Monday, January 5, 2015

Infinite Regress or Circular Reasoning. Take Your Pick.

There are two problematic logical conundrums that most people try to avoid, and which in most cases you can refer to in criticizing an opponent’s theories. If you can show that their reasoning leads to an infinite regress, or incorporates circular logic, you can trounce their arguments and come away victorious.

An infinite regress is a problem in logic for this reason. A logical proof goes like this:

1. If this conditional statement is true, then the conclusion follows.
2. This premise states that the conditional above is true.
3. This conclusion says that the conclusion in # 1 follows from points 1 and 2.

It has a beginning and an end. But an infinite regress goes like this.

1 If the infinitely distant premise is true, then the conclusion follows from premise 1.
2. Premise 1 depends on premise 2
3. Premise 2 depends on premise 3
4. Premise 3 depends on premise 4
5. Premise 4 depends on premise 5
6. Premise 5 depends on premise 6
7. Premise 6 depends on premise 7
Starting to see the problem? If the nth premise as n approaches infinity must be true for the conclusion to be reached, then the conclusion can never be reached, because you can never count to infinity.

In other words, an infinite regress renders a logical proof invalid because the proof is incomplete. It can never be finished. It’s the same as saying this.

1. If A then B
2. If B then C
3. ?

or like this,

1. If A then B
2. it is not known if A
3. therefore, it is not known if B.

It hasn’t been formulated in such a way that the conclusion can be determined. Each of the two above examples are not infinite regresses themselves, but they are what an infinite regress amounts to. A collection of premises with no connection to a conclusion. A series of unknowns and hypotheticals that renders the conclusion unascertainable.

That’s why an infinite regress is logically wrong. Because once you have it, you can prove nothing that depends on the conclusion of the infinitely regressive logical proof. As in the above examples, if you have any other proofs that use as a premise the fact that B is true, none of those proofs can be known to be true, because B can’t be known to be true.

Proof 1:
1. If there is an infinite regress, B can not be known to be true.
2. There is an infinite regress.
3. Be cannot be known to be true.

(this is, ironically, a modus ponens logical proof, and not itself an infinite regress. Fun!)

Proof 2:
1. If B then C
2. B cannot be known to be true
3. C cannot be known to be true.

AND SO ON. Why am I harping on this? What is the issue?

If someone’s worldview depends on a premise that is the conclusion of a proof that contains an infinite regress, then everything they believe is illogical. What? Crazy, right? That’s not to say what they believe may not be true—it may. But they would have no way of knowing, because they could never prove it. So everything they believe is logically suspect. It could all be false, and whatever they believe to be true and false, no matter how logical the individual proofs for those beliefs may be, is ultimately grounded in uncertainty—feet firmly planted in mid-air.

And now, to make this real:

Everyone who believes in the modern conception of the Multiverse, or any other variation on the belief that this universe is infinitely old, believes in something that is logically entrapped with an infinite regress. Even one modern formulation of the Big Bang Theory claims that the matter existed since eternity past, and that it was only time itself that began at the moment of expansion, so this too is a belief in a universe with infinite regression.

It would be easy to offer a thought experiment to say that if the present state of the universe (i.e. the existence of reality itself) is dependent upon Multiverse theory, and the Multiverse’s past is infinite in duration, then by going into the past you could never reach the beginning—or put another way, if you started from the beginning, you could never reach the present day. Since the present day has been reached, we know that an infinitely old universe with a linear timeline (the only way out of the conundrum is a circular, eternally repeating timeline—which wouldn’t be infinite) cannot exist. Anything that exists and has a beginning must be of finite age. But you can use a logical proof to show that an infinitely old universe can’t be true, by utilizing the power of the contradiction. Any logical proof that uses premises that lead to multiple conclusions that contradict each other can’t be true.

1. Each state of the universe is dependent upon the previous state.
2. Nothing that is dependent on something else can be its own cause.
3. Everything that exists either depends on a cause, or must be a-causal.
4. The Multiverse Theory requires that there is an infinite number of preceding states of the universe(s), going backward in time.
5. The end of an infinite sequence can never be reached by linear progression.
6. The end of a sequence of time going from the present toward the past would be the beginning.
7. Due to 4-6, the beginning of the multiverse can never be reached.
8. Due to 1-3, the Multiverse must have a cause.
9. Everything that has a cause has a beginning.
10. Due to 7-9, the Multiverse both has a cause and has no beginning.
11. Due to 9-10 and the Law of Non-Contradiction, Multiverse Theory must be false.

The universe can’t be self-causing, because that would contradict point #1, which is based off of experience that we all share—everything that happens is the result of something else preceding it. It doesn’t “just happen” on its own. All our actions happen because of our choices. All thrown objects fall to the ground. Reactions happen after actions, never before, or simultaneously.

The universe also can’t be self-existent, because then it wouldn’t have a beginning. And if it doesn’t have a beginning, it can’t be infinite in duration. Think about it. You can keep walking along the beach, drawing a line that never has to end, but if you draw a circle, it has no beginning and no end but it will never be longer than the line. The irony is that whereas a temporal universe is never actually infinite, only a temporal universe (one with a beginning) can approach infinity, whereas a self-existent universe (modeling time with a circle) will never be infinite, only endlessly repeating. It’s not the same.

Why do people want to believe that the universe is infinitely old, anyway? Or self-existent, or self-causing?

It’s because everything that doesn’t cause itself, and has a cause, must have a beginning (point 3 and 9 in the proof above). And before that beginning, when that thing did not exist so as to cause itself, something else must have existed in order to cause it.

If that thing is caused by something else, then the same conundrum exists for it. This is the problem with Multiverse Theory. This is its infinite regress. If you can never get to a thing which does not depend on something else, going back unto infinity, then the universe could never be caused. Then it wouldn’t exist. But it does exist. So it must have a finite beginning, and cannot have an infinitely regressing series of causes lying behind it.

So it must have an acausal origin. Something that did not come into existence, and yet was in existence—something self-existent (distinguished from self-causing).

The only ‘thing’ that falls into this category in all of human experience and thought is an eternally existent Creator God. People insist on an eternally old universe simply because they don’t want to acknowledge the consequences of God being behind the universe. If He made it, then He has the right and the power to make rules for us to follow and to punish us if we disobey them. The idea of punishment galls people who want to live life the way they prefer, without consequence for living discordantly with a divine authority. So the root of the reason why people insist on believing something that isn’t logically possible is pride. Arrogance. Hatred. Lust. Did you think it would be anything else?

But critics claim that belief in God is circular reasoning. “You believe in God because the Bible tells you, but you believe in the Bible because it’s the Word of God. Contradiction!”

This is easily dealt with, but philosophical discussions of epistemology (how we can determine truth) see this argument revisited. Christians believe that God is the author of logic, and consequently we see no problem with using logic to prove things about Him. But an unbeliever might gripe that trying to use logic to prove God is circular—that we’re merely assuming that God is logical because we want Him to be, and meanwhile, logic is a tool that belongs to the unbeliever who esteems himself more intelligent than those dopey Christians.

And that’s where we get to the question of circular reasoning. There are actually two types. I’ll use the terms “baseless” or “mere,” and “transcendental,” to refer to these two types of circular reasoning.

Here is an example of the former, baseless circular reasoning.
1. I don’t believe in God because there’s no evidence for His existence.
2. I don’t believe there’s evidence for God’s existence because I haven’t looked.
3. I haven’t looked for evidence because I’m convinced God doesn’t exist.

There’s no separate conclusion, because each statement is a conclusion in itself. That’s what makes the circular argument ‘baseless.’ It is merely the bare assertion of unsupported statements. Now, bare assertions are not always circular reasoning. A valid logical proof can use bare assertions.

1. If God doesn’t exist, I won’t believe in Him.
2. God doesn’t exist.
3. Therefore, I won’t believe in Him.

That’s a bare assertion in point 2, but it’s a valid modus ponens logical proof. In order for an argument to be circular, the premises have to flow into each other in the way that I showed above. You don’t believe in God because the Bible has errors? Have you read the Bible? Oh, you don’t bother reading the Bible because it has errors! It really boils down to,

1. I don’t believe in God because I reject the Bible.
2. I reject the Bible because I don’t believe in God.

Most unbelievers hardly make it this easy, but this is as viciously, baselessly circular as you can get. And it’s what’s ultimately at the core of every nonChristian’s beliefs, on one level or another. And with such an illogical construction at the very root of their beliefs about everything, it’s no wonder nearly nothing they say or believe makes logical sense. Foolish decisions have consequences.

But even so, circularity is necessary for a person to have consistent, logical beliefs.

How? After what we’ve just seen, it seems utterly devastating to one’s ability to reason. Ah, but if you don’t have circular reasoning, you are instead left with unsupported assumptions. And what is an unsupported assumption, but a statement without a reason for believing it? In other words, everything you believe must have a reason for it, down to the axioms. Yes, even the axioms, which are premises that are not given justification for in logical proofs.

What I need to impart on you here is that axioms are not proven in the proofs they’re introduced in. BUT, they must ultimately be proven, otherwise, by definition, it is unreasonable to accept them as true. Think about it. It makes sense. But how do you prove axioms? Well, you do it with other axioms. So you have to somehow have the starting premise of one proof be the conclusion of another proof, and the starting premise of the second proof be the conclusion of the first (for a simplistic example), so that they link together and justify each other.

Here is an example of a circular proof that is not baseless:

1. If there were no laws of logic, we could not make an argument.
2. There are laws of logic.
3. Therefore, we can make an argument.

Note that it isn’t a bare assumption, because in the very act of making this proof, we are using laws of logic. The proof itself is the logical syllogism known as modus tollens. And the best part about it is that any attempt to refute it must fail in one of two ways. 1) the critic must abandon the use of logic, and therefore lose--because the only way to prove something is to use logic, and so by abandoning logic, the critic can't disprove the proof. 2) the critic must use logic to argue that there are no laws of logic, thereby contradicting himself, and therefore lose. There is no way to refute this argument. That’s what makes it a transcendental logical proof. It is circular logic, but it is sound logic.

Isn’t that bananas?

Here’s an example of what I proposed above, about interlinked axiomata:

Proof 1.
1. God’s nature is logical.
2. The creation reflects the Creator.
3. The creation will operate along logical laws.

Proof 2.
1. The creation operates on logical principles.
2. If nothing with a beginning causes itself, logic in the creation must derive from the creator.
3. Nothing with a beginning causes itself. [this refers to yet another proof; consider the long one above]
4. We can extrapolate that God’s nature must be logical.

This is veeery basic, and refers to implied premises more than once (meaning that this can be expanded and really teased out in great detail) and more can be done to flesh these out, but as you see, as you go along, new axioms will spring up, that refer to other proofs. Ultimately, they all interconnect and justify each other in what would be unfair to call “circular” reasoning; a Möbius strip is more appropriate.

The most transcendental of all arguments is this:

1. If there was no God, who underpins laws of logic, uniformity, senses, etc, then we could not reason at all.
2. We can reason.
3. (Using this reason, we can conclude that) there is a God who justifies our ability to trust logic, uniformity of nature, and our senses.

The bad way to argue against this is to argue against the statement that “we can reason.” You’d lose.

The better way to argue against this is to argue against God being the source of logic, consistency and reliability of our experience of the universe, etc. It’s still a lousy argument to make, because as can easily be shown, an unthinking universe of random chance that can’t be proven to have even begun to exist, without invoking God’s agency, cannot support the notion that we can trust our observations and inferences about the universe to be reliable.

Attacking God as the author of reason undermines your ability to reason logically.

So you’re faced with two options in building your world-view. Do you take the route of infinite regress, which is self-destructive? Or do you take the route of transcendental circular reasoning? Do you climb out of your shell and experience the discomfort of resting your confidence in your ability to reason on something other than yourself (which would be illogical anyway, since assuming you know how to reason and justifying it with your own memory of having reasoned correctly is the epitome of mere circular reasoning)? Or do you, as just parenthetically quipped, resort to lesser forms of circular reasoning that don’t lead to truth, only futility?

It’s amazing what you can do with your mind. You can, by refusing to accept inescapable truths, condition yourself to be incapable of thinking logically, so that your thoughts over time become characterized by wrong beliefs, foolish choices, and sheer stupidity. What you don’t want to believe can hurt you.

Free your mind, man. Submit your philosophy to God and He’ll take you to logical heights you never dreamed of.

Not to mention saving your soul from Hell by taking your sin upon Himself as your willing substitute if you repent in faith and seek His forgiveness.

~ Rak Chazak

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