Agrippa's trilemma is about how we justify our belief system. We are talking about the definition of contingent beings. I am asking why can't contingent beings loop around to explain themselves.

You're using the word 'explain' as if it has nothing to do with 'knowledge', and I just don't understand how that works.

And how do cosmological arguments accomplish this?

I'm not an expert on them; I've only just started to become interested via Feser's The Last Superstition and Caleb Cohoe's There Must Be A First: Why Thomas Aquinas Rejects Infinite, Essentially Ordered, Causal Series, although I haven't made it through the latter. What I know is that there's a lot of confusion out there about causation and whether it even exists (e.g. Sean Carroll's "unbreakable patterns"). I suspect that there is some process of people slowly becoming consistent with their presuppositions; actually, I think this happens over multiple generations. One possible result is that metaphysics disintegrates, and ceases to be a fertile ground for generating new science and enhancing existing science.

What cosmological arguments do do is throw the following kind of discussion into question. This is from Richard Feynman:

    We make now a few remarks on a suggestion that has sometimes been made to try to avoid the description we have given: “Perhaps the electron has some kind of internal works—some inner variables—that we do not yet know about. [...] But we have verified experimentally that that is not the case. And no one has figured a way out of this puzzle. So at the present time we must limit ourselves to computing probabilities. We say “at the present time,” but we suspect very strongly that it is something that will be with us forever—that it is impossible to beat that puzzle—that this is the way nature really is. (The Feynman Lectures on Physics, III § 1–8)

Feynman famously made fun of philosophers, but this is a philosophical claim. To see a different point of view, I turn to David Bohm:

    The assumption that any particular kind of fluctuations are arbitrary and lawless relative to all possible contexts, like the similar assumption that there exists an absolute and final determinate law, is therefore evidently not capable of being based on any experimental or theoretical developments arising out of specific scientific problems, but it is instead a purely philosophical assumption. (Causality and Chance in Modern Physics, 44)

My suspicion is that the mental machinery and intuitions deployed around the cosmological argument touch on these matters. These matters are no academic dispute: what one believes will determine what gets scientific funding and what does not. Beliefs can easily become reality, for if you believe nothing can be done, and do not fund it, perhaps nothing will be done because you did not fund it.

Scientific evidence, deductive arguments based on well-defined terms and first principles that are coherent within a belief system, and pragmatism.

Coherentism as epistemology has serious problems, and pragmatism enslaves us to current human desires. These both seem like bad ultimate standards for "knowing" something. Aristotle had a plenty coherent system for his tastes and his justification of slavery allowed his wants to be well-satisfied. Had we gone with 'pragmatism', it's not clear that we would have advanced science to the state it is at, today.

I prefer a priori argumentation.

Really? I'm not sure I've ever run into a self-described skeptic who prefers a priori argumentation. Have you? What famous names can you name in this tradition?

This is better than the usual critique of positivism. :-)

What's the "usual critique"?

I don't know. Do you?

Well, arguments such as Caleb Cohoe's (above) might force us to accept final causation or reject much more than we want to. Otherwise, we might get not just a deflationary conception of truth, but a deflationary conception of causation, as well. All that is solid could melt into air. Then again, I see that as the most drastic method God could employ to remove false beliefs from a group of humans: eat away at all their beliefs.

It predicts the behavior of the universe. Yes, that is something I want. I thought everyone wants that.

It's not clear to me that Syrian refugees want that. It strikes me that actually they want at least the hope of something possibly resembling a good decent life. But this requires study into what is "the good life", which is study of icky human beings with aspects of themselves that look awfully like final causes. It is much easier to pretend that the world of ought is 100% subjective (in the 'idiosyncratic' sense, or at least the 100% socially constructed sense), and restrict talk of science and justified true belief to the realm of formal systems which well-match highly, highly selective patches of reality.

I'm somewhat confused here. Why do you think final causes futz with what I want? I doubt you know what I want - human beings are rather complex. I'm not completely sure myself what I want :-)

If you're unaware of how Natural Law Theory futzes with what people want, I think you have some studying to do. The claim that reality was designed such that how you are acting now is suboptimal is a deeply offensive claim to some people, especially Westerners.

I am very much interested in the description. However, I want the arguments to be consistent, rigorous, and well-defined. Still waiting.

Once again, if you require that things be provided to you on your terms, you can define things out of possibility. It would be as if you mandated that only rational numbers be used, and yet the proof requires the irrationals.

With regard to pragmatism, aren't you the one that favors choosing interpretive stances ;-)

I don't 'favor' choosing interpretive stances; I think that choosing is unavoidable. The only question is whether you are aware of the choice, or whether it is made for you without your knowledge.

So you don't know either. So I guess we agree here?

No, you seem to want to utterly dismiss cosmological arguments because they don't match your exacting standards; I'm well aware that in realms such as this, there simply is no extant philosophy which matches such exacting standards. Things are fuzzier than you will let them be.

I feel taken out of context here.

You are always welcome to correct me. So for example, do you use the term, "the evidence", very differently based on context? Our discussions have ranged over multiple contexts, so I have just started worrying that you are using the term equivocally. But then I recall that you just said "I prefer a priori argumentation.", and wonder whether you ever use "the evidence" in any other way—which would put you at odds with many atheists who argue on the internet.

I will not claim that my intuitional claims are actually empirical claims and I will not make and empirical claim and then try to elevate it about empirical refutation by calling it metaphysics.

Do you think the "empirical" (≠ "the evidence"?) can always adjudicate metaphysics?

Any added local variables will cause the theory to give predictions different from what quantum mechanics predicts. QM is well evidenced, so we don't want different predictions. Thus it is complete locally.

But is even this true? Put QM near a black hole event horizon, for example. You seem to be in violation of Ceteris Paribus Laws, and I've never come across a good refutation of that idea.

That is a possible interpretation.

I suggest a look at Bernard d'Espagnat's On Physics and Philosophy; he argues that Bell's theorem has implications regardless of interpretation: in particular, that of 'nonseparability'; see for example Holism and Nonseparability in Physics.

I think what it shows philosophically more than anything else is that we should be very careful with our everyday intuitions about causes and telos.

But our whole edifice of science is dependent on our everyday intuitions, for that it is where it started. If you start eating away at our everyday intuitions, I say that one ought to try to re-do the history of science with the modified intuitions, to see if it is even possible. If it is not, I question whether falsities have been injected, falsities which will ultimately be poisonous to the unhindered progression of science. I wouldn't be surprised if the worship of idols has analogies to the belief in false conceptions of reality; Owen Barfield explores this idea in Saving the Appearances: A Study in Idolatry. (Barfield was a mentor and close friend of C.S. Lewis'.)

You are apparently talking about 'explanation' which is nevertheless "not a knowledge claim". I really don't know what you're talking about, given that combination.

Agrippa's trilemma is about how we justify our belief system. We are talking about the definition of contingent beings. I am asking why can't contingent beings loop around to explain themselves.

Cosmological arguments seem to want explanations to have a certain 'final character', one which isn't just ad hoc. It would seem that ad hoc explanations lack the kind of 'truth-like quality' that we expect to find.

And how do cosmological arguments accomplish this?

LB: What is your standard for "knowing" something? Do we "know" that we're not brains in vats?

IR: In this case that we have an epistemically justified in accepting a proposition or its negation as true.

LB: C'mon, that isn't an answer to my question.

Scientific evidence, deductive arguments based on well-defined terms and first principles that are coherent within a belief system, and pragmatism.

That seems to be a very point under contention. What it probably requires is that you give more weight to a priori argument, abandoning the class of assertions which put great weight in the power of evidence to lead us to true beliefs.

I prefer a priori argumentation.

Observation is heavily, heavily theory-laden, and we should face this instead of burying our heads in positivist sand.

This is better than the usual critique of positivism. :-)

The contention here will be what 'reality' is. Does 'reality' contain ontological final causes?

I don't know. Do you?

Your use of 'works' is ultimately subjective: it works to get you what you want.

It predicts the behavior of the universe. Yes, that is something I want. I thought everyone wants that.

The thing with final causes is that they futz with "what you want". So if you don't want that futzed with, one way to avoid it is to simply deny final causation any grounding in your epistemology.

I'm somewhat confused here. Why do you think final causes futz with what I want? I doubt you know what I want - human beings are rather complex. I'm not completely sure myself what I want :-)

That wasn't my point; my point was that when you use phraseology such as "we have propositions that do not work well at describing or predicting", you are in danger of enslaving all knowledge to pragmatism. You seem more interested in the "predict" and "control" aspect than the "describe" aspect.

I am very much interested in the description. However, I want the arguments to be consistent, rigorous, and well-defined. Still waiting.

With regard to pragmatism, aren't you the one that favors choosing interpretive stances ;-)

Now, perhaps a first mover is required for final causation; I've yet to work through the interaction between essentially and accidentally ordered series.

So you don't know either. So I guess we agree here?

IR: I suppose a theist should try to show that final causation is being defined out of empirical testing. Personally, I think theists often play very fast and lost with empirical matters. They use empirical justifications for premises and then claim that their arguments are non-empirical.

LB: Heh, there's a lot of "play very fast and loose" on all sides, it seems to me. For example, from you:

IR: I have a more expansive view of evidence than most. I include good arguments and even things based on intuition, although the later can be very misleading.

So...

I feel taken out of context here. Firstly, I want theists to give me the evidence that they consider to be evidence for God or whatever. I am not trying to pin them down on my conceptions of evidence or truth. I want to know why they think what they think. Secondly, my quoted does not mean that I will do both at the same time. I will not claim that my intuitional claims are actually empirical claims and I will not make and empirical claim and then try to elevate it about empirical refutation by calling it metaphysics.

What makes you think that Bell's theorem indicates QM is "complete theory", locally?

Any added local variables will cause the theory to give predictions different from what quantum mechanics predicts. QM is well evidenced, so we don't want different predictions. Thus it is complete locally.

Bell's theorem shows that there exists nonlocal state. We see this in entanglement.

That is a possible interpretation. I think what it shows philosophically more than anything else is that we should be very careful with our everyday intuitions about causes and telos.

Did I?

No, I stand corrected:

LB: That would seem to be the 'circular argument' leg of Agrippa's trilemma.

IR: But it is not a knowledge claim. All I am saying is that one would need to prove that contingent beings could not explain themselves by a looping process of some sort.

You are apparently talking about 'explanation' which is nevertheless "not a knowledge claim". I really don't know what you're talking about, given that combination.

That the conclusions and premises correspond wit reality, and that we are justified in believing the premises to be true.

Yes, that's the abstract schema, at least if we don't think the Gettier Problems are fatal. What about the concrete applications of it? Cosmological arguments seem to want explanations to have a certain 'final character', one which isn't just ad hoc. It would seem that ad hoc explanations lack the kind of 'truth-like quality' that we expect to find. Terminating in brute facts is too easy to see as giving up.

LB: What is your standard for "knowing" something? Do we "know" that we're not brains in vats?

IR: In this case that we have an epistemically justified in accepting a proposition or its negation as true.

C'mon, that isn't an answer to my question.

But there isn't. It is outside our domain of knowledge.

That seems to be a very point under contention. What it probably requires is that you give more weight to a priori argument, abandoning the class of assertions which put great weight in the power of evidence to lead us to true beliefs. However, I'm inclined to think those assertions ought to be abandoned, because they simply fly in the face of how people actually operate. Observation is heavily, heavily theory-laden, and we should face this instead of burying our heads in positivist sand.

I thought their purpose was to be a statement about the nature reality.

The contention here will be what 'reality' is. Does 'reality' contain ontological final causes?

The problem is that I can give reasons why I accept general relativity or quantum field theory. It works!

Your use of 'works' is ultimately subjective: it works to get you what you want. But one does not need ontological matching to get what you want; control theory is well-acquainted with "good enough approximations" which work perfectly well, even though they don't capture how the system actually operates. The thing with final causes is that they futz with "what you want". So if you don't want that futzed with, one way to avoid it is to simply deny final causation any grounding in your epistemology.

Are you saying that a first mover is necessary for final causation? I'm confused as to your point here.

That wasn't my point; my point was that when you use phraseology such as "we have propositions that do not work well at describing or predicting", you are in danger of enslaving all knowledge to pragmatism. You seem more interested in the "predict" and "control" aspect than the "describe" aspect.

Now, perhaps a first mover is required for final causation; I've yet to work through the interaction between essentially and accidentally ordered series. I have requested the book Jayman reviews in Review: “Aquinas’ Proofs for God’s Existence” by Dennis Bonnette from my library; the focus is on "the per accidens necessarily implies the per se".

I suppose a theist should try to show that final causation is being defined out of empirical testing. Personally, I think theists often play very fast and lost with empirical matters. They use empirical justifications for premises and then claim that their arguments are non-empirical.

Heh, there's a lot of "play very fast and loose" on all sides, it seems to me. For example, from you:

IR: I have a more expansive view of evidence than most. I include good arguments and even things based on intuition, although the later can be very misleading.

So...

Bertrand Russell was a realist?

According to SEP: Nominalism in Metaphysics:

Russell (1912, 96–7) and others think that Resemblance Nominalism faces the resemblance regress. But this regress presupposes that resemblances are entities that can resemble one another. Since Resemblance Nominalism does not reify resemblances, the regress does not arise (see Rodriguez-Pereyra 2002, 105–23, for further discussion).

I also found Gonzalo Rodriguez-Pereyra 2001, Resemblance Nominalism and Russell's Regress. Note that the SEP article is written by Rodriguez-Pereyra.

Bell's Theorem.

What makes you think that Bell's theorem indicates QM is "complete theory", locally? Bell's theorem shows that there exists nonlocal state. We see this in entanglement.

Well, you made a distinction between causality and explanation. But how can one have a full explanation without a full accounting of causality—of the entire "evolutionary history", as it were?

Did I? I would like a proponent of the cosmological argument to tell me what they mean by all these terms. We have done variations of the cosmological argument countless times on this site, and every time it is a little different.

An explanation would account for any causality that is present.

Yes. So, what constitutes "work very well" in the domain of cosmological arguments and such? The key here is that demanding perfection seems to be a wrong-headed endeavor.

That the conclusions and premises correspond wit reality, and that we are justified in believing the premises to be true.

What is your standard for "knowing" something? Do we "know" that we're not brains in vats?

In this case that we have an epistemically justified in accepting a proposition or its negation as true. This is not the case with first mover arguments.

It seems like even if there is a probability cloud, we might be able to say things about it.

But there isn't. It is outside our domain of knowledge.

Is that their purpose? The proposition that "all propositions ought to describe or predict", by what you mean by 'describe', does not seem to itself describe or predict!

I thought their purpose was to be a statement about the nature reality. The problem is that I can give reasons why I accept general relativity or quantum field theory. It works! I do not think we are justified in believing in first causes. I am waiting for someone to give me the justification. I can only tell you why I think you should believe in the things that I believe in. I cannot tell you why I should believe in things that I don't believe in. You asked me to justify quantum mechanics and I did. You have to tell me why I should believe in a first cause. :-)

What you've left out (at least) is final causation, but final causation is problematic, because it brings in the specter of ought, and we moderns tend to want that to be 100% locked up in the brain, as something 100% subjective, with really no ontological grounding whatsoever.

Are you saying that a first mover is necessary for final causation? I'm confused as to your point here.

Perhaps, but one can define 'empirical testing' to exclude final causation. What is the theist to do, if such an exclusion is in place—explicitly or implicitly?

I suppose a theist should try to show that final causation is being defined out of empirical testing. Personally, I think theists often play very fast and lost with empirical matters. They use empirical justifications for premises and then claim that their arguments are non-empirical.

We shall have to see how you deal with "know", above. :-p

I hope I am being consistent. I don't always choose the right words though :-) Know was a bad choice.

I heartily suggest Gregory W. Dawes' Theism and Explanation on this matter. I wish it cost less, but perhaps your library has it (perhaps through interlibrary loan).

Even the kindle edition is over $40!

That doesn't mean they're being consistent. :-p But you're welcome to introduce one who has written stuff we can examine together.

Bertrand Russell was a realist?

Source?

Bell's Theorem.
http://plato.stanford.edu/entries/bell-theorem/

Even if it explains itself?

Well, you made a distinction between causality and explanation. But how can one have a full explanation without a full accounting of causality—of the entire "evolutionary history", as it were?

Both theories work exceptionally well. However, we do not yet know how to reconcile them. What we do know is that they work very well in the domains that they try to describe.

Yes. So, what constitutes "work very well" in the domain of cosmological arguments and such? The key here is that demanding perfection seems to be a wrong-headed endeavor.

I am saying that on the basis of cosmological arguments, we do not know if there is a first mover or not.

What is your standard for "knowing" something? Do we "know" that we're not brains in vats?

Thus, the proper attitude towards first movers is that we do not know if there is one or if there is one what it looks like.

It seems like even if there is a probability cloud, we might be able to say things about it.

On the other hand, we have propositions that do not work well at describing or predicting.

Is that their purpose? The proposition that "all propositions ought to describe or predict", by what you mean by 'describe', does not seem to itself describe or predict! What you've left out (at least) is final causation, but final causation is problematic, because it brings in the specter of ought, and we moderns tend to want that to be 100% locked up in the brain, as something 100% subjective, with really no ontological grounding whatsoever. Finding out more about actual final causes would not accomplish the scientific purpose of giving us greater power over reality, more unrestricted power.

Most of the theist posters seem to think that these are philosophical question and this ipso facto are immune to any kind of empirical testing.

Perhaps, but one can define 'empirical testing' to exclude final causation. What is the theist to do, if such an exclusion is in place—explicitly or implicitly?

Proof is a word worth fighting for. If something is proven, then anyone who studies the matter sufficiently will be convinced by the proof.

We shall have to see how you deal with "know", above. :-p

What is the content of an explanation? Given an explanation, how do we know that it is an explanation. I guess we need a definition of what an explanation looks like?

I heartily suggest Gregory W. Dawes' Theism and Explanation on this matter. I wish it cost less, but perhaps your library has it (perhaps through interlibrary loan).

But there are atheists who are not nominalists.

That doesn't mean they're being consistent. :-p But you're welcome to introduce one who has written stuff we can examine together.

It is complete locally.

Source? I have this from Nobel laureate Ilya Prigogine's The End of Certainty: Time, Chaos, and the New Laws of Nature:

    Nearly two hundred years ago, Joseph-Louis Lagrange described analytical mechanics based on Newton's laws as a branch of mathematics.[33] In the French scientific literature, one often speaks of "rational mechanics." In this sense, Newton's laws would define the laws of reason and represent a truth of absolute generality. Since the birth of quantum mechanics and relativity, we know that this is not the case. The temptation is now strong to ascribe a similar status of absolute truth to quantum theory. In The Quark and the Jaguar, Gell-Mann asserts, "Quantum mechanics is not itself a theory; rather it is the framework into which all contemporary physical theory must fit."[34] Is this really so? As stated by my late friend Léon Rosenfeld, "Every theory is based on physical concepts expressed through mathematical idealizations. They are introduced to give an adequate representation of the physical phenomena. No physical concept is sufficiently defined without the knowledge of its domain of validity."[35] (28–29)

Ok, but the set { A, B, C } can still be contingent. I'm afraid I may have completely lost the point.

Even if it explains itself?

Hold on. QFT and GR contradict each other. We don't as a result, throw them in the trash bucket.

Both theories work exceptionally well. However, we do not yet know how to reconcile them. What we do know is that they work very well in the domains that they try to describe.

Suppose fossil evidence produced a radical challenge to the theory of evolution. It wouldn't be trashed as a result; people would continue using it until something better comes along.

Or they would posit a mechanismsm that could reconcile the fossil evidence with the theory of evolution. Evolution is well-evidenced. A challenge to evolution wouldn't cause us to throw evolution out, but rather revise it to fit the new data. Punctuated equilibrium comes to mind.

Newton was well-evidenced. We don't throw out Newtonian physics, but rather realize it is a very good approximation for big and slow moving objects. If relativity didn't reduce to Newton under the right conditions, we would be very worried.

Saying that we should throw out something because it has some problems is a very, very dangerous attitude.

I am saying that on the basis of cosmological arguments, we do not know if there is a first mover or not. We do not know if there are one or many first movers. We do not know what a first mover even looks like. It could be a multi-verse or something that we haven't even conceived of. Thus, the proper attitude towards first movers is that we do not know if there is one or if there is one what it looks like.

I say that needs to be immensely qualified, and once those qualifications are in place, I'm not at all confident that your "alternate proposal" is the best one, in this scenario

I think we are talking about two different things. One is an empirically based knowledge that a theory works very well at describing and predicting. This theory we keep, even if it has problems, because the theory is largely successful.

On the other hand, we have propositions that do not work well at describing or predicting. What does a first mover predict or describe? Most of the theist posters seem to think that these are philosophical question and this ipso facto are immune to any kind of empirical testing. I don't think too highly of this position, but I will ask exactly what does having a first mover predict and in what way does it work.

First mover arguments are deductive arguments based on various assumptions or first principles. If they are false proofs and they do not work, then I would argue that not knowing is the proper epistemological stance.

Well, have fun convincing others to use the word in the same way. Sometimes I fight for the meanings of words, sometimes I find it distracting from truth-seeking.

Proof is a word worth fighting for. If something is proven, then anyone who studies the matter sufficiently will be convinced by the proof.

As to your serious comment, what are you going to do about that observation? Demagogues and snake oil salesman are not a new phenomenon. Neither is sophistry.

Haven't really given it much thought. I tend to only converse online with people who are interested in substantive conversation (like yourself) and those who say things that really annoys me. The latter is a vice I should avoid.

Which battles do you think are most important to pick in this realm? Which ones can you let slide, for the time being?

What is the content of an explanation? Given an explanation, how do we know that it is an explanation. I guess we need a definition of what an explanation looks like?

It allows reality to exhibit mind-like qualities (say, beauty that isn't just an evolutionary adaptation) which are incredibly unlikely to obtain via impersonal causes. Naturalism seems to entail nominalism, which has pretty big costs. I'm not sure you can avoid nominalism without a necessary being.

But there are atheists who are not nominalists.

Only if you think QM is a complete theory instead of being merely predictive.

It is complete locally.

Okay, so how have you examined the nature or material reality? I don't think anyone is very far along in understanding what material reality is, much less reaching conclusions on its nature. What is it about the nature of material reality that convinces you it is contingent? In terms of examining realities what do you look for as an indication of contingency versus necessity? On what grounds do you hold that a necessary reality would have an explanation that you would be capable of appreciating? I would think that there very well could be an explanation that as humans we could not understand. Just because it eludes you doesn't mean it isn't there.

If you believe in a god that is not contingent, what explains this God? If you aren't aware of an explanation, shouldn't you, by your own standards applied to material reality, consider it contingent?

I am saying that it remains to be shown that it is logically impossible to have a situation in which: A is contingent on B which is contingent on C which is contingent on A.

Ok, but the set { A, B, C } can still be contingent. I'm afraid I may have completely lost the point.

The alternate proposal is that we just don't know. This is better than false proofs.

Hold on. QFT and GR contradict each other. We don't as a result, throw them in the trash bucket. Suppose fossil evidence produced a radical challenge to the theory of evolution. It wouldn't be trashed as a result; people would continue using it until something better comes along. Saying that we should throw out something because it has some problems is a very, very dangerous attitude. I say that needs to be immensely qualified, and once those qualifications are in place, I'm not at all confident that your "alternate proposal" is the best one, in this scenario.

I only use the word proof in the context of mathematics.

Well, have fun convincing others to use the word in the same way. Sometimes I fight for the meanings of words, sometimes I find it distracting from truth-seeking.

Well, every bad new atheist argument is in response to a bad apologetic argument. You reap what you sow. ;-) Seriously though, I think the main problem with popular argumentation is that it is more concerned with winning the point than actually knowing the truth.

I'll take that wink to be an acknowledgment that "An eye for an eye makes the whole world blind." As to your serious comment, what are you going to do about that observation? Demagogues and snake oil salesman are not a new phenomenon. Neither is sophistry.

Another issue I think is the cavalier way we talk about explanations.

Pretty much any philosopher worth his/her salt will agree with you. Which battles do you think are most important to pick in this realm? Which ones can you let slide, for the time being?

How does a necessary being explain say the universe?

It allows you to have essentially ordered causal series, it seems. It allows reality to exhibit mind-like qualities (say, beauty that isn't just an evolutionary adaptation) which are incredibly unlikely to obtain via impersonal causes. Naturalism seems to entail nominalism, which has pretty big costs. I'm not sure you can avoid nominalism without a necessary being. Now, I'm by no means an expert on necessary being metaphysics, so I think I'll stop here and let someone else take over.

My distinct impression from quantum mechanics was that it violated PSR.

Only if you think QM is a complete theory instead of being merely predictive.

How is "explain themselves", "not a knowledge claim"?

I am saying that it remains to be shown that it is logically impossible to have a situation in which: A is contingent on B which is contingent on C which is contingent on A.

This is different from saying that A is true because B, B is true because C, and C is true because A.

Ok. But if those deficiencies are not matched against deficiencies in alternative proposals, then you will be taking advantage of the asymmetry that it is easier to critique and tear down, than it is to explain and build up.

The alternate proposal is that we just don't know. This is better than false proofs.

If you ask me if there was a first cause, I will simply say that I do not know. I do object to people claiming that they have a proof.
Although I think I figured out how I would define contingent and necessary sets. A set C contingent if a subset of itself does not explain C. A set N is necessary if it is a subset of all non-contingent sets.

Again, as long as you can match it, be my guest. I simply despise hypocrisy, whether outright or subtly hidden, e.g.:

I only use the word proof in the context of mathematics.

I'm not a huge fan of standard Christian apologetics, but I'm also not a huge fan of standard New Atheism argumentation. I'd love to raise the level of both!

Well, every bad new atheist argument is in response to a bad apologetic argument. You reap what you sow. ;-) Seriously though, I think the main problem with popular argumentation is that it is more concerned with winning the point than actually knowing the truth.

Is the PSR a contingent or necessary fact?

It's not clear that one can know which is the case; one might have to believe.

It also depends on what we mean by possible world.

Another issue I think is the cavalier way we talk about explanations. Granting PSR, we really don't to a very good job of describing the content of the explanations. For instance, why do photons exist instead of not existing? Perhaps this is simply a lack of knowledge on my (our?) part, but reasons given for state of affairs X instead of Y don't seem to be very explanatory.

How does a necessary being explain say the universe?

I am convinced by the argument of David Bohm, who probably should have gotten a Nobel Prize for the Aharonov–Bohm effect:

Interesting. I took a couple classes in QM in college, but this conversation will swiftly move past what I know. My distinct impression from quantum mechanics was that it violated PSR. This is not an argument though. I think Copenhagen is the most popular interpretation among physicists, so that is probably one reason.

But it is not a knowledge claim. All I am saying is that one would need to prove that contingent beings could not explain themselves by a looping process of some sort.

How is "explain themselves", "not a knowledge claim"? As to your "looping process", I am reminded of fractals and such. But if you only ever integrate your prior state plus an algorithm to get your future state, you will be very limited. Fractals are very beautiful, but they are also very limited.

Sure, but I'm just listing deficiencies in cosmological arguments.

Ok. But if those deficiencies are not matched against deficiencies in alternative proposals, then you will be taking advantage of the asymmetry that it is easier to critique and tear down, than it is to explain and build up.

If apologists are going to throw around the word proof, I demand a very high level of rigor.

Again, as long as you can match it, be my guest. I simply despise hypocrisy, whether outright or subtly hidden, e.g.:

    In one definition of the word, it is of course impossible to find any assertions of full skepticism; even silent enactments are difficult. A good general rule is: scratch a skeptic and find a dogmatist. (Modern Dogma and the Rhetoric of Assent, 56)

I'm not a huge fan of standard Christian apologetics, but I'm also not a huge fan of standard New Atheism argumentation. I'd love to raise the level of both!

Is the PSR a contingent or necessary fact?

It's not clear that one can know which is the case; one might have to believe. Take for example, the following:

In 1590, skeptics still doubted whether humans can find universal regularities in nature; by 1640, nature was in irremediable decay: but, by 1700, the changeover to the "law-governed" picture of a stable cosmos was complete. (Cosmopolis, 110)

Had those skeptics convinced everyone, they would have appeared right because nobody would have expended the blood, sweat, and tears to do science. Fortunately, sufficiently many 'scientists' believed that what they were doing was possible. Evidence followed that belief. I suspect the same is the case in significant portions of Christianity, e.g. Rom 8:16–25.

Let us take the PSR for a second. Consider a particle in a box with a wave function. At some point we observe the particle. Is there a reason why we observe the particle at point A instead of some other point?

I am convinced by the argument of David Bohm, who probably should have gotten a Nobel Prize for the Aharonov–Bohm effect:

    The assumption that any particular kind of fluctuations are arbitrary and lawless relative to all possible contexts, like the similar assumption that there exists an absolute and final determinate law, is therefore evidently not capable of being based on any experimental or theoretical developments arising out of specific scientific problems, but it is instead a purely philosophical assumption. (Causality and Chance in Modern Physics, 44)

This receives support in 2006 by quantum physicist-turned-philosopher Bernard d'Espagnat:

    In order to properly understand the nature of this argument, let us first derive from what has been recalled above the obvious lesson that (as already repeatedly noted) quantum mechanics is an essentially predictive, rather than descriptive, theory. What, in it, is truly robust is in no way its ontology, which, on the contrary, is either shaky or nonexistent. (On Physics and Philosophy, 148)

The claim that QM is only predictive means that it is agnostic to the 'substrate', as it were, which generates the phenomena which it predicts. One might compare thermodynamics as predictive model, to statistical mechanics as ontological substrate.