there can be no potentiality in a first cause. Therefore all things that are proper to the nature of a first cause, must already be actual and realized from all eternity, in so far it is the cause of all beginnings. Hence the saying that God is pure actuality.

Conclusion. It is not a matter of comprehending the nature of the first cause, but rather it is about understanding what it must be, regardless of how we may feel about it aesthetically speaking.

 

[Katholish]

The only problem I find with the above analysis is that it does not address the primary reason people disbelieve in a God. It was also the opinion of the Ancients, the eternal universe.

Why does time have to have a beginning? Certainly the idea of an infinite chain of causes in time is not logically inconsistent. Modern athiests simply seem to have their own version of this ancient idea. They might say there was a Big Bang that started the universe, but when pressed, they will admit that even the Big Bang had a cause, and that cause must have had a cause.

In denying an uncaused caused, and hence the existence of timeless being, they are affirming an eternal universe.

Your arguments don’t directly address this objection. How would you reply?

 

[JDaniel]

The only problem I find with the above analysis is that it does not address the primary reason people disbelieve in a God. It was also the opinion of the Ancients, the eternal universe.

I am sorry, but, I don’t know what you are trying to say, in your last phrase. Would you mind re-phrasing it for me?

Why does time have to have a beginning?

Time has to have a beginning by virtue of the definition of “infinity”. There can be no physical infinity per definitionem, therefore, no motion (or change) As time is the measure of motion (and change), and as motion is of or by physical objects, and as there cannot be an infinity of physical objects, therefore, time cannot be infinite. Thus, time is finite, which is the only alternative, therefore it must have a beginning.

Certainly the idea of an infinite chain of causes in time is not logically inconsistent.

Yes it is. See above. Furthermore, in terms of causality, there cannot be an infinite chain of causes. There can only be a potentially infinite chain of causes.

Modern athiests simply seem to have their own version of this ancient idea. They might say there was a Big Bang that started the universe, but when pressed, they will admit that even the Big Bang had a cause, and that cause must have had a cause.

How far back do you want to go? If you continue back towards infinity you will never reach this point. Even if you regard the infinite chain as a gigantic circle of causes and effects, one more can always be added. Now, where do you suppose we can add one more in this gigantic circle? If you say, “anywhere”, then the circle was not infinite. It was finite - very huge, but, nevertheless, finite. Such extremely large numbers are called “transfinite”.

In denying an uncaused caused, and hence the existence of timeless being, they are affirming an eternal universe.

You are quite correct.

Your arguments don’t directly address this objection. How would you reply?

But, you and I just did!

jd

 

[Katholish]

I am sorry, but, I don’t know what you are trying to say, in your last phrase. Would you mind re-phrasing it for me?

I meant that the primarly objection to God is a believe in the eternity of the universe. Believing in an eternal universe is not only the posiiton of modern atheists, but was also the opinion of the ancient philosophers, including Aristotle.

Time has to have a beginning by virtue of the definition of “infinity”. There can be no physical infinity per definitionem, therefore, no motion (or change) As time is the measure of motion (and change), and as motion is of or by physical objects, and as there cannot be an infinity of physical objects, therefore, time cannot be infinite. Thus, time is finite, which is the only alternative, therefore it must have a beginning.

The definition of infitity is limitlessness. The definition of materiality is having parts. There is nothing logically inconsistent with a limitless thing having parts. Hence, your claim that time has a beginning by definition is false. In theory, there could be an infinity of physical objects. What is there to prevent it? I would also point out, as a way of argument from authority, that St. Thomas Aquinas argues that it is not logically inconsistent that there have been an eternal universe (eternal in the sense of infinite time), and that the only way to know Aristotle was wrong is through Divine Revelation.

Yes it is. See above. Furthermore, in terms of causality, there cannot be an infinite chain of causes. There can only be a potentially infinite chain of causes.

What do you mean by a potentially infinite chain? I would point out that the order of time and the order of causality are not identical. That distinction is at the heart of Thomas’s proof from causality.

How far back do you want to go? If you continue back towards infinity you will never reach this point. Even if you regard the infinite chain as a gigantic circle of causes and effects, one more can always be added. Now, where do you suppose we can add one more in this gigantic circle? If you say, “anywhere”, then the circle was not infinite. It was finite - very huge, but, nevertheless, finite. Such extremely large numbers are called “transfinite”.

Infinity does not mean perfection. Just because something is infinite does not mean that it cannot be increased by addition. Are you challenging this proposition?

 

[jkiernan56]

Infinity does not mean perfection. Just because something is infinite does not mean that it cannot be increased by addition. Are you challenging this proposition?

I am not schooled in philosophy, but my gut instinct does challenge your proposition.

What can you add to infinity?
Isn’t infinity by definition something already without limit?

Can you add 1 to infinity?
Can you add 1 to something already limitless?

Isn’t there a contradiction in terms just stating the question?

Yes, I challenge the proposition.
Adding one to infinity is a contradiction in terms.

 

[JDaniel]

I meant that the primarly objection to God is a believe in the eternity of the universe. Believing in an eternal universe is not only the posiiton of modern atheists, but was also the opinion of the ancient philosophers, including Aristotle.

OK. That makes sense to me now.

The definition of infitity is limitlessness.

When the Scholastic uses the word “infinite” he is using it in the quantum mathematical sense. “Limitless” is nothing that a physicist can use.

The definition of materiality is having parts.

From Wikipedia:
“In common usage, matter is anything that has both mass and volume (takes up space). A more rigorous definition is used in science: matter is what atoms and molecules are made of. Matter is commonly said to exist in four states (or phases): solid, liquid, gas and plasma…”

“Materiality”, derived from the word, “matter”, would, in this sense comply with the above stated definition. That being said, it can have parts.

There is nothing logically inconsistent with a limitless thing having parts.

True, providing that all of the parts take up everything that we know of and call “space”. IOW, it would either be " completely empty space" or “completely full space”.

Hence, your claim that time has a beginning by definition is false.

I guess not.

In theory, there could be an infinity of physical objects.

In theory, that cow in the field behind my house can jump over the moon. But, you are partially correct. As a finite existent entity, it could, in thought, potentially become infinite. However, from the fact that matter is finite, and will always be finite, we can never have an infinite set of physical parts. If we could, the resultant universe would become so dense that a sentient being would be utterly crushed like a bug in a bar of stainless steel.

What is there to prevent it?

Only the real definition of the word, “infinity”.

I would also point out, as a way of argument from authority, that St. Thomas Aquinas argues that it is not logically inconsistent that there have been an eternal universe (eternal in the sense of infinite time), and that the only way to know Aristotle was wrong is through Divine Revelation.

Perhaps, but, “eternal” has always had a somewhat different definition than “infinity”. Eternal usually means, has a beginning but no end. Infinite usually means, having no beginning and no end. Aquinas would have known this.

What do you mean by a potentially infinite chain?

Since there can be no such thing as an infinite chain, and, if a chain does exist, and if someone, or something, keeps adding one more thing to the end of the chain, then the existing chain is in potency to becoming infinite. To say that a chain is now infinite is to say that nothing more can be added to it.

I would point out that the order of time and the order of causality are not identical.

Well, despite that I don’t understand what you want from this seeming fragment of an idea, Further, I don’t know what form you want a response in, or, even if you want a response.

That distinction is at the heart of Thomas’s proof from causality.

I can’t even imagine that Aquinas had anything like that in mind! Here is his proof from causality. Nowhere is there any mention of time:

New Advent Summa -
“The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God.”

Infinity does not mean perfection.

In quantum math it does. It means it lacks the imperfection of even one more part.

Just because something is infinite does not mean that it cannot be increased by addition.

Of course it absolutely does. Any huge number that can be added to is finite, per definitionem.

Are you challenging this proposition?

No. I’m challenging your gross misconception of it.

jd

 

[Katholish]

jkiernan (and JDaniel),

There is no definition of infinite which does not mean limitlessness. The is opposed to finite which means having boundaries or limits.

When we say that a thing is infinite, we do not mean a thing is infinite in every respect. Something can have infinte length but finite height. What would its area be? Infinite. What would happen if you added some height (which you could clearly do because the height is finite) would the area increase? Yes. By how much? An infinite amount. You had infinity before, and you still have infinity now, but you have indeed increased the area.

Also on a more obvious level, in mathematics, you can indeed have ∞ + 1 and it be a valid expression.

Another example: I have an infinte set of numbers–the even number set. I have [2, 4, 6, 8, 10, 12, … ∞] I have an infinite number of integers. Can I add more? Yes. I can add all of the odd integers. Now I have [1, 2, 3, 4, 5, 6, … ∞] I had an infinite number before, and I have an infinite number now, but now I have integers which I did not have before.

Just because something is an infinity, doesn’t mean it is everything. Infinity applies to only a certain aspect, otherwise you really almost have to deny the very concept of infinity itself. Is the very idea of infinity an infinite idea? The answer is yes, but not yes in all aspects. If it was infinite in every way, only God could know it, and you and idea wouldn’t even be able to think of it, nor could we speak of it. If it was not infinite, the idea would not be able to compass the thing which is its object. A completely finite thing cannot contain an infinity.

I will address the rest of JDaniel’s comments in another post.

 

[Katholish]

JDaniel,

From Wikipedia:
“In common usage, matter is anything that has both mass and volume (takes up space). A more rigorous definition is used in science: matter is what atoms and molecules are made of. Matter is commonly said to exist in four states (or phases): solid, liquid, gas and plasma…”

“Materiality”, derived from the word, “matter”, would, in this sense comply with the above stated definition. That being said, it can have parts.

Having parts is the definition St. Thomas would have used, but I suppose it is of little matter. Even if you go with mass and volume, that does not by definition exclude a material infinity, which was my only point in bringing up the definition.

True, providing that all of the parts take up everything that we know of and call “space”. IOW, it would either be " completely empty space" or “completely full space”.

You are equating infinity with some notion of perfection or completeness. Infinity does not by definition involve a notion of completeness except in a very narrow sense. The example I mentioned in my last post is apt. I can have an infinite set of numbers using only even numbers. Does this infinity involve all of the integers? No. It is not a complete (or perfect) set of numbers, only an infinite one having no end (or no beining if you include naegtive numbers).

In theory, that cow in the field behind my house can jump over the moon. But, you are partially correct. As a finite existent entity, it could, in thought, potentially become infinite. However, from the fact that matter is finite, and will always be finite, we can never have an infinite set of physical parts. If we could, the resultant universe would become so dense that a sentient being would be utterly crushed like a bug in a bar of stainless steel.

Imagine a steel bar one meter in height, one meter in depth, and having infinite length. Such a thing would not destroy all sentient life, yet it is materially infinite.

 

[MindOverMatter]

jkiernan (and JDaniel),

Just because something is an infinity, doesn’t mean it is everything.

I agree with this, but i disagree with your concept of infinity.

Objection 1
Before there can be such a thing as change, there has to be such a thing as being.
Therefore being transcends change and is the cause of change. Therefore there is a first cause; and it is a cause which is in itself the cause of time. This being cannot be a material cause since moving objects are preceded by changes or causes in time.
Why is there something rather then nothing? That question cannot be answered by change or by things in a state of change.

Objection 2. An infinite chain of changes doesn’t explain change; simply because you can never come to an ultimate reason for the chain of changes within that concept that we call change. You have to go outside of change to explain it. The whole purpose of Aquinas’s arguments is to explain “change”; and by explaining it, we are forced to posit a first cause that exists outside of time. This is true regardless of whether or not the universe is thought to be infinite or finite. The fact is, we don’t know that there is an infinite past, but we do know that if we want to explain change, it cannot be truly explained by an infinite series of changes.

Objection 3 There is no such thing as an infinite chain of causes. An infinite chain of causes is really an infinite chain of effects. All causes that had the potentiality to exist are really just effects, and in-so-far as they cause some other effect, one can only say that they serve as “causal-mediums”. When we speak of ultimates we cannot truly assign the term cause to the individual parts of a system, since we are trying to explain the system as a whole. Each individual effect takes on the nature of a cause only by accident; they are not “cause” by nature of being. Hence; if the universe is infinite, then it is an infinite chain of potentiality. The potentiality is left unexplained as if to come out of nothing. In reality, you have an infinite effect with out a cause. Which is absurd.

**Objection 4 ** An infinite past of actual changes ultimately has no potentiality to change, because the potentiality for any particular event to occur, never explains the whole. And since we have no ultimate cause, we have motion with no ultimate explanation. Therefore it ought not to exist.

Objection 5
You cannot have an actual infinite number because an actual infinite transcends numbers. Therefore, to speak of an infinite, is not to speak of a number of something.

Objection 6 Limitless only means potentially infinite, something that can go on forever. Its not a real infinite. If there is an actual infinite past before this moment, then it is impossible for us to have reached this moment, since this moment is itself in a chain that has an actual infinite number of moments before now. It makes no sense.

Conclusion If you find an infinite past mind boggling, it is only because an infinite past is meaningless.

 

[Katholish]

MindOverMatter,

It is a little unclear to me what your numbered objections are objections to.

Reply to Objection 1:
Agreed. Even if the universe were eternal, there would have to be a first cause. Since that first cause is not a cause-in-time, the necessaity for a first cause is not inconsistent with an eternal universe. This reply suffices for Objection 2 as well.

Reply to Objection 3:
Agreed that an eternal universe would require an *ex nihilo *creation. This seems to be what you are saying in #3. If I understand Objection 4 correctly, this answer would suffice.

Reply to Objection 5:
This assertion cannot be correct because it defies obvious experience. Numbers are immaterial things, and hence their “actual” existence is also immaterial. The infinite number set [2, 4, 6, 8, 10, 12, … ∞] has actual existence. Material things require both matter and form to have actual existence, but purely immaterial things only require form for actual existence. Perhaps you meant that it doesn’t have substantial existence, which in the case of numbers I could agree with since they are accidental forms and to not have substance.

Given my extremely limited understanding of the cosmos, I also to not see it as an impossibility that the universe itself is a spacial infinity, which I assume you would consider more “actual”, even though space doesn’t exactly have a substance either.

Reply to Objection 6:
I do not see your reason for saying that limitlessness only implies a potential infinity as opposed to an actual infinity. What makes an infinity actual? What must be added to limitlessness in order to make a real infinity, and if something must be added would this not have to be in the definition of infinity itself?

You simply say that it makes no sense that we could possibly exist in a single moment if there had been an infinite past. Why would it be impossible for us to have reached this moment? You can have a point on an infinite line, why not a moment in time? You act as if it is an absurd conclusion, but I assure you that the absurdity is not apparent, either to me, St. Thomas, or Aristotle, so perhaps you could explain it with reasons as opposed to simple assertion.

 

[JDaniel]

jkiernan (and JDaniel),

There is no definition of infinite which does not mean limitlessness. The is opposed to finite which means having boundaries or limits.

But, there are a number of definitions, all of which are linguistic attempts to explain/define the essence of the concept. And, each one expresses its own particular “bent”, or “flavor”. Here are some:

*“bottomless, boundless, countless, endless, illimitable, immeasurable, immense, incomprehensible, indefinite, inexhaustible, innumerable, measureless, no end of, no end to, no holds barred, no strings, numberless, unbounded, uncalculable, undefined, unending, unfathomable, unlimited, untold, vast, wide-open” *- Thesaurus.com

Without going through each one, one by one, you can simply look at the derivatives of the words and conclude the “flavor” meant (intended by the user). So, why must we use the one you’ve chosen?

When we say that a thing is infinite, we do not mean a thing is infinite in every respect.

Yes we do.

Something can have infinte length but finite height.

What “something”?

What would its area be? Infinite.

Again, what “something”?

What would happen if you added some height (which you could clearly do because the height is finite) would the area increase? Yes. By how much? An infinite amount. You had infinity before, and you still have infinity now, but you have indeed increased the area.

What “something” are you referring to? Where is this something? Can I see it? Can I touch it? Can I experience it in any way?

So, it’s a conceptually-based exigency. It only has existence inside a mind. And, it is a very limited concept.

Also on a more obvious level, in mathematics, you can indeed have ∞ + 1 and it be a valid expression.

It is only a valid expression in a mind. It is invalid outside of a mind. If I want to play with mathematics, I can hypothesize whatever I want to mean whatever I want. Then, play with the math and see where it leads.

Another example: I have an infinte set of numbers–the even number set. I have [2, 4, 6, 8, 10, 12, … ∞] I have an infinite number of integers. Can I add more? Yes. I can add all of the odd integers. Now I have [1, 2, 3, 4, 5, 6, … ∞] I had an infinite number before, and I have an infinite number now, but now I have integers which I did not have before.

All sorts of things can be done in our imaginations. I just imagined that that cow in the field behind me just jumped over the moon.

Just because something is an infinity, doesn’t mean it is everything. Infinity applies to only a certain aspect, otherwise you really almost have to deny the very concept of infinity itself. Is the very idea of infinity an infinite idea? The answer is yes, but not yes in all aspects. If it was infinite in every way, only God could know it, and you and idea wouldn’t even be able to think of it, nor could we speak of it. If it was not infinite, the idea would not be able to compass the thing which is its object. A completely finite thing cannot contain an infinity.

You are then limiting the concept of infinity to only its non-quantum speculative usages. What is God, then? Is God a different kind of infinity from the infinity you’re describing?

You are meaning “finity”, and substituting the word “infinity” in its place. You are confusing a conceptual exigency for a potentially real exigency. I say “potentially real” because, in the absence of anything that is infinite, there is no fully real infinity. You can’t even think infinity, you can only think of the seven-letter word. Then you apply imperfect linguistics to it.

jd

 

[JDaniel]

Having parts is the definition St. Thomas would have used, but I suppose it is of little matter. Even if you go with mass and volume, that does not by definition exclude a material infinity, which was my only point in bringing up the definition.

Perhaps, if he was considering limited, spacial concepts for the purpose of playing math games.

You are equating infinity with some notion of perfection or completeness. Infinity does not by definition involve a notion of completeness except in a very narrow sense.

Not so. I define infinity in a realist sense (as opposed to a conceptual sense), thus, it means that it lacks nothing.

The example I mentioned in my last post is apt. I can have an infinite set of numbers using only even numbers. Does this infinity involve all of the integers? No. It is not a complete (or perfect) set of numbers, only an infinite one having no end (or no beining if you include naegtive numbers).

You are describing a finite again. This can always happen whenever we use the adjective to modify a finite exigency.

Imagine a steel bar one meter in height, one meter in depth, and having infinite length. Such a thing would not destroy all sentient life, yet it is materially infinite.

What is it? May I touch it? Or, do I have to imagine that I am sensing it?

jd

 

[JDaniel]

You are equating infinity with some notion of perfection or completeness. Infinity does not by definition involve a notion of completeness except in a very narrow sense. The example I mentioned in my last post is apt. I can have an infinite set of numbers using only even numbers. Does this infinity involve all of the integers? No. It is not a complete (or perfect) set of numbers, only an infinite one having no end (or no beining if you include naegtive numbers).

In support of our position, I will leave you with this, from the The Catholic Encyclopedia:

“The infinite, as the word indicates, is that which has no end, no limit, no boundary, and therefore cannot be measured by a finite standard, however often applied; it is that which cannot be attained by successive addition, not exhausted by successive subtraction of finite quantities. Though in itself a negative term, infinity has a very positive meaning. Since it denies all bounds – which are themselves negations – it is a double negation, hence an affirmation, and expresses positively the highest unsurpassable reality. Like the concepts of quantity, limit, boundary, the term infinity applies primarily to space and time, but not exclusively, as Schopenhauer maintains. In a derived meaning it may be applied to every kind of perfection: wisdom, beauty, power, the fullness of being itself.”

jd

 

[MindOverMatter]

Reply to Objection 5:
This assertion cannot be correct because it defies obvious experience. Numbers are immaterial things, and hence their “actual” existence is also immaterial.
The infinite number set [2, 4, 6, 8, 10, 12, … ∞] has actual existence. Material things require both matter and form to have actual existence, but purely immaterial things only require form for actual existence. Perhaps you meant that it doesn’t have substantial existence, which in the case of numbers I could agree with since they are accidental forms and to not have substance…

Clearly my arguments were in respect of “physical events” in time; not abstract numbers. To have an infinite number of physical events, is to transcend all descriptive numbers. Which means you would be transcending all physical events. Which doesn’t make any sense, since you would no longer be talking about physical events. In other words, there can be no such thing as an infinite “number” of events. An infinite is not a quantity of something. A true infinite, transcends quantity; and thus transcends time.

If you cannot make up an infinite by adding one number to another, then what makes you think that you can meaningfully apply an infinite number of something to the past?

In any case, infinite or not, Aquinas’s arguments do not fail in proving the necessity of a first cause.

 

[MindOverMatter]

You simply say that it makes no sense that we could possibly exist in a single moment if there had been an infinite past. Why would it be impossible for us to have reached this moment?

If there is a finite moment in the past that exists an infinite number of events away from the present, it shouldn’t be hard to realize the impossibility of reaching the present moment. You can walk a finite distance, but it is meaningless to say that one can walk from an infinite distance away to some other point.

This is not assertion.

 

[AndyT_81]

If I can just weigh in with my 2 cents. I agree that it is impossible to traverse an infinite series of causal events. If there is an infinte past, at this point in time, T1 an infinite number of past events would have occured. However, an event T2, a trillion, trillion, billion years ago an infinite number of past events would still have occured. Therefore the same amount of past events would have occured before both T1 and T2 (i.e. an infinite number), yet T1 and T2 are seperated by a trillion, trillion, billion years. This is self-contradictory (and renders time meaningless) and therefore the existence of an actually infinite set of past events is impossible.