Well this is what I'm asking NotReady for. The best I can find from Craig directly is "What's infinity minus infinity?" the link NotReady posted earlier (though for the Hilbert quote, not for the content) kind of spelt out this argument more - not sure if it's Craig's or not. Essentially it goes:

If you take an infinite set, let's say the numbers (1,2,3,...) and then subtract the infinite set of odd numbers you get (2,4,6,7,...) which is also an infinite set. However if you subtract the same sized infinite set (4,5,6,....) from the original you get the finite set (1,2,3). In other words Infinity minus Infinity sometimes equals Infinity and sometimes equals three - since you can't get two contradictory answers to the same question this is an absurdity.

Presumably there's something better there (the link posted continued, believe it or not with: "While we can avoid these contradictions in the mathematical realm by making up rules like you can't subtract or divide when using infinity, we cannot in the real world prevent people from taking books out of libraries.") however I havent yet seen it.

The 'distinction' between broad logic and strict logic smells like a dodge to me - especially since I havent seen any explanation of what it is beyond examples (which seem incorrect to me anyhow - or at least make it in no way clear which form of logic is taught at universities). Craig references this so often on his site, I figure he must have put something more persuasive together somewhere however all I could find was repeated statements that actual infinities lead to absurdity.

Irritated I guess, but not mad - I'll send you a PM...

I do appreciate the effort. Cheers

What's the difference?

EDIT: In response to how so? I guess it might not - I was referring to those formulations I've seen which have been fleshed out and which include it as a premise. My whole beef is with this premise of course - ultimately I think God does exist but that we can't know it, so I don't particularly care whether the Kalam Cosmological Argument works or not. My original contribution to this thread was spurred by "What's infinity minus infinity?" - I don't think Craig is trying to logically prove God's existence in his debates, in fact I don't think he's even trying to persuade anyone. I think he's trying to appear as an intelligent Christian able to hold their own against smart atheists so that believers can feel comfortable thinking that "it all makes sense to smart guys like Craig - I don't have to worry if I get confronted with a curly logic question."

This says he hasn't bothered to learn any of the math involved.

Bolded mine - ahahaha. I mean, you're a very gracious guy bunny. But at some point don't you have to conclude "this guy doesn't exactly grasp the concept of infinity?" It seems like the more bad arguments you read, the more convinced you are that there "must be something persuasive" in there somewhere. When I see a couple of these I just conclude the author has no credibility.

In case it wasn't clear - that quote wasn't from Craig it was from Michael Horner. I don't give him any maths/logic credibility at all, I figure he's paraphrasing what he's read elsewhere or parrotting something back poorly - I'm quite sure he doesn't understand infinity and would even go further to say he doesn't understand maths. (The less charitable alternative being that he is being dishonest).

In Craig's case, however, I agree with NotReady that he takes time to understand opposing views and tries to ensure his theology is consistent with our best scientific theories/understanding of the world. I do think he engages in obfuscatory debate tactics and I also think he has probably opined on some topic without fully understanding it - this example may well be a case in point. Nonetheless, I'm willing to give him the benefit of the doubt - more out of respect for NotReady than anything else, to be frank.

If Craig doesn't have anything more than repeated assertions then I will certainly lower my rating of him as an intelligent and logical apologist.

Wait.... is this a level? (That is a serious question by the way)

Not at all. I think NotReady is one of the best theist posters on RGT (he was definitely the best in SMP even if he doesnt participate so much anymore - call it residual credit). I've certainly got an enormous amount out of discussions with him over the years and although I haven't read much of Craig's stuff, I am willing to trust NotReady's judgement as to his goals, methods and approaches given our past interactions.

In my opinion, it helps to bear in mind that one of NotReady's underlying premises is that the Christian God definitely exists and communicates infallible truths to us through the bible in a way we are able to understand. Granting that for the sake of a discussion can prove fruitful, even if I ultimately don't share his certainty in God's existence, nor his confidence in the bible and our ability to interpret it.

Fair enough... I find your opinion very surprising.

Sorry, I haven't been following too closely.

He may take time, and he may try, but I don't think he succeeds well in either case. I mean, he says the basic perspective of atheists is that the universe is a horrible void, and many of his premises contradict the leading interpretations of modern science .

Fair enough, I suppose.

Is this in his debates though or his 'scholarly works'? As you said quite early in this thread, his debates are not about constructing sound arguments. They are about winning in the eyes of the audience.

Grudgingly, I have to agree. NR has been one of the more consistent religion posters on 2+2.

Touche.

(Sometimes I worry that someday I'll try to say that and instead call someone "douche" by accident.)

from Henri Bergson's An Introduction to Metaphysics:

"Philosophical empiricism is born here, then, of a confusion between the point of view of intuition and that of analysis. Seeking for the original in the translation, where naturally it cannot be, it denies the existence of the original on the ground that it is not found in the translation. The method is analogous in both cases; it consists in reasoning about the elements of a translation as if they were parts of the original."

"Thinking is to go from concepts to things; intuition is to go from things to concepts. Reality is revealed through intuition, not analysis."

I'm really quite confused by this discussion. For example, does it make sense to say: "The universe has a (spatial) boundary"?

I wouldn't think so. To have a boundary you need an 'inside' vs. an 'outside'; and why wouldn't the 'outside' always also belong to the universe?

And if it's absurd to say the universe is bounded, surely it is infinite?

The surface of the earth is neither bounded nor infinite. It may require higher dimensions for the universe to have this property but it isn't inherently contradictory.

I took propositional calculus years ago and haven't used it since then, so let's see how I do here

I think there are a few inconsistencies in the way you defined some of the propositions below and from that some of the XORs were also wrong.

I would change (q) to "not everything which begins to exist has a cause."

From this, we have to make some changes here as well:

Why did you change (q) here? In your first formulation both (p) and (q) start with "whatever begins to exist", but here Q starts with "something does not begin to exist". Here's how I would phrase it, based on the change I made in (q) above:
.
1.4 With q: (q→ q') if (q) something does begin to exist, then (q') there may or may not be a cause or reason why something exists.

From here we get "There is necessarily a cause or reason why something exists XOR there isn't necessarily a cause or reason why something exists.

Say all your reasoning is correct. Substitute "universe" with "God" in the above logical operations and tell me how you don't reach the same absurdities. People who invoke the cosmological argument reach a point in which they have to assume a changeless, timeless, spaceless, all-powerful being to resolve the alleged absurdity, without realizing that that being itself requires the same amount (if not a lot more) explanation as the universe itself. And notice that positing the existence of God in no way logically follows from the argument, even if we assume that it is true. It is a form of argument from personal incredulity: "I find a contradiction if I assume that the universe always existed, so it must have started to exist at some point. But how can something start to exist without having a cause? I cannot think of anything else other than there being a God who created the universe. Therefore, God exists."

As I said in the previous post:

I don't get it. I mean, I know a sphere has no 'boundary' in the mathematical sense, but clearly the surface of the earth is a bounded physical object.

Also, why wouldn't the higher dimensions invoked to 'bound' the universe themselves be part of the universe?

This is not true. Extra dimensions (beyond the 3) are not required for the universe to be like the surface of the Earth in that sense (compact in Euclidean spaces).

It is allowed based on topology and nothing from physics has convinced anybody that it is impossible for the universe. We don't know if it is actually correct, but I can't think of any good arguments against it.

Hmm. I can certainly reconcile 'without boundary' and 'finite' in bunny's example.

But I only seem to be able to do this because any 3-manifold embeds in a canonically infinite space; so 'finite' has a well-defined meaning. (I.e. there are coordinates outside the manifold.)

The thing that confuses me: How can it ever be well-defined to say something is "outside" the universe?

Most likely, it's that there are different senses of the word "universe" and some do not admit an "outside" whereas others do.

That's fine. I just wanted to make sure that we were meaning the same things with the words that we used.

That's what you called them earlier. And I guess what I'm reading is that you're drawing an arbitrary line about what constitutes authority and what doesn't. There isn't anything inherently wrong (because the line must be drawn somewhere), but it does show intellectual bias. Let's recall the two statements that I compared at the start of this discussion:

I claimed that these are both appeals to authority, and that they are at the same level of appeal. He's saying that the scientific community has not accepted the idea of an infinite past for our universe and you're saying that the scientific community has not accepted the claim "Out of nothing, nothing comes." Neither of you have presented any argumentation in favor of these claims (nor cite any specific evidence), and so you're both doing the same thing.

At what point is he appealing to experts' intuition? You keep going back there, but as far as I can tell, I was the one who introduced the notion of intuition, and that was in reference to getting the audience to accept an argument. At least as far as the issues I've addressed, I do not see anywhere that a scientist's intuition has been called upon.

See above. I don't see anywhere that Craig does not allow one to challenge his appeal. Nowhere does he say "The universe has a beginning because the scientists say so, and who are you to argue against the scientists?" In fact, he even offered that there were other theories of the beginning of the universe within the scientific community, but that those theories did not gain acceptance. So it's not as if the claims about the big bang have gone unchallenged in the past.

In the rest of your paragraph, you go back to scientists' intuition, and again I don't know where you're getting that from.


So what else is new? Your belief in the universality of gravity is based on scientists' views. This is what I mean by intellectual disingenuity. Human belief systems are a subset of human thought, and therefore any argument about anything about the nature of universe will be within the realm of human thought. How is it possible for a theist to argue "above" the level of human thought and have a coherent argument understandable by human thought? Essentially, you are setting an impossible standard that must be met by the theists.

The only arguments that can sidestep the observational aspect of this are arguments for God on the basis of logical necessity (ontological arguments). But as I've expressed (and I think most people would agree), those arguments are not particularly persuasive.

I tried to explain myself earlier, but I didn't manage to very well I guess. The point I was trying to make when I mentioned the scientists and philosophers was that when he invokes authorities, he does it as if all of them are unanimous. I criticized this by saying that even if we accept his argument from authority it's still wrong. If he hadn't appealed to authorities, I wouldn't have mentioned scientists and philosopher at all.


When he was talking about mathematicians recognizing that an actual infinity is impossible. He did mention certain arguments like Hilbert's paradox (which in my opinion is also a matter of intuition, rather than an actual argument against the existence of actual infinity, as is being discussed by others itt) but all the other arguments he used were pretty much based on other authorities' intuition.

I guess we won't agree on the fact that the existence of God cannot be treated the same way as other scientific theories, so applying those standards is ridiculous. I will ask again, if those views change, do you think Craig would admit that the arguments for the existence of God are no longer there? If the answer is 'no', then his arguments are unfalsifiable and therefore meaningless. Scientists, on the other hand, would not have a problem giving up theories if they are falsified (that is the goal of science after all: falsifying theories and replacing them with better ones).

P.S. I want to put the focus back on the other fallacies: why is he making them while his opponents aren't (or making them extremely rarely)? That was the main purpose of my thread, not discussing the individual fallacies. As I said, I just put them there in order to not appear as if I am not backing up my claims.

With the advent of terms like "multiverse" I think it's safe to say that "universe" now means "that which is available to make inferences about."

It's easy enough to adapt a perceptual model of "the universe" by inserting something external to it. This is especially true if by "the universe" we mean "that which is currently available to make inferences about," and we posit something that we may be able to make inferences about only in the future.

At least as far as the example presented goes, it's the question of "Why is there something instead of nothing?"

Now this question has no definitive answer, at least as far as I know. So he leads the listeners through a series of observations:

1) (Intuitively) An infinite past is absurd.
2) (Scientifically) The universe has a definite beginning.
3) (Intuitively) If you start with nothing, you end with nothing. (As an aside, the word means a true nothing, not just a vacuum or something that assumes the existence of spacetime).
4) Therefore, it is reasonable that something started the universe.

I have a hard time getting a sense of what the "error" is. You may disagree with the intuitive statements, but that's not really an error in the argument, that's merely a rejection of the premises (since those intuitive statements are indeed premises).

So I guess I don't actually understand your criticism.

By the Hilbert paradox, do you mean the Hilbert Hotel? I'm not really sure you want to be calling these things mathematical intuition. The terms can be well-defined in the strongest mathematical sense as a one-to-one mapping from the set of natural numbers to the set of natural numbers except 1.

And none of these comments speak to "actual" infinity (which is NOT a well defined mathematical concept, but rather a statement about the "actual" universe). I haven't read the back and forth on this actual infinity business, but I will say that in a strict sense, mathematics says NOTHING about the "actual" universe. Rather, it exists in its own world of models and assumptions.

It depends on whether the scientific theory is a CENTRAL piece of the argument, or if it's a supporting non-contradictory statement. For example, in the argument that we've been discussing, it is not NECESSARY to invoke scientific theories of the universe in order for the argument to proceed. Fundamentally, it's the intuitive statement that an infinite past is an untenable idea. The fact that science supports instead of rejects this is merely something to strengthen that position.

It *IS* important that the scientific theories are in non-contradiction (for example, scientific theories are in contradiction with a young earth creationism, and this undercuts the credibility of young earth creationism), but it that the universe has a beginning not strictly DEPENDENT upon a scientific result.

I will have to sit through the debate to see whether I agree that his opponents actually do not invoke the same "fallacies" as Craig. But I will note here that when I listen to their arguments, I will be looking at them with the same level of criticism as you hold Craig. I've already expressed my expectation, but for the sake of practice and argument, it would be interesting to see you summarize his opponents' positions in the same way that you've summarized Craig's, and see whether they do conform to similar patterns of argumentation or if Craig's are objectively different in the way that you suggest.