Proofs... So what?

[Nirvana-Eld]

After some thinking I am willing to accept that there must have been a first cause that initiated the series of events we call existence. I think that this is the underlying substratum of causuality. Here the problem. So what? I do not see the connection from "there must have been a first cause" to "this is a being which we all call God" (quod omnes dicunt Deum). I see the point of the First Cause Idea more as pointing to a natural process, not a Christian God and or the classic "Omnipotent, Omniscient, Omnibenevolent God". There seems to be no connection.

I would like the proponents of the First Cause Argument who believe in the God of the three "O's" to logically make the connection between a process and a God. Civility is a must! I just glanced through a thread by a "killingevolution" ( ) and I would like this thread to be cleaner. 8)

[Bugmaster]

They say to you that they don't remember the room number, but someone calling from the room furthest from room 1 ordered a pizza and they need to deliver it to them.

Bzzzt ! That's wrong. In my scenario, the pizza company would never do this. Instead, they'd say, "Someone in room 1489673 ordered a pizza, and our pizza guy is lost. He is standing right outside room 1. Can you give him step-by-step directions to get to room 1489673 ?" Your contention all along has been that, just because there's an infinite number of rooms, there is no way to direct the pizza guy from room 1 to room 1489673; I have been trying to demonstrate why this is absurd.

Again: given two specific, fixed, finite integers, we can always compute the difference between them. This difference will, in itself, be a fixed, finite integer.

I realize that you're jumping up and down right now, exclaiming: "but you need to have the First Cause in order for it to be a cause at all, and, under infinite regress, that First Cause will be an infinite distance away !". That's nice, but you have to prove why you need the First Cause at all before it becomes relevant. Otherwise, you're just begging the question.

As the Harvey hotel demonstrates, there is not a finite number of rooms between you (in room 1) and the guy who ordered the pizza (in the room furthest from room 1).

If the room numbers are integers, then the "room furthest from..." anywhere does not have a room number. It is not an integer. It is not in the set. Duh.

Why are you suggesting that effects cause their causes?? That seems like a Straw Man.

I thought you were the one suggesting that...

By "timeline" I'm not referring to measured time but am referring to the entire causal history of events.

Ok. At some point, you should post some kind of a glossary. Many words you use, such as "miracle", "time", "cause", "probability", etc., have very different definitions in Harvey-speak, as compared to common parlance.

But, by postulating an infinite regression of events you are postulating that there are events that existed an infinite number of events ago, correct?

No. If we took any two specific events, the number of events between them is finite. Similarly, if we took any two finite integers a and b, then a-b is a finite integer.

Okay, thanks for that program but I think you better debug it for me. Here's my problem, while the program was executing I kept looking at the clock, and I noticed that the program never arrived at infinity. When will this program arrive at infinity?

Never, but note that this program itself has a finite length, which is something that you said was impossible.

But why must an infinite set of events be a given?

That's how logical arguments work. I assume that infinite regress is true, and then you try to show me how this assumption leads to a contradiction, which would mean that infinite regress is impossible. I eagerly await your proof.

[OccamsRazor]

Okay, thanks for that program but I think you better debug it for me. Here's my problem, while the program was executing I kept looking at the clock, and I noticed that the program never arrived at infinity. When will this program arrive at infinity?

I wrote this program an infinite time ago, the Universe had already existed for an infinite time before I wrote the program. The program just finished 10 minutes ago. It will now spend an infinite amount of time printing the results but luckily the Universe will keep going for an infinite amount of time after it has finished printing.
I don't see any problem with this.

[harvey1]

As the Harvey hotel demonstrates, there is not a finite number of rooms between you (in room 1) and the guy who ordered the pizza (in the room furthest from room 1).

If the room numbers are integers, then the "room furthest from..." anywhere does not have a room number. It is not an integer. It is not in the set. Duh.

Why doesn't the furthest room from room number 1 have a room number? As I said in the scenario, every room is full, and the hotel has an infinite number of rooms from 1 to infinity (2, 3, 4, 5, ...). What this tells me is that you want to treat infinity like a finite set, and you cry foul when shown that you can't do that. Maybe you heard there's no crying in baseball, well, there's no crying in infinity.

In the case of an infinite regress in causes, there is nothing to bring about (cause) each member (event) in the set (universe) except the finite procedure used to construct a finite set. Therefore, the infinite collection of causes must be constructed by each cause occurring in a finite process called the present. However, you can't construct an infinite set using a finite process. If that were possible, then the Axiom of Infinity would be proven. All you would need to do is show how a finite process constructs an infinite set, and then you would have your proof of the axiom.(...)I noticed that the program never arrived at infinity. When will this program arrive at infinity?

Never, but note that this program itself has a finite length, which is something that you said was impossible.

I don't recall saying a program of finite length is impossible. Why would I say that when all human constructed programs are of finite length?

In any case, if you can't construct an infinite set from a finite number of steps, then I return to my main point:

In the case of an infinite regress in causes, there is nothing to bring about (cause) each member (event) in the set (universe) except the finite procedure used to construct a finite set. Therefore, the infinite collection of causes must be constructed by each cause occurring in a finite process called the present. However, you can't construct an infinite set using a finite process. If that were possible, then the Axiom of Infinity would be proven. All you would need to do is show how a finite process constructs an infinite set, and then you would have your proof of the axiom.

I never said that it was possible for a finite mind to encompass an infinite set. All I said that, given an infinite set of events.

But why must an infinite set of events be a given?

That's how logical arguments work. I assume that infinite regress is true, and then you try to show me how this assumption leads to a contradiction, which would mean that infinite regress is impossible. I eagerly await your proof.

No, wait. I'm allowing you the opportunity to show how infinite regress can establish that you don't need a First Cause (i.e., a finite beginning). I'm not granting you the assumption of having a completed infinity based on the first assumption of a regression of causes. I'm just granting you the option to show how an infinite regress works. Do you see the difference?

Let's start formalizing all of this a little so that we can see exactly what is the problem. Here is your argument as I understand it.

1) There is no first cause, each event is caused by a preceding cause that extends to an infinite number of previous events

2) Any event in the past is a finite number of events ago

3) The collection of all past events composes a completed infinite set of causes (C) [from 1, 2], and an omniscient mind could comprehend all the member events in C

4) Therefore, there is no need for a first cause since all previous causes in the infinite regressive timeline can account for any effect within the timeline[from 1, 2, 3]

The problem with that argument is that (2) contradicts (1) and (3) since you can't refer to infinity by assuming (2). That is, (2) contradicts the assumption of infinity mentioned throughout your argument. The other problem is that you are trying to prove an infinite set can exist by advocating an omniscient mind, but you do not show how an omniscient mind could comprehend a complete infinity without assuming the Axiom of Infinity.

You've failed to make your argument since you have never shown how you can refer to the term "infinite" without advocating the Axiom of Infinity. Mathematically, it is impossible to treat any set as an infinite set without this axiom.

[Bugmaster]

Why doesn't the furthest room from room number 1 have a room number?

Simply by definition. Anything that doesn't have a room number is not a room at all. Aleph-null is not an integer.

What this tells me is that you want to treat infinity like a finite set, and you cry foul when shown that you can't do that.

Infinity is not an integer, and I will keep crying foul each time you try to treat it like one. Again, you're confusing the cardinality of a set with members of that set. I can define S as "an infinite set of apples", but it doesn't follow that infinity is an apple. Why is this so difficult to for you understand ?

In the case of an infinite regress in causes, there is nothing to bring about (cause) each member (event) in the set (universe) except the finite procedure used to construct a finite set.

Obviously, I disagree. An algorithm with an infinite execution time would be able to enumerate all integers, and thus, all events. So, there exists something (an infinitely-long-running algorithm) which can enumerate all events.

More importantly, however, I don't see how it matters. Why is it important that a finite algorithm cannot enumerate all integers ? Why does this render infinite regress impossible ?

Therefore, the infinite collection of causes must be constructed by each cause occurring in a finite process called the present.

I don't see how this even follows from your previous statement. What does the present (which is a fixed point in time, which is a property of our universe, which in itself is a result of some event in the chain) have to do with anything ?

I don't recall saying a program of finite length is impossible.

I thought that's what you meant by "a finite algorithm", but I guess you meant, "an algorithm with a finite execution time", instead.

In any case, if you can't construct an infinite set from a finite number of steps, then I return to my main point...

You have just said, "since infinite regress is impossible, let me return to my main point..." Sorry, but that doesn't work. The whole point of infinite regress is that I don't need to construct anything. The infinite set of events simply exists.

I'm just granting you the option to show how an infinite regress works.

Why do I need to even care about this option ? You claim that infinite regress is impossible. This means that you need to show why infinite regress leads to a contradiction. This is different from saying that infinite regress is not only possible, but is actually taking place, in which case the burden of proof would be on me.

Let me clarify your definitions a bit (my text is in bold)

1) There is no first cause, each event is caused by a preceding cause that extends to an infinite number of previous events
2) Any specific event in the past is a finite number of events ago relative to any specific event in the future.
3) The collection of all past events composes a completed infinite set of causes (C) [from 1, 2], and an omniscient mind could comprehend all the member events in C
4) Therefore, there is no need for a first cause since all previous causes in the infinite regressive timeline can account for any effect within the timeline[from 1, 2, 3]

The problem with that argument is that (2) contradicts (1) and (3) since you can't refer to infinity by assuming (2). That is, (2) contradicts the assumption of infinity mentioned throughout your argument.

How so ? I challenge you to show me two specific integers, such that the difference between them is not an integer. Keep in mind that infinity is not an integer.

The other problem is that you are trying to prove an infinite set can exist by advocating an omniscient mind...

No, that is not my goal. I am merely using an omniscient mind as an illustration. My infinite set of events would exist even if there were no omniscient minds anywhere.

but you do not show how an omniscient mind could comprehend a complete infinity without assuming the Axiom of Infinity.

I claim that the cardinality of the set of items that an omniscient mind could comprehend would be at least aleph-null, by definition of omniscience. If you disagree, then please provide an alternative definition of omniscience (you are so fond of alternative definitions...).

[OccamsRazor]

I have been reading this thread in the attempt to work out what the argument is.

As I understand it you are arguing whether in infinite regression of events can possibly have a first cause or not and BugMaster has introduced the infinite line of integers as an analogy.

I don't really see the issue here because any infinite series may or may not have a start and/or an end.
Using the example of an infinite series of integers you may say that it has no start nor end. The series of negative integers has an end and the series of positive integers has a start. The series of real numbers between 0 and 1 has both a start and an end.

Furthermore I don't see the issue with BugMaster's point about the finite difference between integers. If you take two integers n1 and n2 where -aleph-0 < n1 & n2 < +aleph-0 then there is still a finite and calculable difference between n1 and n2 (simply |n1-n2|).

Have I misunderstood the point?

[harvey1]

Using the example of an infinite series of integers you may say that it has no start nor end. The series of negative integers has an end and the series of positive integers has a start. The series of real numbers between 0 and 1 has both a start and an end.

Let me outline my argument as a reductio ad absurdum argument:

1) There is no first cause (Bugmaster's assertion of a possible truth)

2) Each event in the world can be caused by a previous cause, and that cause would be an effect of a previous cause, ad infinitum

3) Causes must be actual events that can be referred to as occurring (i.e., if it is logically impossible to reference that event, then it cannot be a cause to an event that you can reference)

4) A complete infinite set is not obtainable except by invoking the Axiom of Infinity

5) By (4), it is not possible to refer to a completed infinite set C containing all causes that have occurred in the past without invoking the Axiom of Infinity

6) (2) cannot refer to every cause contained in a complete infinite set C without invoking the Axiom of Infinity [from 4, 5]

7) Invoking the Axiom of Infinity to advocate that set C exists is begging the question since a complete infinite set of causes, C, does not require a beginning by definition of it being a complete infinite set

8) There can be no actual causes that occurred in the infinite past--all causes occurred in the finite past [from 3, 6, 7]

9) Hence, (1) is false [from 8].

[OccamsRazor]

Lets rerun your argument using integers.

1) There is no first (lowest) integer

2) Each integer can be reduced by 1 giving a "previous" integer, and that integer would be one greater then a previous integer, ad infinitum

3) All integers are actual values and can therefore be quoted by this actual number.

4) A complete infinite set is not obtainable except by invoking the Axiom of Infinity.

5) By (4), it is not possible to refer to a completed infinite set C containing all integers without invoking the Axiom of Infinity.

6) (2) cannot refer to every integer contained in a complete infinite set C without invoking the Axiom of Infinity [from 4, 5]

7) Invoking the Axiom of Infinity to advocate that set C exists is begging the question since a complete infinite set of integers, C, does not require a beginning by definition of it being a complete infinite set

8) There can be no actual infinite negative integers--all negative integers are finite [from 3, 6, 7]

9) Hence, (1) is false [from 8].

This is clearly nonsense. Yoy cannot say that there must be an integer which has the lowest negative value. The point of the Axiom of infinity is that the set of integers (or BugMaster's hypothetical set of causes) is an inductive set. This means that the values in the set all do have a value (or a historical date in the "causes" set) but this value is a purely relative one.

[harvey1]

Lets rerun your argument using integers... This is clearly nonsense. Yoy cannot say that there must be an integer which has the lowest negative value. The point of the Axiom of infinity is that the set of integers (or BugMaster's hypothetical set of causes) is an inductive set. This means that the values in the set all do have a value (or a historical date in the "causes" set) but this value is a purely relative one.

Okay, the problem with your analogous argument with negative integers is that you failed to label the integers as computable, and this affected how you worded (3). The word "cause" is a label like the word integer is a label. Causes must represent actual events, which means that it is at least logically possible (not necessarily physically possible) to label the event by tracing (computing) back to the event (e.g., Cause event #: 1504). If it is logically impossible for the event to be numbered after tracing back like this, then the cause cannot be an actual event since "occurrence" would have no meaning. Similarly, if you can't count to back to an integer, then it can't be a computable integer.

So, here's the argument as it applies with computable integers:

1) There is no first (lowest) computable integer

2) Each computable integer can be reduced by 1 giving a "previous" computable integer, and that computable integer would be one greater then a previous computable integer, ad infinitum

3) All computable integers must be countable to be a valid computable integer (i.e., if it is logically impossible to count back to any computable integer, then it cannot be reduced by 1 so "that this computable integer would be one greater then a previous computable integer")

4) A complete infinite set is not obtainable except by invoking the Axiom of Infinity.

5) By (4), it is not possible to refer to a completed infinite set C containing all computable integers without invoking the Axiom of Infinity.

6) (2) cannot refer to every computable integer contained in a complete infinite set C without invoking the Axiom of Infinity [from 4, 5]

7) Invoking the Axiom of Infinity to advocate that set C exists is begging the question since a complete infinite set of computable integers, C, does not require a beginning by definition of it being a complete infinite set

8) There can be no actual infinite negative integers that are computable--all negative computable integers are finite in quantity[from 3, 6, 7]

9) Hence, (1) is false [from 8].

[Bugmaster]

Okay, the problem with your analogous argument with negative integers is that you failed to label the integers as computable...

How do you define "computable" ?

Here's an algorithm that, given any negative integer, will count from 0 to that integer. I claim that this algorithm will execute in a finite time for each negative integer in the set of negative integers.

Code: Select all

function count(i: a negative integer) {
  let j = 0;
  do {
    print j;
    j = j - 1;
  } while (j > i);
}

I challenge you to implement this algorithm in Lisp (because Lisp supports integers with arbitrary precision), and then show me an integer which will cause this algorithm to go into an infinite loop.

Causes must represent actual events, which means that it is at least logically possible (not necessarily physically possible) to label the event by tracing (computing) back to the event...

Tracing back from which point ? If you take the present as your starting point, then I'd agree. 0 is an integer, any negative integer is an integer by definition, the set of integers is a closure under subtraction, so (0 - any negative integer) is an integer.

1) There is no first (lowest) computable integer...
9) Hence, (1) is false [from 8].

Does this mean that there exists a lowest computable integer ? If so, what algorithm would we use to compute it ?

[harvey1]

Okay, the problem with your analogous argument with negative integers is that you failed to label the integers as computable...

How do you define "computable"?

A finite Turing machine must be able to compute the number using some finite Turing algorithm to arrive at the number.

Here's an algorithm that, given any negative integer, will count from 0 to that integer. I claim that this algorithm will execute in a finite time for each negative integer in the set of negative integers... I challenge you to implement this algorithm in Lisp (because Lisp supports integers with arbitrary precision), and then show me an integer which will cause this algorithm to go into an infinite loop.

That's not my point. I realize that if I gave you a negative integer that you could compute that integer if given enough time. However, what you cannot do is produce an infinite complete set. At any time in the future you will always have only computed a finite set of integers.

Tracing back from which point? If you take the present as your starting point, then I'd agree.

Starting from yesterday is fine.

]1) There is no first (lowest) computable integer... 9) Hence, (1) is false [from 8].

Does this mean that there exists a lowest computable integer ? If so, what algorithm would we use to compute it ?

No. It means for that first assumption this assumption is proven false. The reason it is false may not be because there is a lowest computable integer, it might be false because it is absurd (hence the name of the argument: reductio ad absurdum). For example:

1) There is no lowest blue integer

2) Numbers do not interact with photons

3) Color is caused by the interaction of photons with physical objects

4) Therefore, (1) is false