There Are No Part To Whole Actual Infinities

[Major]

Ok, I will try.

It seems that you imagined some kind of argument for necessity of creation. I think it is not working well at this level.
Let’s consider a bit silly model: let’s assume that big-bang/big-crash are transitions between independent states of universe. Each state you can label with integer number and they are apearing in this ordering one after another. To make them distinct let’s say that in each of them fine structure constant is equal a=0.07+0.01pi ArcTan (to keep it in the reasonable bounds) thus each of those states is distinct form another.
You have infinity of different states preceding one in which we are living. Even if we discover for example that last iteration was skipped for some unknown reason still there will be infinity of states. Even if all even iterations were skipped - still infinity…

 

[IWantGod]

Each state you can label with integer number

You can, but objectively (ontologically) speaking there is no being or state that is by nature an integer. No state can said to be - 1 accept arbitrarily.

 

[Major]

All labeling is kind of arbitrary.

 

[Dovekin]

When somebody argues for the existence of an infinite regress of irreducible distinct states,

When has anyone ever argued for such a thing?

they are in fact arguing for an infinite number that can only be defined by the quantity of its parts.

That is not how infinity is ever defined, so this is a doubtful assertion.

Otherwise it’s infinity has nothing to do with the number of distinct irreducible states and it is therefore meaningless to describe it as an actually infinite number of something.

Generally, infinity is defined by a series or grouping, ie 2,4,6 describe irreducible states, but the infinity is all even numbers, which leaves elements unlisted. That is not the same as being a number of irreducible states, nor does it have nothing to do with those states. There is no reason to jump to it is meaningless; infinity might help reconcile distinct states, squares to circles etc.

Every set of existing things is finite. That an imaginary infinity has no significance for existing things is not obvious, if that is what you mean by meaningless.

 

[IWantGod]

All labeling is kind of arbitrary.

Not really. Otherwise there would be no such thing as a distinct number of states. But where there are a quantity of states there are a number of states. So you can justifiably say you have real number of something. What you can’t do is arbitrarily define those quantities as something more than they present.

For example lets say you have two apples that cannot be reduced to parts, you cannot divide them in to smaller numbers. You can say you have two apples. What you can’t do is label them - 1 and + 1 and expect the result you get from that concept to reflect the actual objective reality of the apples and their quantity.

 

[IWantGod]

When has anyone ever argued for such a thing?

Whenever somebody argues for a regress of distinct irreducible states. What is it that you think they are arguing when that say there is no beginning to a progression of distinct states? And what do you think the logical consequences of that is (an infinite regress of distinct states).

 

[IWantGod]

That is not how infinity is ever defined, so this is a doubtful assertion.

It doesn’t matter how you defined it. That is what they are arguing for, an infinite regress of distinct irreducible states.

 

[IWantGod]

Generally, infinity is defined by a series or grouping, ie 2,4,6 describe irreducible states,

I do not doubt that. I am not arguing for a new mathematical theory. I am simply addressing the claim that there has been an infinite number of distinct irreducible states before this point in time. The word state referring to an actual progression of irreducible states in actual reality. Not 2,4,6.

 

[lelinator]

Whenever somebody argues for a regress of distinct irreducible states. What is it that you think they are arguing when that say there is no beginning to a progression of distinct states? And what do you think the logical consequences of that is ( an infinite regress of distinct states ).

I think that you’re being a bit simplistic in assuming that there’s even a discernible sequence of causes, infinite or otherwise.

First mover arguments are based upon the reasoning that A was caused by B, which was caused by C, which was caused by D, and so on until one inevitably comes to a first cause, because an infinite regression of causes is presumably impossible. But it may be that no such orderly sequence of causes actually exists, and that even if the number of causes isn’t infinite, there still may be no identifiable first cause.

So there may in fact be an infinite sequence of causes because no matter how far one traces the sequence of causes, one will never be able to reach a first cause.

 

[IWantGod]

So there may in fact be an infinite sequence of causes because no matter how far one traces the sequence of causes, one will never be able to reach a first cause.

Not if an infinite number is impossible. Can you argue for it’s possibility? Or are you
just saying it may be possible just because

 

[IWantGod]

First mover arguments are based upon the reasoning that A was caused by B, which was caused by C, which was caused by D,

It is a bit more complex than that. We identify a cause because it actualised some potential thing or the potential in some thing. And we identify an effect because a potential thing cannot actualise itself from nothing. We see change as a progression of actualized potential in some way shape or form. It is the fact of change that is being considered when arguing for an uncaused cause. And S.t Thomas doesn’t consider the reality of an infinite regress as a logical impossibility; at least he wasn’t convinced of it’s impossibility. And neither did he think that the existence of such a thing would effect the argument for God’s existence.

 

[lelinator]

Not if an infinite number is impossible. Can you argue for it’s possibility? Or are you
just saying it maybe possible just because

Imagine yourself on the surface of a globe, how far would you need to travel before you reached the beginning of the globe? If reality has no discernible first cause, because causation isn’t the simple linear progression that you presume it to be, then one would have to trace the line of causation forever.

 

[lelinator]

We identify a cause because it actualised some potential thing or the potential in some thing.

So tell me, if the first cause is pure actuality, what potential could it possibly have actualized. And if there were no potential for it to actualize, how could it possibly have caused anything?

 

[IWantGod]

If reality has no discernible first cause, because causation isn’t the simple linear

This is besides the point. This goes beyond simply describing causal relationships between two points in time. This is about about whether or not a quantity of states can be comprised of an actually infinite number. For Aquinas it is about the fact that things are changing and that is why he infers a cause - an existential-cause.

 

[tafan2]

Ok, that is not a definition of what I requested. But we will try anyways.

When somebody argues for the existence of an infinite regress of irreducible distinct states

What exactly do you mean by an “infinite regress of irreducible distinct states” ? Perhaps if you provide a reference of the argument you are referring to, we could understand exactly what you are talking about.
Until then, I will try to help, a quick google defines:
“infinite regression” as “a sequence of reasoning or justification which can never come to an end”
Irreducible, in mathematical terms, means it cannot be broken down any further, we get that.
“distinct states” - would be a, I suppose a state of being of something, examples could be as used in in automata theory or discreet logic systems or perhaps turing machines. Of course, those examples are not typically endless.
Putting that all together, it easily falls within set theory, of course almost anything can fall within set theory, it is the basis of mathematics.
So inifinity is defined as a set of limitless size. Period, so you are talking about a set of limitless size. There are two types of infinities, if you will. Countable infinities, those which have a one-to-one and onto mapping from the set of natural numbers. And those that are uncountable, eg the set of real numbers.
With either one, your idea that if you remove one element from the set, it is no longer infinite is false.
While infinity is used to define the size of these sets, it is not being used as a number. There is no such thing as an “infinite number”. So no one is arguing for that.

 

[tafan2]

What argument??? For cryng out loud, don’t you see, no one knows exactly what you are talking about. If you cannot define it, just point us to this argument you keep referring. Then we might be able to get somewhere.

 

[lelinator]

This goes beyond simply describing causal relationships between two points in time.

You’re right it does, because it may in fact be that causation is more than just a simple relationship between two points. Causation may be holistic not simplistic.

For Aquinas it is about the fact that things are changing and that is why he infers a cause - an existential-cause .

But perhaps Aquinas was mistaken about the holistic relationship between the cause, the effect, and everything else.

 

[halogirl]

My head just exploded and there are numbers everywhere. And I just hoovered.

 

[IWantGod]

While infinity is used to define the size of these sets, it is not being used as a number.

Then we are not talking about the same thing. A state here is being described as an actualized potential. In agreement with Aquinas i see the progression of being as a sequence of actualized potential, a set of actualised states. Different states of being are distinguished by their irreducibilty, and i use that word to emphasise the fact that one state cannot be reduced into two states; in other-words i’m describing the smallest units of change.

Distinct Irreducible states cannot be an infinite number.

 

[tafan2]

Ok, I now have an idea of what you have been talking about.

Distinct Irreducible states cannot be an infinite number.

Why?