when it comes to discovering facts of nature general human intuition that one can appeal to has a pretty terrible track record. most advances have come from counterintuitive leaps by a handfull of geniuses.

If we say everything has a cause people like Dawkins say, "OK, then God had a cause", blah blah blah.

Here's an interesting article on Einstein and intuition:

http://www.mtnmath.com/whatrh/node107.html

Intuition and intellect are not mutually exclusive. Intuition inspires intellect, intellect informs and corrects intuition. Both are necessary for knowledge.

Nice explanation.

interesting in that in the case of QM einstein's intuition led him incorrect conclusions?

human intuition and facts about the workings of nature more often than not are. way more often. as i said most major advances have been decidedly counterintuitive.

when it comes to nature human intellect/intuition are worthless unless informed by empirical facts. in the case of an AI there are no facts available.

it's funny to be discussing infinity in this context since we don't even know what spacetime is or how an AI would apply to it. craig is just in way, way over his head here as usual, pretending simplistic human intuition-based philosophy has ever had any correlation to the empirical facts underpinning nature - trying to appeal to morons that know nothing about science.

Googled some interesting quotes:

It is through science that we prove, but through intuition that we discover.
—Henri Poincare

There are children playing in the street who could solve some of my top problems in physics, because they have modes of sensory perception that I lost long ago.
—J. Robert Oppenheimer

Intuition will tell the thinking mind where to look next.
—Jonas Salk

The neural processes underlying that which we call creativity have nothing to do with rationality.
—Rodolfo Llinás 75

I wonder why I wonder why. I wonder why I wonder. I wonder why I wonder why I wonder why I wonder!
—Richard Feynman

I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.
—Galileo Galilei

Research is what I'm doing when I don't know what I'm doing.
—Wernher Von Braun

All new ideas have an element of foolishness when they are first conceived.
—Alfred North Whitehead

Edit: I REALLY like Von Braun's quote - he nails it as it pertains to cutting edge science

Well you gave me quotes of people who attributed those beliefs to them. When I went to the source material the actual quote from halbert was definitely not saying that. As I pointed out earlier, the quote you cited was incomplete and out of context - in that paper, hilbert was speaking of the mathematical concept of infinity for one. His "no basis in reality" remark was contrasting the "new" approach with formalizing infinity with the older, flawed (and intuitively based)ones.
Does the number four? Pythagoras' theorem? Circles?
I'm not citing failure in some cases - I'm citing failure in this specific case! hilbert's hotel (among other "paradoxes" of infinity) demonstrates that our intuitions fail when we try to predict the properties of the infinite based on "what makes sense". This is what hilbert was referring to in the paper your citation quoted - we have to use the formal tools of maths to understand the infinite since our experiences can provide no intuitive grounding (the way they do for basic number theory, for example).
Me neither - but when we learn that quantum weirdness means our intuitions about matter, time and space are screwy (for example) he's not going to look kindly on an argument based on an intuitive understanding of those concepts. We now know our intuitions about time are wrong - any arguments involving time should be updated to reflect our new understanding acquired through physics. The same is true of the infinite - gallileo got close to overcoming his intuitive thinking, it took the genius of cantor to push through the "paradoxes" and to realize that they were, in fact, just peculiarities and not contradictory at all.

nice bunch of irrelevant quotes there. WLC is making an empirical claim based on philosophical intuition. he's not using intuition to look for a direction for physical research.

anyway many more "intuitive" scientific theories turn out to be wrong than right, so there's no point either way here.

he does seem to have a firm grasp of the obvious.

I don't think all of our intuitions about time are wrong. Those that matter in real life work fine. The fact that weird things might happen at the speed of light doesn't invalidate the normal experience at the level of everyday life. We can and do use simultaneity for many important tasks.

A word about Hilbert. I don't know what he thought about actual infinities. I believe the quote I gave indicates he had doubts about it. Nevertheless, his understanding of AI and the motive for the Hotel are not central to Craig's argument. He uses other illustrations without reference to Hilbert and I don't know that I've ever heard him appeal to Hilbert as evidence that AI is absurd or even that Hilbert himself meant his Hotel that way. If he does do that and he's wrong about Hilbert, that still doesn't invalidate the Hotel or other similar examples as illustrations of our intuition. If you don't have that intuition then the KCA doesn't speak to you. The KCA is just one theistic argument, and for that matter, arguments themselves are not central to Christianity.

I do have the same intuition (or did, anyway before I studied infinity). What hilbert's hotel demonstrates is that I shouldn't rely on it. Thinkers as great as galileo were led astray by their intuitions.

I think in such a situation (where we know intuition leads us to make errors) we have to rely on the experts if we don't have the time to learn the topic ourselves. The experts on I finite are mathematicians.

They're still wrong (even if they are useful, they're not true). Newtonian physics works fine in everyday life, despite being definitely incorrect. Whereas it makes sense to build bridges without regard to relativistic considerations, can the same be said for speculations about the creation of the universe? Our best theories suggest that quantum weirdness/relativity had much more significant roles in the early universe. A putative account of such based on what we've learned from catching baseballs gives us no reason to think it's correct.

But the Hotel is just an illustration of something - it is not itself a demonstration that our intuition is wrong. There is no empirical evidence that an AI is possible(or impossible). So why can't the Hotel be an illustration that our intuition is correct? Given that both Hilbert and Cantor seemed dubious about an AI.

I'm not aware that anything in relativity or quantum mechanics detracts from any theistic argument.

All good quotes. Feynman's is funny. Like a limmerick. Whitehead's is good, too.

They are never going to be able to explain the spark (spirit) behind consciousness before they reveal more sophisticated layers of design behind human beings. Even Chomsky says humans appear to be designed for language. Jochnowitz quotes him as saying:

"The fact that all normal children acquire essentially comparable grammars of great complexity with remarkable rapidity suggests that human beings are somehow specially designed to do this, with data-handling or 'hypothesis-forming' ability of unknown character and complexity."

http://www.jochnowitz.net/Essays/ExtremistPolReg.html

Note: link provided as cite for quote. I'm not intending to derail thread by discussing link, thx.

Because infinity is well understood axiomatically and has been demonstrated to be consistent. Intuition, in this context, is just inference from what we know to a previously unencountered situation - in this case an improper inference from the finite sets we have experience with to the infinite sets we've never encountered.

Our intuition is that a set cannot be placed in one-to-one correspondence with a subset of itself. In actuality, this is only true of finite sets - infinite sets do have this property (which results in the union of two disjoint infinite sets sometimes being the same size as one of them - ie an infinite hotel with no empty rooms could accomodate an infinite number of new guests - the fact no such hotel exists doesn't change the truth of that conditional).

EDIT: Also - Hilbert wasn't dubious about the existence of an actual infinity. Read the actual paper that quote came from - if there is a real distinction between actual infinity and a mathematical infinity, Hilbert was speaking of the latter. The quote was also chopped - the complete quote (in context as the conclusion to his talk) was a statement that previous attempts to formalise the infinite had failed but that the new approach had been a success.

Suppose we have a line segment we can divide into infinite segments. Can we really say we're recognizing an infinite set of actual segments that already exist, or are we simply creating segments by dividing the line? If the latter, can we really say what we're talking about is an actual infinite, or isn't more just a potential infinite?

I'd argue that the set of natural numbers, (1,2,3, . . .n, n+1, . . .) is a potential infinite, not an actual infinite, because we're just creating the numbers with 'n+1' in a similar manner as we create an infinite set of segments by dividing the line.

So I'd distinguish infinites by saying a potential infinite is created by adding, dividing, etc., whereas with an actual infinite the segments are actual existents that aren't created but simply labeled through an infinite labeling process.

If the Hilbert Hotel is an actual infinite, then rooms aren't created (n+1) as a new guest arrives as with a potential infinite. The rooms are actual existents and what we're doing is an infinite labeling process for room numbers. However, creating a new label would not seem to create new room.

And if you say everything has a beginning, the same people will direct the same requirement for God... Nothing has changed.

I think it's the former, same as with the natural numbers. Mersenne primes existed before we thought of them. Other mathematical objects we haven't yet discovered have the same properties, structures and interrelationships we will eventually learn. We have no choice about these things - they are there, they're real and they have an objective existence quite separate from us.
The approach you're talking about seems like constructivism to me (though it's been many, many years since I read anything on it). I didn't find any of the arguments for it appealing, to be frank. I'm a relatively extreme platonists - the epistemological problems being something I'm comfortable with given my theism and dualism.

Correct me if I don't remember correctly, but aren't fractals examples of actual infinities in the universe?

Nah they don't retain their fractal structure at molecular levels. They are just a useful approximation at larger scales. (assuming you mean fractals existing in the sense of clouds or coastlines. In my view, of course, they do exist. Notready is claiming a distinction between maths objects and "real" objects)

In one of our classes we were having a discussion about fractals (2 years ago) and our professor was saying that some people regard them as examples of... something like "infinite structure in finite space". I might be totally reconstructing.

There are similar results regarding fractals as arise from Hilbert's hotel and perhaps this is what he was referring to.

If you consider the Koch curve (for example) you find a closed curve with infinite length which circumscribes a finite area. Craig or NotReady may be tempted to cite this as evidence that a Koch curve can't possibly exist 'in reality' as it leads to absurdity. In my view, this is illustrating the problems with extending finite intuitions to infinite settings - the infinite just behaves strangely.

If you take the curve 1/x with a domain from 1 to infinity and rotate it about the x-axis, you will end up with a tapering 'funnel' which has infinite surface area but finite volume. Meaning you can pour in a finite amount of paint and paint an infinite surface.

There are many results like this - what I am arguing here is that such results don't mean we should conclude "Oh well they must not exist then". Rather they say "If we want to know the properties of anything 'infinite' we better not rely on our commonsense intuitions. Screwy things happen with infinity".

Similarly, I don't think that the relativity paradoxes imply that relativity must be wrong. They imply that when considering things moving near the speed of light or the curvature of spacetime, we shouldn't rely on what our everyday experiences tell us. We know that bizarre stuff happens, so we will do better to trust the maths.

"Begins to exist" is a huge qualifier. Think of it this way, a universe that is said to be eternal (much like it was thought to be for most of history) would not be addressed by the KCA.

So the standard CA does not imply "begin to exist" as it is possible that certain things have always existed. Much like some people believe sets and abstract objects have always existed.

And those "same people" will be told for an actual infinite time that there's a difference between a definition and a judgement, e.g. 'a square is a polygon with four equal sides and angles' is not a judgement; it's a definition. That 'a first-cause is its own cause' is the definition of a first-cause.

Do you consider '2+1' to be a discovery of 3?