P: It seems to me that you do not realize that logical possibility is epistemically indistinguishable from physical possibility. That is, if something is logically possible (whether you may see it as such or not) then it is physically possible.
That's utterly false, under any non-tendentious definition of "physically possible". It's a commonplace in modern philosophy that logical possibility is a strict superset of nomological possibility.
P: The reason is that naturalism is purely phenomenological.  Judeo-Christian theism is what histori-logically compelled the view that all phenomenon has regular order
False, and false.
H: That's why you assign a confidence range to your estimates.

P: On what bas(e)(i)s do you do so?

On roughly the same bases that scientists use when assigning confidence ranges to their probability judgments.
Suppose you are very young [..]
Once again, the point of your analogy eludes me.
 It is no different than the One Black Swan problem
See my book for an explanation of Hempel's Paradox.  Hempel's Paradox simply does not make it impossible to assign relative probabilities.
H: Consider the theories:
A) The universe exists and is self-caused or uncaused or has no known cause.
B) The universe was caused by God, who is self-caused or uncaused or has no known cause.
C) The universe was caused by God, who was caused by SuperGod, who is self-caused or uncaused or has no known cause.

H: I'm saying that B is more parsimonious than C, and A is more parsimonious than B. I'm saying that without parsimony, you have no reason not to believe in SuperGod, and SuperDuperGod, ad infinitum. (I of course here rely on the fact that any attribute of self-causedness or uncausedness that can be imputed to God can be imputed to the universe itself.)

P: First, the type of parsimony you have here is an arbitrary one. It is thus more parsimonious for me to suppose that you, Brian, are a computer than that you are a real person, or that this computer monitor in front of me has nothing but styrofoam inside of it
My argument applies even in conjunction with all the empirical knowledge humans have, whereas your argument collapses when so conjoined.
Second, a hypothetical or known object/set that is said to be self-existent, necessary, eternal, and infinite cannot then be said to have a cause, whether caused by itself (which is a contradiction), caused by nothing (which is a contradiction), or caused by something else.
I repeat: any attribute of self-causedness or uncausedness that can be imputed to God can be imputed to the universe itself.
In other words, either you grant that there is such an object/set (what I've called the foundation), or you admit that everything you can ever argue is meaningless.
Non sequitur.
Going back over arbitrary parsimony:  if it is makes sense to argue that an uncaused universe is at least as parsimonious as an uncaused (i.e., self-existent) God who cause(d)/(s) the universe, then it makes essentially (essentially) no less sense to argue that the idea that this sentence is uncaused is more parsimonious than the idea that I caused it.
Non sequitur.
You will object that it is not essentially true that the idea that this sentence is uncaused is more parsimonious than the idea that I caused it, but you cannot prove it any more than you can prove that the universe is uncaused:
"Prove" it in the sense of apodictic certainty?  Of course not -- all synthetic knowledge is subject to at least some doubt. It's sophomoric to say this proves that all theories are equally parsimonious or equally justified.
What bit of the universe are you going to point to and say that it is obviously eternal?
What part of "God" are you going to point to and say that it is obviously eternal?  I don't say that the universe is "obviously eternal"; I merely say that any attribute of self-causedness or uncausedness or eternality that can be imputed to God can be imputed to the universe itself.
P: There are two main options for a 'foundation', that is, for an entity/entities that has/have 'se existence':

H: I don't agree that anyone knows any particular options for how an entity could be self-causing, or how a fact could be self-explaining.

P: ?

I'm asserting that you don't know your "there are two..." statement to be true.
H: I'll take your 'foundation' to mean the property by which an entity is self-causing or a fact is self-explaining.  On this reading, I don't see that you've given any explanation whatsoever as to how in particular a fact or entity could be foundational.

P: I'm not sure you understand what I'm talking about.

I'm not sure either of us understands what you're talking about. ;-)
I do not imply any particular fact, entity, or set (all of which I call a 'thing'), I mean only the idea that "there is such a thing as an uncaused thing".
Let 'P-foundational' mean "the property by which an entity is self-causing or a fact is self-explaining". Do you claim that
(A) it is necessary that there is at least one thing that is P-foundational?
I claim that nobody has demonstrated (A) to be true.
H: I agree that I am not self-causing or self-explaining.  So?

P: Then is there nothing that you think you are justified in asserting as a basis for argument, even the basis of parsimony?

That conclusion does not follow from my assertion above.
If you grant that you are not self-existent/necessary (which means that you grant that you are contingent), then on what basis do you argue anything;
Sorry, the Transcendent Argument for the existence of God is fallacious.
do you think that you logically grant that there is such a thing as a necessary thing, seeing that you grant that you are not it, or, contrarily, do you think that you grant that you cannot even know whether there is such a thing as a necessary thing?
I have no reason to think it's logically impossible that there could be an ontologically necessary being. I have no reason to think humans can or cannot know whether an ontologically necessary being is logically necessary, logically possible, or logically impossible.
There are three options here:
a) all things have only indirect causes,
b) there is something that directly causes something else, or
c) ___?.
Another option is: c) there is something that is entirely uncaused.
Now the question: Are you
1)merely asking a rhetorical question to find out more about my position,
2)asserting that it is not obvious which option of a), b), or c), is the case, or
3) asserting that a) or c) is the case?
I'm asserting that we don't know whether the Principle of Sufficient Reason is true or false.
H: for our purposes (viz., of answering "why?" questions), the concept of an explanation generalizes the concept of a cause.
P: when you say that the concept of an explanation generalizes the concept of a cause, are you saying that 'explanation' is the epistemic version of 'cause'?
I'm saying that it's possible for a "why?" question to not be answerable in terms of causes but nevertheless be answerable in terms of explanations.
I assume the principle of sufficient existence, i.e., that something (as opposed to nothing, which is "properly" called 'infinite regress') must be self-existent.
I don't see the distinction with PSR, and I don't agree with your assumption that your principle is true.
Some thing must be uncaused (i.e., self-existent, necessary)
If this is an argument for your principle, then it's circular.
All "why" questions (i.e., a given "why" question) are either; a)meaningless (such as "why does a verb therefore?"),  b)required (such as "why is does the sky look blue?"),or,   c)self-referencing (such as "why ask why?" or "why does there have to be a purpose to anything?").
I'm not sure I understand or agree with your taxonomy of "why" questions, and I don't see how it supports your principle.
If by 'religion' you mean 'the refusal to even grant the fact that one doubts something that one wishes to believe true', then the proposition, 'fear of uncertainty explains more about religion than it does about naturalism' is self-defining. But, if by 'religion' you mean 'belief that something exists that is transcendent to any physical thing (time, space, and matter)',
I gave you my definition of 'religion', and it was neither of the above.
Does the concept of necessary existence obtain, or not?
Are you asking whether the P-foundational attribute is instantiated, or are you asking merely whether it is possible to be instantiated?  I have no reason to think either is the case, but I cannot demonstrate that either is not the case.
Where did your argument about parsimony go?
It's exactly where I left it.
Does even parsimony, in any sense of the idea, have a quality of objectivity or not (ethical, epistemological, quantitative, or any other sense of objectivity)?
Judgments about parsimony are indeed obviously not purely subjective. Nor can they be purely objective.
is there anything that you value above anything else and, if so, what thing or things do you value the most?
Yes; see http://humanknowledge.net/Thoughts.html#AssertedValues.
H You made no reply to my diagnosis of its speciousness, so I'll repeat that diagnosis: It's specious to define 'faith' as any occasion in which not all evidence about X is univocal and paradigm considerations (i.e. evidence about evidence) play a role in ultimately deciding between X and not-X. This is yet another facile attempt to make 'faith' into a meaningless label that makes no practical distinctions whatsoever.
I'll take your continued silence here as an admission that it's specious to say that there is no interesting distinction between most theists and most atheists that can be called 'faith'.
Is the idea of 'parsimony' 'exempt from doubt'?
No. See the discussion under 'Faith' in 1.2.2. Philosophy / Metaphysics / Theology.
If it is not 'except [exempt?] from doubt', then by all means offer a proof that that is the case.
Do you not believe my self-report that there is no principle or proposition that I claim should be exempt from doubt?
P: you seem to choose, for your foundation, that thing which is not even solid, namely knowledge of the third-person phenomenological world, [..]
P: If, after reading all of my new replies above, you still do not see what I mean here
I see merely that you incorrectly assume that I must have a "foundation".
AI researcher Steve Grand believes that qualia may in fact be a product of certain dynamic physical organizations. This means that these certain organizations have the power to produce qualia
He's wrong to the extent he disagrees with my discussion of qualia.
Why can't we keep involving ourselves in one-upmanship so that, no matter what entity we come up with as being all powerful, we can simply invent another one even more powerful still?
The only reason not to terminate such one-upsmanship is Parsimony, which indeed is why it is inadvisable to "one-up" the idea of a brute-fact Universe with a brute-fact God.
We have logic (as in 'logically possible') as one inherent, irreducible order, so how would physics lack an inherent order? [..] One cannot reduce true power to something else [..] the very standard by which they conceive of omnipotence as an anti-qualified power allows that power to violate that very conception: [..]
I still don't know what you mean by 'power'. Is this an entirely novel concept of yours, that can't be stated in standard philosophical terms?
The idea that there are lesser and greater infinities is (partly) founded on the same error of one-upmanship,
The hierarchy of infinities is firmly grounded in set theory.
for there can no more logically be two actual infinities than there can logically be two actual omnipotences.
Nobody has ever given a convincing demonstration that actual infinity is logically impossible. Are you claiming instead that this is a settled question in modern philosophy?
To them, nothing is allowed to be superior to "true omnipotence", otherwise, they think, it isn't true omnipotence.
I agree with you that such arguments against "true omnipotence" are lame and uninteresting, and I'm not sure why you keep bringing them up.
Finding out important truths is like trying to follow dance instructions given over the phone
Is there really nothing I can say to get you to stop repeating these phone analogies to me?
H: I still don't know what you mean by "power", but you're obviously using some in-principle qualitative similarity to wish away an obvious quantitative difference in probability.

P: Do you wish to revise, or retract, that?

H: No.

What about now?

No. (Do you see a pattern here?)
H: I mean that there is no irony in rationality not being used for rationality's intended purpose X if one does not think there exists any intender behind the existence of rationality. Do you dispute this?

P Believe it or not, I do, but that is not the irony I was referring to. I'll wait until another reply to qualify.

If the contention you have in mind is anything like your denial here, then you may not want to bother, as I'm really not interested in debating propositions that I consider this obvious.
P: If an A or B 'foundation' exists, then there is no true error of 'the God of the Gaps'. [..]

H: I've seen no convincing demonstration of this from you.

P: It has to do with the concept of 'true'. If there is no truth, or if no one can ever know it, then there is no true error either way.  But, if there is truth and if we can know it, then a provisional error regarding that truth is not a true error.

It's specious to say that because all synthetic knowledge is provisional, all synthetic propositions have equal merit.
[..] the atheist falls down the sudden epistemic hole, and the theist standing down there gets the dirt in his eyes. The Christian theist is always buried in the dirt looking up, so that once the new hole appears, the atheist, who had been standing he thought firmly enough on the ground, falling into the hole brings dirt down with him. [..]
Please, please, please, no more metaphors or analogies.  Due perhaps to some difference between our past intellectual experiences, your metaphors and analogies are not helpful to me at all.
H: It's laughable to say that because atheists posit certain brute facts, it's not unparsimonious for theists to posit god(s) merely for the purpose of "explaining" those facts.

P: Unparsimoniousness is not the error I was referring to here.

But, if there was no person in the world who was a theist asserting that "God makes the lightning", and assuming everyone lived in relative peace, then parsimony would not even be the issue that it is: everyone would be concerned with physics really only for practical uses.  The same would be the case if everyone in the world were Christian theists living in peace amongst themselves (defined as such, not defined simply as 'Christian theists', since not all Christian theists in the world today get along so well as that).

If you doubt this principle

What principle? I don't understand your lightning story, and I don't see how anything you've said here justifies the positing of god(s) to "explain" facts that atheists posit to be brute.
H: You should use 'all' when you mean 'all', otherwise use 'almost all'.  If you can't do that, then we shouldn't be having this discussion.

P My assertion about the nature of communication stands.  I did (did) mean all, not 'almost all', But, I did not mean what you thought I meant by 'prove' and 'things' [in "prove all things"]

So you were being precise in your use of 'all' but careless only in the phrase that 'all' modifies? By this reasoning, nobody has ever used the word 'all' carelessly.
If you don't see how my last reply there applies to the core subject of this debate, namely the claim that a human was raised from the dead
I don't. We are far, far removed from the Resurrection, and instead seem to be exploring the idiosyncratic philosophical rationalizations you use to justify your (prior?) religious beliefs. (What are the odds that your intellectual biography is free from the potential confounding factors I identify here?)
H: Your phone/arm analogy wasn't very useful before, and it doesn't help me here either. :-)

P: [..] earth [..] flat [..] spheroid [..]

I didn't take the time to read all of this.  If your point is anything other than that precise communication can be difficult, then can you summarize your point in one or two sentences??
P: Like I said, dancing [..]
Sorry, I'm now just skipping the remainder of any paragraph when I see 'dance' or 'phone'.
H: Only insofar as science is based on skepticism, which is incompatible with the faith on which so much religion is based.
P Some of those ancient Greeks were quite religious then
H: Recall from my definition of 'religion' that it does not necessarily require faith. However, for probably 99% of religionists, it involves faith or mysticism, which are antithetical to skepticism.

P: How do you justify this assertion,

Tell me what you think the percentage is, and I'll be happy to argue over any difference.
and do you think it applies (%-wise) to Orthodox Christianity?
A little higher than otherwise.
Also, do you think that, of all the science-worshipping atheists in the world, the same percentage of 'faith' does not apply to them? (Leave off the mysticism, though, for that is not the issue here unless you want me to bring up the science-worshiping-atheist version of it).
Bring up whatever you want. Atheists are much harder to study as a group than are religionists, but I'd guess that at least half of atheists make some mistake I'd call mysticism, and probably half of non-mystical atheists are sloppy enough in their reliance on authorities to be considered to have faith.
H: The fact that we might be wrong about our causal relationships is not a good reason to say that arbitrary hypothetical entities exist.

P: Please explain what you mean by 'arbitrary'.

H: See Merriam-Webster.

P I'll not. Philosophical arbitrariness essentially means misapplication.

No, here it obviously means sense 3a, e.g. "take any aribitrary positive number".
I can define 'faith' as belief in a supernatural
You could, but that wouldn't capture nearly as well how the term is used by the relevant linguistic community -- which is why reference works define it closer to how I do than to how you do here.
P: If you do not further define your use of the term 'religion' to include the notion that religion is simple-minded, then I concede that I am incorrect in my impression.
H: Faith and mysticism are usually (but not always) more simple-minded than skepticism, and religion at any rate need not be based on either faith or mysticism.

P: I thought you used the term 'faith' in your definition of 'religion'?

If you've lost the definition I gave you for 'religion', then let's table this discussion until you locate it again.
that would seem to be a necessary thing, not a usual thing
No, because skepticism too can be simple-minded to the point of cynicism and nihilism.
Assuming you know what an algorithm is, and what an axiom is in relation to it
I have an M.S. in Computer Science with an emphasis in Artificial Intelligence, and I'm somewhat well-read in philosophy of mind, but I've never heard of an algorithm having an axiom.
It's real simple (once you see it), and part of it has to do with the infinite-ness of the 'foundation' and how humans are not individually infinite.
You again seem to make too much of infinity -- so to speak.  It's been over a century since set theory demystified the notion of infinity, but too many people still find it mystifying and mystical. The only intersection between metaphysics and infinity is this simple observation: actual infinitude is not empirically demonstrable, and will likely never be shown to be theoretically impossible.  Anything else purporting to be a metaphysical conclusion based on the notion of infinity is likely to be meaningless or wrong.