Yet it's an idea. I'll need to read what Hilbert says because I can't see how a mathematical idea can fail to provide a legitimate basis for rational thought either. I appreciate the reference though.
Yeah I understand - I just haven't seen any demonstration of that, merely an assertion. (And Hilbert doesn't give it to him with "infinities don't exist". Having said that, see my above comment - 'can't provide a basis for rational thought' may well give it to Craig, though Cantor will be distressed).
Of course - but the comment you made was about my reference to different types of infinities with a (presumed) implication that I was being inconsistent. This:

"I think an infinitely divisible continuum is logically possible, but not physically possible in our universe (given quantum discreteness and all that jazz..) "

Is consistent with this:

"Is it inconceivable for the universe (not just the bits we can see) to extend infinitely? With an actual infinite number of stars? I don't see what's impossible about that."

(If you weren't ever challenging that, well then I misunderstood, so sorry again.)

Something from Cantor:

This link was pretty poor, I don't know if you've read it, but it provides a neat demonstration (with the infinite library example) of the problem I'm talking about - he regards infinity as 'a really big number' which is an error and is what leads to the 'absurdities'.

Of relevance here is the quote he attributes to Hilbert. If you look at Hilbert's paper (quite good though it's both intuitionist and pre-Godel and contains some opinions Hilbert would have recanted later) you'll see he has actually cut out a significant part:

"In summary, let us return to our main theme and draw some conclusions from all our thinking about the infinite. Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought — a remarkable harmony between being and thought. In contrast to the earlier efforts of Frege and Dedekind, we are convinced that certain intuitive concepts and insights are necessary conditions of scientific knowledge, and logic alone is not sufficient. Operating with the infinite can be made certain only by the finitary.

The role that remains for the infinite to play is solely that of an idea — if one means by an idea, in Kant's terminology, a concept of reason which transcends all experience and which completes the concrete as a totality — that of an idea which we may unhesitatingly trust within the framework erected by our theory."

Hilbert was definitely not saying the infinite was absurd, but rather that Frege and Dedekind's previous attempts to provide a satisfactory grounding of the theory of the infinite had failed and that it was necessary to include finite operations in developing the correct theory of the infinite. He even talks about 'actual infinities' within the paper and explains they are well explained thanks, primarily to Cantor (this paper includes the famous quote "No one shall drive us out of the paradise which Cantor has created for us.") He does maintain that no actual infinity exists in nature - but as I have been stressing, this does not establish that it is absurd, nor impossible (and relied on some probably out of date physics research, given that it was published in 1927 - as I understand it, the question is open).

Having said all that - it doesn't really matter to the Kalam argument, since what's required there is that there has not been an infinite number of past events - something arguable from the Big Bang theory together with quantumness of the world I suspect.

If it's true that infinity can provide no basis for rational thought, he'd be distressed. It doesn't matter if he thought (like I do) that there are no actual infinities.

I'd need to read cantor directly to understand his last comment - I don't accept that he thought the set of natural numbers was not "truly infinite" as that quote seems to imply. It's conceivable he was as wrong about that as he was about the inconsistency of infinitesimals.

You keep saying infinity whereas the quotes I gave are about the actual infinite. I see a similarity here with the idea of imaginary time as used by Hawking in his theories - there is no real imaginary time, it's just a mathematical idea which allows working with concepts, but it isn't something that is ontological.

As for the two papers, I didn't cite them for their content, but for the quotes.

It does matter. The Big Bang could fall tomorrow. The KCA was devised hundreds of years before the BB.

Craig relies far, far more on the philosophical argument for KCA (which includes actual infinite) than the BB. The BB is just gravy, something that seems to support premise 2, at least for now. I find the philosophical arguments far more persuasive and reliable than the BB approach.

Thanks for the effort. It's appreciated.

Im going to say it again. I really really really hope the answer to how we got here is an infinite regress of creator Gods. It will screw everyone.

I will claim again, with regard to *, that if you were to give his opponents the same treatment, you would reach the some conclusion. That you would present it as you have smells like a strong intellectual bias.

If he claimed that he was going to present a formal deductive argument for the existence of God, and he has done something other than the standard ontological arguments (which I don't find particularly convincing, as I'll explain below), then this is a very clumsy error.

I'm addressing the criticism insofar as it is appropriate and legitimate to appeal to authority in this type of debate, and in many arguments. What is going on here gives the appearance of intellectual bias as above. For example, if he were to question the age of the universe, it would be appropriate (and sufficient) to claim that cosmologists have computed the age of the universe and found it to be close to 14 billion years old. It would not be necessary to present or even mention or even understand the details of how such a conclusion was reached. This is directly an appeal to authority.

I've never claimed it wasn't an informal fallacy. I'm pointing out that informal fallacies are not necessarily errors of reasoning. Whereas you seem to be holding the idea that if it's an informal fallacy, it's an error. This is a distinction between a deductive argument and an inductive one. An inductive argument that appeals to authority is resting upon the past credibility of the person or persons to successfully fill the gap of the argument.

So I'm not really sure that you understand the nature of these types of informal fallacies. Here's a short wiki-summary:

http://en.wikipedia.org/wiki/Argument_from_authority

This is what must be considered when appealing to an authority. Is the authority actually authoritative? You can challenge the authority, but if the appeal to authority is valid, the challenge will presumably be subsequently met by the authority. It's not just presented as the end-all of the discussion, but presumably the one arguing against the authority will not be able to mount a successful challenge against the authority.

This is a strange presentation. Shifting between "showing that" and "asserting that" and the appeal to Behe's intuition basically makes no sense to me. They are both appeals to authority because neither argument actually presents an argument in favor of the position OTHER THAN some smart guys said so.

The word "correct" in that context was not referring to a "correct conclusion."

Again, you must first understand that informal logical fallacies are not necessarily logical errors. Informal fallacies rest upon the actual content of the argument, not the underlying structure of the argument (symbolic logic). This is why I'm so firmly convinced that you are the one who is not understanding the nature of the fallacy. You keep trying to bring it back to a structural argument, not one of content.

For example, the heap fallacy (one of vague definition) may or may not actually be an error. Simply because a heap is not a well defined object does not mean that the argument itself is therefore necessarily wrong. Sometimes, it's the person objecting to the argument is the one who is holding an unreasonable standard of definition.

So you have to take a close look at the content before it can be decided as to whether the fallacy is actually fallacious, and making arbitrary substitutions of words will not reveal what's going on. (And this is what you've attempted to do by introducing the Behe argument.)

I don't find the ontological arguments to be particularly convincing. A lot of it has to do with definitional games and that sort of stuff. Nobody who has already decided that they don't believe in God will be persuaded to change their mind on the basis of an ontological argument. Rather, it serves a role as part of a larger, more inductive system of reasoning, where this is one of many plausible approaches to the consideration of the existence of God.

The philosophical arguments for no actual infinite being...?

This is what I was asking you for - I can't find anywhere that Craig spells out what they are, he just asserts that an actual infinite leads to an absurdity (the only things I could find from a cursory examination of his site were arguments along the lines of the michaelhorner.com article you provided which not only quoted Hilbert incompletely in order to change the context of his comment, but also made the common error of treating infinity as a number).

Actually, he supports the first premise with the principle of sufficient reason*. The 'actual infinity is impossible' proposition is in support of the second premise.

*The principle has a variety of expressions, all of which are perhaps best summarized by the following:

• For every entity x, if x exists, then there is a sufficient explanation why x exists.
• For every event e, if e occurs, then there is a sufficient explanation why e occurs.
• For every proposition p, if p is true, then there is a sufficient explanation why p is true.

I don't think the context was changed at all. The part you bolded doesn't support the existence of an actual infinite but rather the need for infinity as a mathematical concept, which Craig agrees with and argues that though the math system is internally coherent, that is no argument for the existence of an actual infinite. Again, it's hard to see the purpose of Hilbert's Hotel other than to illustrate the absurdity that would result from the existence of an infinite, just as one might construct an illustration to show the absurdity of the ontological reality of imaginary time.

I'm not claiming there are philosophical arguments against an actual infinite, but that the impossibility and absurdity of the actual infinite form part of the philosophical argument for the existence of God via the KCA.

Here's a quote from a Craig article on Oppy about this subject:

Craig makes clear in many places that he uses the theistic arguments as plausible positions, not 100% certain proofs. He shows the absurdities that result from denying premises like the impossibility of the actually infinite or that something can't begin to exist uncaused, and his position is that it's more plausible to believe one way rather than another, forcing the opponent to adopt the negation. The proper counter to Craig is to simply say "I believe the actual infinite can exist" and you can then say you believe no absurdities result or that it doesn't matter if they do or whatever. I can't prove actual infinites don't exist - I can't even prove that absurdities would result. But the point is you have to take the position that they do exist or could, and if they do then they aren't absurd or their absurdity doesn't matter.

If absurdity matters all ideas on how the universe came to be (if it did) are in trouble.

Okay, I will give you that. I might be biased (although definitely not on purpose) and never see any fallacies people who defend the position I am holding make. Having said that, I watched the debate really carefully and was monitoring for logical fallacies in Shook's arguments (as well as Craig's opponents in the other debates that I watched) and I think I did a good job. Now, in order to have a discussion, you really need to watch at least part of the debate and show how there is no significant qualitative or quantitative difference between Craig and the other side in terms of the fallacies they resort to in their arguments. You don't have to watch the whole 2 hour debate for this, by the way. Just watch the 7-10 minute opening statement of Shook and see if you can find any fallacies there (since most of the fallacies Craig made were in his opening statement). If you don't want to do this, I can't request this from you obviously, but your argument that it's not just Craig but everybody (resorting to fallacies) is not justified so far, it's just your opinion.


I rewatched some of the debates and to be fair, he doesn't use the word "formal", he just uses "deductive" on several occasions. I am not being able to fully understand what he means.


That's not necessarily true. For example, whenever Dawkins is being asked about the age of the universe or the age of the Earth, he doesn't simply say "astronomers and geologists computed it..." but he mentions the methods used in computing it (like measuring the Hubler constant, radioactive dating, etc.) My claim was that by taking away the focus from the scientists you are no longer appealing to authority, in that people can look into the methods and have an opinion of their own if those methods are legitimate for determining those ages. When you just mention a name, on the other hand, you don't know if that scientist/philosopher used an objective empirical method to come to the conclusion he had, or if he didn't just use his intuition*. If it's the former, then it's an argument from authority only on the surface, whereas if it's the latter, it is the argument from authority. You have to give the audience the necessary information to know which one it is.

*There are numerous examples of scientists' intuition failing, and I personally don't think it's reliable enough to be cited.


I am familiar with the nature of the argument from authority, I have read about it from other sources as well.

http://en.wikipedia.org/wiki/Fallacy

It's still erroneous to invoke fallacies, regardless of whether they are formal or informal. To be honest, this is the first time I'm hearing anybody claiming that it's not an error to use informal fallacies in debates just because you have limited time. Please give a more detailed justification for this. Also, as I said on many occasions, the people from the other side of the debate don't have the need to use informal fallacies.

I guess this all boils down to what I said in the earlier posts. Arguing for the existence of God is too strong to use scientists as authorities. Since in order for *those* arguments for the existence of God to really work (as I explained before), the authority must be indeed infallible in principle and exempted from criticism.

Well, no, that's what I'm trying to say. When you appeal to their studies, you're not saying "some smart guys said so", but "some guys showed this with objective empirical studies..." Notice that it doesn't matter if the researchers are actually smart or dumb, or whether they are famous and popular in their field. If the study has internal, external, ecological validity, etc. (all logical requirements for a good empirical study), you no longer care about who conducted it.

You're right, the infinity was actually supporting the second premise. This doesn't change much though, since the truth of the argument depends on the truth of both premises.

As for the principle of sufficient reason, it is again a form of appeal to authority. I read the wiki article very carefully and didn't see an actual justification for that principle. So, what reasons do we have to believe that Craig's first premise is correct, other than Liebniz' (and other philosophers') intuition?

I would personally agree with the quote you gave (about the entities, events, and propositions), in the universe today. I don't know if the same principle would necessarily apply to the first cause of the universe, however. Notice that if we apply it to God (assuming God would go in the category of entities), we still need an explanation for his existence. Has anybody ever presented such an explanation?

By analogy to the question "Why is there something rather than nothing?" we can ask "Why is there a God, rather than there not being a God?" Is the answer to the second question obvious or self-evident? Absolutely not.

I agree that I'm not speaking on direct knowledge of this particular debate.

The way I use the words is that "formal" logic is an argument that can be precisely phrased as symbolic logic ("if P then Q; P; therefore Q"). Whereas "informal" logic is a looser argumentation where you cannot get this type of strict formalism.

"Deductive" logic is an argument based on clear premises. That is X and Y are premises, and from this we can conclude Z. It can be both formal and informal, depending on the actual topic being discussed. "Inductive" logic is a logic of building upon observations. We observe that if X happens, then Z seems to follow, and since X is similar to Y, then we expect that if Y happens that Z should follow. In a real sense, it's the difference between going from general to specific (deductive) or going from specific to general (inductive).

You're moving closer to the idea. But even this is an appeal to authority. Why? Because he's not actually *MAKING* the argument. He is leaving gaps in the argumentation that are to be filled in by the knowledge of the authority. This is fundamentally why it's an APPEAL to authority. Because the argument itself is not present.

I think you're taking the intuition to the wrong place. The intuition (in terms of the debate) rests on the audience, not the speaker. It is the speaker's goal to persuade the audience, and this is done by establishing common ground with them. That is most easily done by giving them a statement that they can find intuitively plausible (otherwise the train never leaves the station).

This is not a reference to the intuition of the scientists or even the speaker.

There's a bit of a language thing here. Some would say that "an appeal to authority is an informal fallacy" and I would agree with them as a general statement. Some might also say that "this appeal to authority is not wrong" and I would agree with that as well. I understand the word fallacy to talk about the nature of the argument (what is the complaint that is being raised against this argument?) but not necessarily a judgment on the argument (is it actually wrong?).

My analogy for appeal to authority comes from a strictly mathematical perspective, because math is probably the cleanest.

Theorem: 2^10 - 1 is divisible by 11.

Proof: See Fermat's Little Theorem.

This is an appeal to authority because I did not actually demonstrate Fermat's Little Theorem, so I did not actually complete the demonstration of this mathematical fact. I have made an appeal to a previously completed work that is supposedly valid.

Compare this to the following presentation

Theorem: 2^10 - 1 is divisible by 11.

Proof: Note that 2^10 - 1 = 1023, and that 93 * 11 = 1023.

In this case, there is no appeal to authority. I have made the argument without reference to external authorities on the subject.

An appeal to authority is valid when the authority speaks effectively on the subject. This is because the appeal to authority is supposed to be like citing a reference. "For more information, see X's work." I hope the example above will suffice to explain how I understand it.

This is a really strange criticism, and not the first time you've invoked something like this. Why is it that when humans argue about God, that humans must reach a God-like standard in order to address the question? The question itself lies in the domain of human thought, and therefore the necessary domain of knowledge is also in the realm of human thought.

Again, see above. The appeal to authority happens because the actual argument is not being made in the context of the debate/discussion. Rather, it is an *APPEAL* to some *AUTHORITY* on the subject to fill in the gaps instead of making the argument himself.

I know all these distinctions. I reconstructed the word "formal" and put it in Craig's mouth, while in fact he didn't say it.

Just to remind again that even though most of the fallacies he invoked were informal, some of the them were actually formal fallacies.


Okay, but THIS is something done in order to save time. As long as somebody is appealing to studies, I don't have a problem with the argument. And not all quotes Craig makes are appeals to authority.



The speakers do appeal to the intuition of the audience. But these are two different things. I am talking about the arguments with which he is appealing. Is he appealing by citing studies or is he appealing by relying on other experts' intuition? This is the distinction I am talking about. Otherwise, of course you can't rely on people fully processing all the arguments and empirical study you present them in 90 minutes.



Okay, so I would have no problem with making this argument. Either of the arguments work. The reason I am saying this is because you are leaving a chance to the person you are debating to criticize (falsify) your argument. When you appeal to a theorem, the other person (given he is familiar with it), can say "No, actually this theorem is flawed for this and that reason". But if you don't appeal to the work of a scientist but to their intuition, what can your opponent say? "Well, I don't trust his intuition." And the discussion has reached a dead end, because all you two can do is repeat what you've already said. I was a bit reluctant to give an example because I couldn't find the references and I'm not sure if that's really true, but several years ago one of the physics professors had said that Einstein once claimed that cars will never be able to achieve a speed higher than 30 mph. If we assume that he really claimed such a thing, we can see how even the most brilliant physicists' intuition can fail miserably and it is not a reliable source for argumentation.

Well, because if you base the truth your arguments for the existence of God on the truth of certain scientists' views, you are placing yourself on a very shaky ground. What are you going to do if those views change? Are you actually going to admit that there are no longer any arguments for the existence of God (and by "you" I mean Craig). God is qualitatively extremely different from the scientific hypotheses scientists discuss. While you can easily get rid of a hypothesis when it's falsified, you can't do the same thing with God. And I am sure that Christians won't. This leads to the problem of falsifiability. If the rejection of the premises of your arguments won't lead to the rejection of the claim that God exists, the arguments become rather meaningless.

Logic, reason, and the intellect are inextricably intertwined with "form". The nature of our present day intellect mandates, per force, that there is "form" or "structure" to our intellectual meanderings.

If one counts, 1,2,3,4,5,6,.... then the integers give credence to the "form" of the mathematical model. The individual integers present with an individual "form' and I believe there were (are) some philosophers who thereby posit "monads"(Leibniz?) as a basis for their philosophy. The aforesaid displays how that structural mathematics and the intellect are of course related.

"Infinity" is a nebulous conception which doesn't really fit in with our "form fitting" mentalities. Yes, you can say that the very fact that the word "infinity" exists displays the intellects ability to speak to nebulous conceptions. In one aspect that's true for similar to the use of the word "brother" which is highly specific the word "brothers" becomes nebulous in the same aspect as the word "infinity" relates to the individual number.

From the above one can glean that the intellect "individualizes" through the aspect of "thought" into "words" via our language. We receive this "structure" not as our individual creation but as the "structure" of the world via perception. And so, in our "exploration' of forms, given to us through our perceptions we are able to connect one "form" to another. If we like or dislike the connections of forms then we are living in our own particular "truth" and in a real sense have not completed the task. The "connections" or "logic" of the situations or 'forms" are present for each to "see" and in this is not related to our particular predilections (not that they are wrong, but more like incomplete).

In the above one approaches the nature of "truth" which can be appreciated by others but only if each stands at the same particular spot. The old adage, look at the tree in winter from different aspects and only in this way can one approach the "truth". This is not a call for "opinion" but of actual appreciation of "truths" as they stand in the world of our perceptions. Going out on a limb here but if Man were to "appreciate all truths at the same time" he would have to immerse himself into the World Being, sans time and certainly space. He would be dead to earthly perceptions. I use the words 'time" and "space" and in fact our particular language only for understanding as one must realize when speaking of these matters the language of the earth has to be used even though it is mostly appropriate for earthly perceptions.

Back to number, infinity and the beginnings of this post (actually we have never left the beginning, it just seems so). In one of the posts i noted that Dr. Craig stated that the scientist deals with "infinity' but in observing the perceptual world it is not to be found. He said that "infinity' was in the "mind" of the scientist and only in his "mind" not in the earthly perceptual world. Who can disagree with this? I see no numbers or infinity in the world and therefore the connection between the perceptual world and my "mind" or intellect is questionable if not downright false ala Kant (he always pops up). This is the question for philosophy of our present age, the "merging" if you will, of our intellects, nay our very individual being, with the world of our perceptions.

From the above one can readily see this "merging" can lead to a pantheistic loss of individuality and we can all "flow with Tao" or attain our individual "satori" which is really a loss of individuality. But these are considerations of another time not for the present. the "intellect" has accomplished one thing strongly, the individuality of man. Not matter how you cut it, we are strong in our thoughts, and through this we have fed our individual "I" or " Ego". We are then self centered and one can see the difficulty with and negative aspects of the intellect's work, the individualization of the human soul. The question becomes "how does the individual man gain insight or understanding of the perceptive world with a method( intellect) which, in a sense, negates his attempts"?

In the ideal, we would like to "merge" with the perceptual world and retain our present identity or "Ego". One can grasp a hint of this activity which was noted in the early paragraphs. We noted that "infinity" was a more "nebulous" conception than the individual number "one". We are experiencing a "feeling" with the infinity conception which stands out more than the individual 'feeling" of "one". But make no mistake about it, "one" has a feeling aspect which can be readily appreciated if one approaches without presumptions. The world of "feelings" raises it's head (bad term I know) withing our perceptual world. Whether perceiving a "concept' in pure thought or perceiving an earthly tree the "feeling" experience will present itself. Man can best deal with "feeling" if the example of color is appreciated. The "feeling" of blue which presents with a devotional sense is different than red which appears to approach or come out at you.

This of course is the qualitative aspect of the world which our present science denigrates with the word "qualia". The "t-square and caliper" mentality will not allow a qualitative aspect to a science of the world for it is immersed in a dry abstract intellectuality. the solution (long) is a "warming up" of the intellect which presents with an artistic approach to nature but in this we would have to give up our "t-squares" and see the world as it really is, immersed nay,but as warmth of soul to the individual man.

I've just reached the point of inchoate incomprehension but I hope some understanding of the intellect is comprehensible and others can carry it from there. Aphoristically, I am speaking to "spiritual science"which is "science of the spirit" to which the spiritual activity of Man, his thinking, is explored. this word is a generic word to which the activity of the Anthroposophical Society is manifested. An artistic approach to the world, within science, is an ennoblement of the individual man. Even as i write these words I experience the "what's in it for me?" feeling, the "Ego"speaks, that feeling in our time while the artistic approaches the perceptions for its own truths to which the "Ego' becomes selfless'. No one said it would be easy.

Well, we don't know if premise (1) is true. However, we can determine if the logical disjunction (1.1) in which the premise is framed is true along with determining if it qualifies as an exclusive disjunction (1.2).

1. Whatever begins to exist has a cause.
1.1. EITHER (p) whatever begins to exist does have a cause OR (q) whatever begins to exist does not have a cause, where 'p V q' is true if at least p or q is true.
1.2. If the members of the disjunction are contradictory then we have an exclusive disjunction where 'p XOR q' is true if exactly one and only one of the members (p or q) is true. (Either the window is open or the window is shut.)

So whether you like it or not, you can't simply retreat into skepticism when you enter the debate. As NotReady said:
FWIW, the second premise is framed in the same manner:
2. The universe began to exist.
2.1 ('r V s') EITHER (r) the universe did begin to exist OR (s) the universe did not begin to exist.
2.2 'r XOR s'.

From here we can determine the conditionals of each proposition (p,q,r,s):

1.3 With p: (p→ p') if (p) something does begin to exist, then (p') there is a cause or reason why something exists.
1.4 With q: (q→ q') if (q) something does not begin to exist, then (q') there is no cause or reason why something exists.
2.3 With r: (r→ r') if (r) the universe did begin to exist, then (r') the universe had a beginning.
2.4 With s: (s→ s') if (s) the universe did not begin to exist, then (s') the universe always existed.

So if (p XOR q), then (p' XOR q'); if (r XOR s), then (r' XOR s').


With (1) it's not usually challenged because it's impossible to prove otherwise, the foundation of empirical science is causation and the consequent (q') of the disjunct (q) seems absurd. But note that your argument isn't really directed at (1) in the way you're thinking, because 'exist' is not the operant of the premises' first term, 'begins/began' is.

When you argue against (1) by stating "the universe could have always existed" it's a non sequitur because 'exist' isn't the issue of the premise, 'begins/began' is. In other words, you're not denying that what begins has a cause, you're denying a beginning. I'm not saying you can't argue such, but the place to do so is against the second premise, not the first.

In logic "absurd" (in the reductio ad absurdum sense) used to be reserved for conclusions that were clearly wrong (ie, conclusions that everybody involved in the discussion agreed could not be true).

Nowadays it's applied to conclusions that "seem silly" to the person presenting the argument. Reduction to this kind of "absurdity" is irrelevant.

The fact that Craig can show that my beliefs seem silly to him does not mean that he's capable of challenging my beliefs with logic.

Your claim was that he considered it 'not a basis for rational thought' and therefore absurd. He clearly is not saying it's absurd - he thought actual infinities didn't exist, sure. He also thought that previous attempts to articulate the precise meaning of infinity had failed. The quote (in it's entirety and in the context of the paper) is clearly a claim of success at having worked out how such a thing makes sense.
Again, it's not. The purpose of Hilbert's Hotel is to illustrate the difference between infinite sets and finite sets.
Sure - I already did that and you responded "... Hmmm" (though you never responded to my interpretation of your remark and subsequent explanation so I'm not sure how I was supposed to take the comment). What I explicitly said was:

"Is it inconceivable for the universe (not just the bits we can see) to extend infinitely? With an actual infinite number of stars? I don't see what's impossible about that."

Craig claims it is absurd, ie logically impossible. If he wants to change it to "The possibility of an actual infinite existing is implausible to me" then fine, but the Kalam Cosmological Argument requires that it be impossible and he hasn't established that - so far all I've seen in this thread are two posts by other people which are poor and a question from Craig "What's infinity minus infinity?" which I think you conceded was careless - it also doesn't establish anything other than he's not thinking of infinity properly.

You also had a go at me for talking about infinity rather than the infinite - hopefully reminding you of what Craig's quote which I'm discussing actually is will make it clear why I am doing so. "The infinite" is not well defined as far as I can see whereas infinity is (it's like this supposed distinction between broad logic and strict logic which I still have no idea how I'm supposed to treat it).

I'm not really clear where to go since you don't want to explain broad/strict logic other than saying "married bachelors" are only broadly inconsistent whereas "married unmarried men" are inconsistent in both logics - both things mean the same thing and I see no advantage other than obfuscation in inventing a 'broad logic' without stipulating what it's rules are. Furthermore, you have said that Craig has written lots about this but don't have any actual references (not that you owe me any, I'm just not clear what the point of a discussion is if we're not going to talk about the arguments but rather just assert "Clever people agree with me"). Finally you have this odd interpretation of Hilbert's Hotel as being "obviously" designed to show the absurdity resulting from an existing actual infinite. I don't know where you are getting this from - it seems equally obvious to me that it's an illustration of the differences between infinite sets and finite sets, the strange things that happen and why we shouldn't rely on our intuitions from finite numbers when trying to understand how infinite sets behave.

The Kalam Cosmological Argument relies on the truth of "Actual infinities do not exist". Do you have any argument from Craig or elsewhere for why this is plausible beyond "What's infinity minus infinity?" If the Kalam Cosmological Argument is not meant as a "strict" logical argument but rather a "broad" logical argument - what are the rules of "broad logic"?

Well sure. I'm assuming that when Craig says "The existence of an actual infinitie would lead to absurdity" I'm assuming he means more than "I don't think one exists". Maybe there's a subtle distinction between 'strictly' absurd and 'broadly' absurd.

I really think it only goes as far as "Hilbert's Hotel seems silly to me, so I have established by reductio ad absurdum that infinities can't exist."

Do you see any logical argument greater than that?

I mean, he's definitely doing more than that in tactical terms - for example, he's relying on his argument to be persuasive among those who agree with him that the Hotel seems silly (and he's right to do that - few people want to go against their intuitions, and I've seen people absolutely refuse to accept the right answer to the Monty Hall problem because it "seems like 50%" to them).

But as far as actual logic is concerned, do you see any more to it? Even in his appeals to authority he's cherry-picking and not claiming consensus (which would be necessary, as far as I can tell, if he wanted his appeals to hold the weight of his conclusions, logically).

I guess I made you mad somehow. Sorry. I think what I've said is correct but just don't have the energy to fight over details. There's a wealth of stuff on Craig's site in all sections - try his scholarly articles where he addresses these issues re Oppy and Mackie.

How so?

In regard to the impossibility of an actual infinite existing, Craig seems to use that more in defense of the second premise than to affirm its truth, IMO. At first thought, it seems that 'an actual infinite could exist' AND 'the universe began to exist' can both be true. Only if 'the universe is an actual infinite' would the second premise be false. But just because an actual infinite could exist, still doesn't establish that the universe is in fact an actual infinite, it just gives more plausibility to his opponent's theories, like Hawking's u-turn. That's why I'm thinking he employees 'an actual infinite is impossible' more in defense than offense and uses big bang cosmology, primarily, to support the second premise.