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)

[harvey1]

This is the same as saying if we don't know everything that we cannot know anything and is just silly. Not knowing all causes back to the beginning DOES NOT mean that events are random, but is the main reason scientists always say things are PROVISIONALLY true and that there are no certainties in scientific investigation, just degrees of certainty.

That's not what f(e), f(f(e)), etc., is showing. It means that to refer to the necessary and sufficient causes of E, the reference must point to causes that "occurred" an infinite time ago. However, according to the view of a universe without a beginning, these infinite causes never occurred because no matter how far back in time you go, a "the nth (infinite) cause" did not happen by definition. (Since if it did, you could always go back a day or year, or trillion years earlier than that.) So, those nth causes don't exist.

[Bugmaster]

That's not what f(e), f(f(e)), etc., is showing. It means that to refer to the necessary and sufficient causes of E, the reference must point to causes that "occurred" an infinite time ago.

This is true, if you replace "time" with some other concept that can span the creation of universes.

Therefore, E does not have a cause in your scenario--it is a random event.

This is false. A random event (as I understand it) is an event for which there is no cause at all. However, in my example, every event e has a cause -- given by f(e) -- and therefore no event is random.

Consider, again, the number line. There is no smallest number on this line. And yet, the numbers on the line are not random. For any number n, we can call f(n) = n-1 to get the previous number. If the numbers were totally random, this would not be possible.

This is the whole point of my argument: if we can apply f(e) to any possible event, then no event is random, because all events have causes.

It doesn't matter that, as you put it, "infinity is not reachable". As long as every event has an immediate cause, you cannot call any event "random" -- unless you want to redefine the word "random" in some new and interesting way.

In fact, if you were omniscient (meaning, possessing an infinite knowledge of everything), then you would be able to comprehend all of the causes of every event, because your mind would encompass the entire causality chain, infinite though it may be. Similarly, if you were omniscient, you would be able to know all of the digits of Pi, and every single number on the number line. I don't see a problem here.

[Bugmaster]

This is the same as saying if we don't know everything that we cannot know anything and is just silly.

This is a bit of an ontology/epistemology confusion: for the purposes of this discussion, we're not concerned with knowing things, we're concerned with what things are actually like.

However, it's a good analogy nonetheless. Harvey, would you say that, since we do not know everything, we know nothing ? If not, how is this different from saying that since there is no first cause, then every event is random ?

[harvey1]

Therefore, E does not have a cause in your scenario--it is a random event.

This is false. A random event (as I understand it) is an event for which there is no cause at all. However, in my example, every event e has a cause -- given by f(e) -- and therefore no event is random.

However, in my last post I showed that there would need to exist an infinite cause for your construct to work. Your example of cause, however, can never show an infinite cause since it is unreachable by counting causes back to infinitiy. Therefore, this is a contradiction. You need an infinite cause, but there cannot be an infinite cause. Therefore, an infinite cause is random since not every event (e.g., an infinite cause) has a cause.

Consider, again, the number line. There is no smallest number on this line. And yet, the numbers on the line are not random. For any number n, we can call f(n) = n-1 to get the previous number. If the numbers were totally random, this would not be possible.

And, similarly, if you willing to agree that the causal nexus of the universe is caused by the axioms of mathematics just like those axioms allow us to construct that line, I would be happy to agree with you. However, you're a nominalist, so that example does not endorse your position.

As long as every event has an immediate cause, you cannot call any event "random" -- unless you want to redefine the word "random" in some new and interesting way.

Well, I would define random in terms of "no algorithm exists" that can predict the outcome, but that's sort of in the same venue as what you are suggesting with cause since a cause is a reason, and a reason can be construed in this way.

In any case, you have to show how your view is consistent. If your view requires an infinite cause, and that infinite cause cannot be demonstrated by showing how an infinite cause produces a finite cause, then your perspective is not consistent.

In fact, if you were omniscient (meaning, possessing an infinite knowledge of everything), then you would be able to comprehend all of the causes of every event, because your mind would encompass the entire causality chain, infinite though it may be. Similarly, if you were omniscient, you would be able to know all of the digits of Pi, and every single number on the number line. I don't see a problem here.

If there were a cause for an infinite line or sequence (e.g., the axioms of math), then the cause of any event (infinite or finite) emerges from the top down. I agree that an omnscient mind would be able to know the contents of the entire line or sequence because the line or sequence has a reason for its knowability. However, as a nominalist, I don't see how you could argue for such an account since there is no top down heirarchy in your perspective. An infinite cause exists because it just so happens to exist. It is a contingent fact. If a contingent fact, then how is that not random?

[Bugmaster]

However, in my last post I showed that there would need to exist an infinite cause for your construct to work. Your example of cause, however, can never show an infinite cause since it is unreachable by counting causes back to infinitiy.

Unreachable by our puny finite mortal minds, perhaps, but that doesn't mean that an infinite chain (graph, whatever) of causes doesn't exist. Surely, an omniscient God would be able to grasp it. You need to logically prove to me that an infinite graph of causes could not exist in principle, not merely assert it, or claim that since we can't know it, it doesn't exist.

And, similarly, if you willing to agree that the causal nexus of the universe is caused by the axioms of mathematics...

I'm not saying "math proves my point", all I'm saying is that the number line illustrates my point. The number line is completely analogous to an infinite chain of causes and effects (as I have shown in every post since my opening statement). The number line is not random. Neither is an infinite chain of causes and effects. That's all I'm saying.

Well, I would define random in terms of "no algorithm exists" that can predict the outcome, but that's sort of in the same venue as what you are suggesting with cause since a cause is a reason, and a reason can be construed in this way.

If we are truly omniscient (and, for the purposes of this discussion, we are), then we don't need to predict anything, because we can see every single event at once. So, you need a better definition of "random". If you say, "a random event is an event that happens for no reason whatsoever", then there are no random events, since the reason for each event e is given by f(e).

If your view requires an infinite cause, and that infinite cause cannot be demonstrated by showing how an infinite cause produces a finite cause, then your perspective is not consistent.

Ok, I don't understand what you mean by "infinite cause" vs. "finite cause".

I agree that an omnscient mind would be able to know the contents of the entire line or sequence because the line or sequence has a reason for its knowability.

I don't see how this is relevant. An infinite mind would be able to grasp an infinite number line, regardless of any reasons for it.

[harvey1]

Ok, I don't understand what you mean by "infinite cause" vs. "finite cause".

An "infinite cause" is a cause that f(e) references as having occurred an infinite time ago. A "finite cause" is a cause that f(e) references as having occurred a finite time ago.

Unreachable by our puny finite mortal minds, perhaps, but that doesn't mean that an infinite chain (graph, whatever) of causes doesn't exist.

If it did exist, then there would be a cause prior to that because that cause is the effect of yet another cause. Since that is always true, you cannot have a cause that occurred an infinite time ago (i.e., assuming the cause of E is an event and not a logico-mathematical structure).

The number line is completely analogous to an infinite chain of causes and effects (as I have shown in every post since my opening statement). The number line is not random. Neither is an infinite chain of causes and effects. That's all I'm saying.

What is the largest and smallest number on your number line?

If we are truly omniscient (and, for the purposes of this discussion, we are), then we don't need to predict anything, because we can see every single event at once.

But, why do we see every event at once? In the case of God, God can see all events at once because all events occur at once. For every event that occurs, God is there to witness that event while witnessing other moments at other times (earlier and later to that point in time). In the case of your f(e) example, the events don't happen at once, they happen at different times. Since f(e) references a cause E that happened an infinite time ago, there must be a time when that event occurred. However, as I said, that event E cannot exist since if it did, you would have have an earlier moment (E-1) that would make E an event that occurred a finite time ago (and not an infinite time ago).

So, you need a better definition of "random". If you say, "a random event is an event that happens for no reason whatsoever", then there are no random events, since the reason for each event e is given by f(e).

But, f(e) refers to a cause that happened an infinite time ago, and that cause has no reference since you would have an earlier moment (E-1) that would make E an event that occurred a finite time ago (and not an infinite time ago).

I agree that an omnscient mind would be able to know the contents of the entire line or sequence because the line or sequence has a reason for its knowability.

I don't see how this is relevant. An infinite mind would be able to grasp an infinite number line, regardless of any reasons for it.

You need to show how God can know every number of an infinite line without just saying that God would. Why would God know this? My contention is that God knows it because (A) God possesses the algorithm to construct that number line (or arrive at a specific nth number on that number line), or (B) God exists at all points on the line and there are good reasons why God's mind in that instance should be treated as unity. If there is no cause for the timeline as you say, then that eliminates (A). In order for (B) to be true, all the events would have to exist at once. If they didn't, then God wouldn't know a future event before it occurred because that event doesn't exist yet and there is no way to know and reach infinity by counting to it (or remembering infinity ago by remembering each day as they occurred until you reached an infinite time ago).

What you seem to be advocating is Mystery (i.e., an irrational account of causality).

[Bugmaster]

An "infinite cause" is a cause that f(e) references as having occurred an infinite time ago. A "finite cause" is a cause that f(e) references as having occurred a finite time ago.

This makes no sense, because f(e) always references the immediate reasons for e. So, if ball A hits ball B, then f("B is moving") == "A hit it". There's no infinite anything involved here.

Furthermore, time is irrelevant in our case, because we're talking about causality which (for the purposes of this discussion) can span the creation of time itself.

Since that is always true, you cannot have a cause that occurred an infinite time ago (i.e., assuming the cause of E is an event and not a logico-mathematical structure).

I actually don't care if it's an event or not. If f(e) evaluates to some "logico-mathematical structure", then f(f(e)) would evaluate for the cause of that structure. In other words, I don't care what e is.

What is the largest and smallest number on your number line?

Exactly ! There is no smallest or largest number, and yet the number line is not random. If we are going to proceed anywhere in this argument, you need to either accept this, or prove that the number line is random.

But, why do we see every event at once? In the case of God, God can see all events at once because all events occur at once. For every event that occurs, God is there to witness that event while witnessing other moments at other times (earlier and later to that point in time).

What kind of events are we talking about here ? Not all events in our Universe occur at once; for example, if I hit ball A, and it pushes ball B 3 seconds later, then these two events are 3 seconds apart. You could always say, "God perceives all events as though they were happening at once", but that's not the same as saying, "all events occur at once".

Since f(e) references a cause E that happened an infinite time ago...

This is false. f(e) references the immediate cause of e, which, in our Universe, happened a finite time ago, for any given e. Outside of our Universe, there's no such thing as time, so your statement is still false.

I find it odd, however, that you're so focused on the notion of time... why is time important at all ? It's causality we're concerned with, not time.

By the way, you still need to either agree to my definition of "a random event" ("an event that happens for no reason whatsoever"), or come up with your own. Until you do that, you can't use the word "random" to convince me of anything.

You need to show how God can know every number of an infinite line without just saying that God would.

Why not ? Knowledge of everything at all times, that's what omniscience is ! By definition. It doesn't matter how omniscience works; I am only concerned with the fact that it does. We can argue whether omniscience is self-contradictory or not some other time.

So, again:

You need to show me why infinite regress is impossible. So far, you have said that infinite regress is impossible because it would render every event random. You have not defined what you mean by "random", however (you seem to disagree with my common-sense definition).

I have shown how we can map causes and effects onto a number line, which, while infinite, is not random (by the common-sense definition). Thus, I have shown that the chain (graph, whatever) of causes and effects can be infinite, and yet not random.

[harvey1]

This makes no sense, because f(e) always references the immediate reasons for e... f(e) references the immediate cause of e, which, in our Universe, happened a finite time ago, for any given e.

Okay. e <-- f(e)

* The necessary and sufficient causes pointed to by f(e) bring about the effect(s) e.

e <-- f(f(e)

* The necessary and sufficient causes of f(e) (along with f(e)) are needed to show why e was a necessary and sufficient effect for the causes that preceded it.

If true, then

e <-- f(e) or more accurately,
e <-- f(f(e)), or still more accurately,
e <-- f(f(f(e))), .... or more accurately
e <-- f(f(f(..ad infinitum..(f(e))...)))

Notice that an infinite cause is needed to have the necessary and sufficient causes to bring about e. As you say, f(e) is the immediate (approximate) reason for e, but it is not a reason at all if f(f(e)) does not exist. (Or, especially if the infinite cause does not exist.) However, an infinite cause never existed!

Furthermore, time is irrelevant in our case, because we're talking about causality which (for the purposes of this discussion) can span the creation of time itself.

Since one of your premises is that time did not have a beginning, causality cannot exist prior to time.

The number line is completely analogous to an infinite chain of causes and effects (as I have shown in every post since my opening statement). The number line is not random. Neither is an infinite chain of causes and effects. That's all I'm saying.

What is the largest and smallest number on your number line?

...There is no smallest or largest number

If there is no such number, and a number represents an event, then your analogy breaks down since positive and negative infinity (aleph-null) is a number used by mathematicians to represent the greatest and least number on a line. If you do not dwelve into infinities, then you are saying that the line cannot be represented as "an infinite chain of causes and effects."

You could always say, "God perceives all events as though they were happening at once", but that's not the same as saying, "all events occur at once".

You can if you think that the past, present and future already "exist."

you still need to either agree to my definition of "a random event" ("an event that happens for no reason whatsoever"), or come up with your own.

I can work with that definition for now.

In fact, if you were omniscient (meaning, possessing an infinite knowledge of everything), then you would be able to comprehend all of the causes of every event, because your mind would encompass the entire causality chain, infinite though it may be. Similarly, if you were omniscient, you would be able to know all of the digits of Pi, and every single number on the number line.

I agree that an omnscient mind would be able to know the contents of the entire line or sequence because the line or sequence has a reason for its knowability.

An infinite mind would be able to grasp an infinite number line, regardless of any reasons for it.

You need to show how God can know every number of an infinite line without just saying that God would.

Why not? Knowledge of everything at all times, that's what omniscience is! By definition. It doesn't matter how omniscience works; I am only concerned with the fact that it does. We can argue whether omniscience is self-contradictory or not some other time.

You introduced omniscience to show that I would have knowledge of the "infinite cause," however when I asked you to show me how this knowledge is possible you reverted to saying that this is your definition of omniscience. You can't introduce omniscience to show that your view is tenable without providing reasons why I should agree that an infinite cause exists. Just arguing that your view is true by definition doesn't fly.

[Bugmaster]

Notice that an infinite cause is needed to have the necessary and sufficient causes to bring about e. As you say, f(e) is the immediate (approximate) reason for e, but it is not a reason at all if f(f(e)) does not exist. (Or, especially if the infinite cause does not exist.) However, an infinite cause never existed!

This makes no sense. Are you saying that, after a certain point, negative integers on the number line stop existing ? That's false.

The whole point of f(e) is that it can be applied to any event you like, reliably. f(e) is defined for all events e.

Since one of your premises is that time did not have a beginning, causality cannot exist prior to time.

When did I say that ? I see "beginning of time" as just another event e. Whatever caused it is given by f(e), as usual.

If there is no such number, and a number represents an event, then your analogy breaks down since positive and negative infinity (aleph-null) is a number used by mathematicians to represent the greatest and least number on a line.

Ouch, Harvey ! Coming from you, this is quite a shock. Surely, you know that aleph-null is not a natural number ? It's the cardinality of the set of all natural numbers, which is infinite. Aleph-null is not part of this set.

Essentially, what you just told me is, "I can give you the smallest possible natural number". I claim that you can't, because I can always call f(n) = n-1 on it, and get an even smaller number. Same thing goes for the largest number, of course.

So, if we map each event to a natural number line, we can have an ordered line of events, which is infinite in size. No event will be mapped to aleph-null, because aleph-null is not part of the set.

you still need to either agree to my definition of "a random event" ("an event that happens for no reason whatsoever"), or come up with your own.

I can work with that definition for now.

All right. In this case, no event e is random, because for each event e we can call f(e) to retrieve all the immediate reasons for this event happening. So, you need another defence.

You introduced omniscience to show that I would have knowledge of the "infinite cause"...

Again: there is no such thing, just as there is no smallest natural number. You can't know something that doesn't exist. However, if you were omniscient, the countability of the events you could perceive would be aleph-null (at the very least).

[harvey1]

If there is no such number, and a number represents an event, then your analogy breaks down since positive and negative infinity (aleph-null) is a number used by mathematicians to represent the greatest and least number on a line.

Ouch, Harvey! Coming from you, this is quite a shock. Surely, you know that aleph-null is not a natural number? It's the cardinality of the set of all natural numbers, which is infinite. Aleph-null is not part of this set.

That's not what I meant. Positive infinity and negative infinity are represented by an order type using Cantor's transfinite ordinal numbers (e.g., w and w*), and for natural numbers this comprises an aleph-null cardinality:

This [w] is the "smallest" of Cantor's transfinite numbers, defined to be the smallest ordinal number greater than the ordinal number of the whole numbers.

The order type of the negative integers is * w called (Moore 1982, p. 62), although Suppes (1972, p. 128) calls it w*.

Notice that an infinite cause is needed to have the necessary and sufficient causes to bring about e. As you say, f(e) is the immediate (approximate) reason for e, but it is not a reason at all if f(f(e)) does not exist. (Or, especially if the infinite cause does not exist.) However, an infinite cause never existed!

This makes no sense. Are you saying that, after a certain point, negative integers on the number line stop existing? That's false.

No, I'm saying that the order type is w* (i.e., transfinite number omega*), but this representation cannot really exist since if an event actually happened it must have happened a finite number of events ago in order for it to have actually occurred. That would mean that any set of occurring events should be represented as an order type having a finite ordinality, not a transfinite ordinal. The fact that we could count back the number of events to when the event occurred by definition means that we can only represent events using finite ordinal numbers. However, in that case, in an infinite regress argument you have causes that happened an infinite time ago, which requires an order type of transfinite ordinality. Do you see the contradiction?

Since one of your premises is that time did not have a beginning, causality cannot exist prior to time.

When did I say that? I see "beginning of time" as just another event e. Whatever caused it is given by f(e), as usual.

Here:

I'm not sure I understand what you mean by "the" cause. Do you mean, the First Cause that has no cause in itself? Granted, if we assume that infinite regress is true, then the First Cause does not exist, by definition... by why is this a problem?

If you assume an infinite regress as true, then time did not have a beginning.

you still need to either agree to my definition of "a random event" ("an event that happens for no reason whatsoever"), or come up with your own.

I can work with that definition for now.

All right. In this case, no event e is random, because for each event e we can call f(e) to retrieve all the immediate reasons for this event happening. So, you need another defence.

All of your events represented by f(e) have a order type of finite ordinality, and therefore events that happened an infinite number of events ago are uncaused (i.e., random).

Again: there is no such thing, just as there is no smallest natural number.

As I mentioned, the order type of a such a line is transfinite ordinality, however all of your events are finite in number, which is why you cannot use the set of all natural numbers as analogous to your argument.

You can't know something that doesn't exist. However, if you were omniscient, the countability of the events you could perceive would be aleph-null (at the very least).

If they were aleph-null, then the ordinality would be transfinite. However, as I showed, you are using order type of only finite ordinality. That's a contradiction.