Hawking theory about something coming from nothing

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alright for a show discovery channel called curiosity. For their first show they brought in Stephen Hawking and the entire show he talked about could our universe have a creator.

It was very obviously skewed to bash religion. They talked about how the vikings had a clearly false idea about the wolf God in the sky who created the solar eclipses.

it even talked about how JPII said we can’t question the idea the God created the universe, and it was painted in a light to try and discredit JPII

but we eventually get to an example of a cup of coffee. HE says well we know its made of milk and coffee and some other stuff, and that comes from places and such. Then the show goes down into the subatomic level and he says that at this level we can see where something is created from nothing. Apparently protons can create themselves out of nothing but only in the short term. He says then now that we know something can come from nothing, he never explains why it happens just just explains that it happens, it must be possible for the universe to come from nothing because at one time it was smaller then protons.

Now my question does this theory hold much water, does he actually have a good theory for the how the universe can come from nothing?

if he does then the first 3 of Aquinas’s proofs loose lots of credibility. Actually I would find it very difficult to find a place for God in this universe if a universe can create it self from nothing.

is there anyone here who can actually explain how protons can create themselves out of nothing or where someone may come up with that idea. Its far beyond my basic understanding of the science.

Lets say this is true where is God’s place for in this.

thanks for any (name removed by moderator)ut.
 
Don’t worry, classical metaphysics is not at all endangered by the “universe from nothing” scenarios. They result from a silly, amateurish equivocation of the physical “nothing” of the quantum vacuum, which definitely has properties, with the philosophical nothing which is indeed nothing at all, and thus is without any properties whatsoever as well.

Here are two excellent rebuttals by cosmologists Stephen Barr and Luke Barnes:

firstthings.com/onthesquare/2010/09/much-ado-about-ldquonothingrdquo-stephen-hawking-and-the-self-creating-universe

letterstonature.wordpress.com/2011/04/01/of-nothing

The first article successfully argues that Hawking himself is actually aware that physics cannot answer the questions:

“Why a system obeying quantum mechanics, M-theory, superstring theory, or whatever laws of physics that make scientific speculations possible in the first place? Why not no system at all, with no laws at all, no anything, just blank non-being?”.
 
By the way, when Stephen Barr says:

“Right up front, it must be noted that this idea is extremely speculative, has not yet been formulated in a mathematically rigorous way, and is unable at this point to make any testable predictions. Indeed, it is very hard to imagine how it could ever be tested. It would be more accurate to call these “scenarios” than theories. It would be a mistake, however, for religious believers to dismiss these scenarios as mere fanciful conjecture or as motivated merely by atheist ideology. Based on a plausible analogy with the experimentally observed and well-understood phenomenon of the quantum creation of particles, the idea of quantum creation of universes is not without merit”,

I have to object as a scientist (a biochemist) who is used to work from hard experimental facts, and not from theory. Those scenarios indeed are mere fanciful conjecture, since, as Barr concedes, they cannot even be experimentally tested, not even indirectly, let alone directly, at this point. And to say that the analogy is “plausible” is quite a stretch of imagination with no data whatsoever to back that up. As a die-hard experimentalist I am quite appalled by what is sometimes viewed as “science” among some physicists and cosmologists. Such things would never have even a remote chance to fly in the field of biochemistry. We deal with hard observational facts, and not with untestable fanciful speculations.

When looking for a successful theory in cosmology that is based on actual observational facts, the Big Bang theory would be fit the bill.
 
does hawking every try to explain why it happens?

and if so how does he describe it.

and those are some very good objects. thanks
 
Don’t worry, classical metaphysics is not at all endangered by the “universe from nothing” scenarios. They result from a silly, amateurish equivocation of the physical “nothing” of the quantum vacuum, which definitely has properties, with the philosophical nothing which is indeed nothing at all, and thus is without any properties whatsoever as well.

Here are two excellent rebuttals by cosmologists Stephen Barr and Luke Barnes:

firstthings.com/onthesquare/2010/09/much-ado-about-ldquonothingrdquo-stephen-hawking-and-the-self-creating-universe

letterstonature.wordpress.com/2011/04/01/of-nothing

The first article successfully argues that Hawking himself is actually aware that physics cannot answer the questions:

“Why a system obeying quantum mechanics, M-theory, superstring theory, or whatever laws of physics that make scientific speculations possible in the first place? Why not no system at all, with no laws at all, no anything, just blank non-being?”.
Thank you for those articles. Another good rebuttal, I have heard from others as I still need to read it, is Fr. Robert J. Spitzer’s “New Proofs for the Existence of God” where he takes on Hawkings and Dawkins and others.
 
Stephen Hawking’s theory on the creation of the universe essentially boils down to “Gravity created something out of nothing”. Think about that for a second. Gravity is a natural force that exists because things have mass. How can anything have mass if it doesn’t exist? So therefore, how can gravity exist in the pre-universe nothingness?

That means something else had to cause the birth the universe. Who/whatever caused the universe to exist had to be something/someone transcendent, and of immeasurable power. It couldn’t have been the universe that gave birth to the universe, because the universe didn’t exist. That rules out gravity, or any force that requires matter to exist, in order to exist. God as described in the Bible is the perfect candidate to fill this void. He is acknowledged as all-powerful, all-knowing, and existing outside of space and time as we know it.

If you want to learn more (and read stuff by people who can explain this better than I ever could), check out the writings of Thomas Aquinas, and of William Lane Craig. Both provide great arguments for God. In addition, Edgar H. Andrews specifically provides arguments against Stephen Hawking’s comments about the origin of the universe.

Andrews: God, Black Holes, and Stephen Hawking

Andrews: Fatal Flaws in Stephen Hawking’s Atheism

Craig: The Cosmological Argument

Aquinas: The Five Ways
 
alright for a show discovery channel called curiosity. For their first show they brought in Stephen Hawking and the entire show he talked about could our universe have a creator.

It was very obviously skewed to bash religion. They talked about how the vikings had a clearly false idea about the wolf God in the sky who created the solar eclipses.

it even talked about how JPII said we can’t question the idea the God created the universe, and it was painted in a light to try and discredit JPII

but we eventually get to an example of a cup of coffee. HE says well we know its made of milk and coffee and some other stuff, and that comes from places and such. Then the show goes down into the subatomic level and he says that at this level we can see where something is created from nothing. Apparently protons can create themselves out of nothing but only in the short term. He says then now that we know something can come from nothing, he never explains why it happens just just explains that it happens, it must be possible for the universe to come from nothing because at one time it was smaller then protons.

Now my question does this theory hold much water, does he actually have a good theory for the how the universe can come from nothing?

if he does then the first 3 of Aquinas’s proofs loose lots of credibility. Actually I would find it very difficult to find a place for God in this universe if a universe can create it self from nothing.

is there anyone here who can actually explain how protons can create themselves out of nothing or where someone may come up with that idea. Its far beyond my basic understanding of the science.

Lets say this is true where is God’s place for in this.

thanks for any (name removed by moderator)ut.
I am not a phisicist but I love it: maths and physics.
ONe day I had to study light and I discovered that the same photon may pass through 2 holes at the same time and I was etremely happy for I like things like these.

Now, it seems they say that in quantum phisics particles come aout of nothing. Nut these are particles that do not last long time. And the Universe has got millions of years.

Out of nothing? sure there is nothing where phisicist say that there is nothing or is it empty of something?

And how can Hawkings say that He is sure of it through Quantum Physics if Physics say the People who say that tthey understand Quantum Physics are lying?

Tehre must be an explanation but the same photon passing 2 holes at the same time it is a feat…
 
alright for a show discovery channel called curiosity. For their first show they brought in Stephen Hawking and the entire show he talked about could our universe have a creator.
I’ve never seen it, but apparently it was aired a few months ago also because there was a thread on it from it’s last airing.
 
alright for a show discovery channel called curiosity. For their first show they brought in Stephen Hawking and the entire show he talked about could our universe have a creator.

It was very obviously skewed to bash religion. They talked about how the vikings had a clearly false idea about the wolf God in the sky who created the solar eclipses.

it even talked about how JPII said we can’t question the idea the God created the universe, and it was painted in a light to try and discredit JPII

but we eventually get to an example of a cup of coffee. HE says well we know its made of milk and coffee and some other stuff, and that comes from places and such. Then the show goes down into the subatomic level and he says that at this level we can see where something is created from nothing. Apparently protons can create themselves out of nothing but only in the short term. He says then now that we know something can come from nothing, he never explains why it happens just just explains that it happens, it must be possible for the universe to come from nothing because at one time it was smaller then protons.

Now my question does this theory hold much water, does he actually have a good theory for the how the universe can come from nothing?

if he does then the first 3 of Aquinas’s proofs loose lots of credibility. Actually I would find it very difficult to find a place for God in this universe if a universe can create it self from nothing.

is there anyone here who can actually explain how protons can create themselves out of nothing or where someone may come up with that idea. Its far beyond my basic understanding of the science.

Lets say this is true where is God’s place for in this.

thanks for any (name removed by moderator)ut.
Let’s consider the larger picture behind your OP, as well as that which led to the atheistically skewed Discovery presentation.

First, Hawking is a dogmatist— a very bright atheist dogmatist. He appears to have given considerable thought to the God-question, and probably forgets more about how the universe works in one day than the average person will learn in an entire lifetime. After consideration and study he has concluded that there is no God— but he seems to have narrrowed his definition of God to the God as defined by Christianity.

In that respect I agree with Hawking. The existence of such a God is inconsistent with all observations of reality. (I’ve written on this elsewhere in CAF for those interested in details.)

However, my personal take on the evidence provided by the universe is that it demands that we accept that the universe and its various aspects, such as biological life are engineered. This requires a Creator, or as seems more likely, lots of creators. The illogical properties of omnipotence and omniscience are not necessary to any creators. (You may want to consider the writings of Alfred Russel Wallace, who came up with Darwinism independently of Darwin, but differed from Darwin in not being an atheist.) For more current material, Michael Behe’s books provide the best science-based refutations of atheism I’ve found.

Hawking’s real mistake is disbelieving in the wrong God— the God of Christianity.

While the materialization of protons (or anything else) from nothing is an absurd speculation rising from a theory build upon approximations and probabilities (quantum mechanics), it would be good for Christian dogmatists to be mindful of its origins.

“Creation from nothing,” was first invented by the Catholic Church. “Nothing” is what God is supposed to have created the universe from. The concept is equally false whether held by Christians or atheists.
 
If Hawking said a proton can be created from nothing then clearly he was being economical with the truth. An electron - positron pair can be created by hitting an electron with a suitably energetic photon. But to create the pair you need lots of energy [kinetic energy] & you need a photon and you need an electron. That is not nothing.
The experts say that at the moment of the Big Bang, or thereabouts, all of the universe was concentrated into an infinitely small point. One could ask where this point came from. There is literally nothing outside it, everything is within the point. The point expanded violently. But why? Nothing outside it could have added to it and changed and destabilized it. Did this point exist forever, then why did it, or how could it expand? If it always existed and so never changed.
This infinitely small point must contain the potential of the universe. There would be nothing moving in it as nothing is created at that point. There is no kinetic energy in that point.
That infinitely small point has two origins.
  1. It always existed, and so never changed, and so it could not have expanded.
  2. It was created itself, but from actual nothing, as opposed to from particles and energy.
This leads to a logical conundrum. Nothing, and I mean the total lack of anything, space, energy, dimension, potential, light, dark, nothing, in fact, cannot create something. As any potential in nothing also does not exist. If it did exist it would always have existed and would not have a beginning, a BB. And we already know there was a beginning.
The alternative is that something which is not energy, potential, matter or any physical quantity or quality created everything at a particular point. Something totally immaterial created a beginning within itself.
 
Let’s consider the larger picture behind your OP, as well as that which led to the atheistically skewed Discovery presentation.

First, Hawking is a dogmatist— a very bright atheist dogmatist. He appears to have given considerable thought to the God-question, and probably forgets more about how the universe works in one day than the average person will learn in an entire lifetime. After consideration and study he has concluded that there is no God— but he seems to have narrrowed his definition of God to the God as defined by Christianity.

In that respect I agree with Hawking. The existence of such a God is inconsistent with all observations of reality. (I’ve written on this elsewhere in CAF for those interested in details.)

However, my personal take on the evidence provided by the universe is that it demands that we accept that the universe and its various aspects, such as biological life are engineered. This requires a Creator, or as seems more likely, lots of creators. The illogical properties of omnipotence and omniscience are not necessary to any creators. (You may want to consider the writings of Alfred Russel Wallace, who came up with Darwinism independently of Darwin, but differed from Darwin in not being an atheist.) For more current material, Michael Behe’s books provide the best science-based refutations of atheism I’ve found.

Hawking’s real mistake is disbelieving in the wrong God— the God of Christianity.

While the materialization of protons (or anything else) from nothing is an absurd speculation rising from a theory build upon approximations and probabilities (quantum mechanics), it would be good for Christian dogmatists to be mindful of its origins.

“Creation from nothing,” was first invented by the Catholic Church. “Nothing” is what God is supposed to have created the universe from. The concept is equally false whether held by Christians or atheists.
Hello, Greylorn:

Actually, ex nihilo is not an ‘invention,’ per se, rather it is a deduction from the dialectic that compels the understanding and belief that there can be no actual infinities, that there was absolutely nothing (except the necessary spiritual cause of all physical reality) prior to a beginning, and that nothing actually means “no-thing (or things).” It was science and physics that added matter, energy, fields, curvature(s), space, gravity, and additional gravitas to the referent (idea) for the word. The Catholic Church has said something quite different. The Church says (and has said) that creation is whence something (e.g., the universe) is brought into being where there was absolutely nothing before, i.e., no matter, no energy, no fields, no curvature(s), no space, no gravity, i.e., absolutely no exigencies of any kind whatsoever are added to, or become an embellishment of or for, nothing.

Unfortunately, our language does not have a concept that is a good referent for the word nothing. Our own immature conceptions color that word and therefore make it mean considerably more than it is supposed to mean. No man has ever witnessed nothing. We have seen nearly empty space. We have caused the near expulsion of everything from bell jars. But, matter, energy, fields, curvature(s), space, and gravity always leave behind, or rather, co-exist with sub-quantum residuals, such as quarks, virtual particles and such. In fact, even virtual particles cannot be said to enter the universe in the manner we understand as “Creation.”. We only know that virtual particles come and go now: after the existence of everything, after the Big Bang, and that they are subject to the Laws of Physics.

What it must have taken for a pure spiritual being to compose that primordial, physical proton had to have been emmence. To pack it together with all there is plus the Laws needed to regulate its expansion into a universe, or multiverse, is beyond ours, or any giant entity’s capability to comprehend.

God bless, my friend,
jd
 
If Hawking said a proton can be created from nothing then clearly he was being economical with the truth. An electron - positron pair can be created by hitting an electron with a suitably energetic photon. But to create the pair you need lots of energy [kinetic energy] & you need a photon and you need an electron. That is not nothing.
The experts say that at the moment of the Big Bang, or thereabouts, all of the universe was concentrated into an infinitely small point. One could ask where this point came from. There is literally nothing outside it, everything is within the point. The point expanded violently. But why? Nothing outside it could have added to it and changed and destabilized it. Did this point exist forever, then why did it, or how could it expand? If it always existed and so never changed.
This infinitely small point must contain the potential of the universe. There would be nothing moving in it as nothing is created at that point. There is no kinetic energy in that point.
That infinitely small point has two origins.
  1. It always existed, and so never changed, and so it could not have expanded.
  2. It was created itself, but from actual nothing, as opposed to from particles and energy.
This leads to a logical conundrum. Nothing, and I mean the total lack of anything, space, energy, dimension, potential, light, dark, nothing, in fact, cannot create something. As any potential in nothing also does not exist. If it did exist it would always have existed and would not have a beginning, a BB. And we already know there was a beginning.

The alternative is that something which is not energy, potential, matter or any physical quantity or quality created everything at a particular point. Something totally immaterial created a beginning within itself.
This is an excellent argument. I make the same point in my book, but your presentation is more concise. If fact, if you don’t mind, I’d like to paraphrase your arguments and use them if I have time.

Nonetheless, there is the matter of your final paragraph. What is the basis for its statements?
 
Hello, Greylorn:

Actually, ex nihilo is not an ‘invention,’ per se, rather it is a deduction from the dialectic that compels the understanding and belief that there can be no actual infinities, that there was absolutely nothing (except the necessary spiritual cause of all physical reality) prior to a beginning, and that nothing actually means “no-thing (or things).” It was science and physics that added matter, energy, fields, curvature(s), space, gravity, and additional gravitas to the referent (idea) for the word. The Catholic Church has said something quite different. The Church says (and has said) that creation is whence something (e.g., the universe) is brought into being where there was absolutely nothing before, i.e., no matter, no energy, no fields, no curvature(s), no space, no gravity, i.e., absolutely no exigencies of any kind whatsoever are added to, or become an embellishment of or for, nothing.
JD,
There’s a tad too much doublespeak in this for my logical mind to wrap itself around. “* …nothing (except the necessary spiritual cause of all physical reality)…*” is not really nothing.

I don’t know of a mathematical statement which is quite the equivalent of this. “0 except for 1”, perhaps? What might that equal? I think if you did a poll among people with functional minds, the answer would have to be, “1,” since it cannot be “0.”

Since your premise is, to my linear mind, a philosophical absurdity, I cannot go further with your argument.
Unfortunately, our language does not have a concept that is a good referent for the word nothing. Our own immature conceptions color that word and therefore make it mean considerably more than it is supposed to mean. No man has ever witnessed nothing. We have seen nearly empty space. We have caused the near expulsion of everything from bell jars. But, matter, energy, fields, curvature(s), space, and gravity always leave behind, or rather, co-exist with sub-quantum residuals, such as quarks, virtual particles and such. In fact, even virtual particles cannot be said to enter the universe in the manner we understand as “Creation.”. We only know that virtual particles come and go now: after the existence of everything, after the Big Bang, and that they are subject to the Laws of Physics.
You are obfuscating the issue with this talk about particles. The word “nothing,” is a perfectly useful word. I know exactly what it means, as do most people. Of course I treat it as an abstraction, the linguistic equivalent of zero.

What we do not have a word for is your peculiar space of “0 except 1,” and since you, or some philosophers have made it up, it is their (or your) responsibility to invent a word for it.

Then you and they could stop incorrectly describing their concept of the beginning with the inapplicable word, “nothing.” This would go a long way toward eliminating confusion. Of course, I suspect that this will never happen, because the confusion is intentional.
What it must have taken for a pure spiritual being to compose that primordial, physical proton had to have been emmence. To pack it together with all there is plus the Laws needed to regulate its expansion into a universe, or multiverse, is beyond ours, or any giant entity’s capability to comprehend.

God bless, my friend,
jd
I don’t know the meaning of “emmence,” which seems to be a non-word. Nonetheless, while you and I disagree on most things, we both believe in a Creator. I speculate freely and superficially in my book on what it took to construct a universe from raw, unformed and unstructured, energy. (The “from nothing” dogma does not work for me any better than it does for atheistic physicists. However, the concept of a primitive form of energy works nicely.) Since my God-concept is of a thinking Creator Who does not know everything, He had to figure out how to make this universe from scratch, Awesome work!

I would never presume to suggest that it is work which any human-like mind could ever have done, but I have some positive expectations for the future of human understanding which is not limited by religious doctrine. I’m working for the integration of science and theology, and if that ever happens, the day will come when advanced astrophysics degrees will require courses like, Reverse Engineering Theory— How a Creator might have constructed matter.
 
JD,
There’s a tad too much doublespeak in this for my logical mind to wrap itself around. “* …nothing (except the necessary spiritual cause of all physical reality)…*” is not really nothing.

I don’t know of a mathematical statement which is quite the equivalent of this. “0 except for 1”, perhaps? What might that equal? I think if you did a poll among people with functional minds, the answer would have to be, “1,” since it cannot be “0.”
Greylorn:

OK, I’ll give you that it looks like “0 except for 1.” But, really, it’s not. It’s zero physical, period. Spiritual is not physical. We believe that God did not make the universe out of a piece of Himself, so, in the absence of anything physical, there is nothing: no matter, no energy, no gravity, no fields, etc. (In the small units of space we have to write in, I do not want to write a book, so I depend on you to think it through.) 🙂
You are obfuscating the issue with this talk about particles. The word “nothing,” is a perfectly useful word. I know exactly what it means, as do most people.
I tend to disagree. Hawking’s newest work does not. Krauss’ writings do not. There are many people (some in these fora, in fact) that do not. I am happy, though, that you do.
Of course I treat it as an abstraction, the linguistic equivalent of zero.
And that is precisely the problem: nothing is not an abstraction. Of the three orders of abstraction, the physical, the mathematical, and the metaphysical, nothing represents no speciation whatsoever. It is nothing, not nothingness. It is a bird, not bird-ness.
Then you and they could stop incorrectly describing their concept of the beginning with the inapplicable word, “nothing.” This would go a long way toward eliminating confusion. Of course, I suspect that this will never happen, because the confusion is intentional.
Greylorn, let’s remain polite, please. I have fairly adequately defined absolute nothing for you. It is odd that when such a definition is given, it is often quite ignored. Nothing still means, for many people, though perhaps disingenuous people, to refer to that which they cannot see.
I don’t know the meaning of “emmence,” which seems to be a non-word.
(Sorry, I meant to write “immense,” I believe.)
Nonetheless, while you and I disagree on most things, we both believe in a Creator. I speculate freely and superficially in my book on what it took to construct a universe from raw, unformed and unstructured, energy. (The “from nothing” dogma does not work for me any better than it does for atheistic physicists. However, the concept of a primitive form of energy works nicely.)
However, we are still left with the conundrum of extant stuff, perhaps having infinite existence.
Since my God-concept is of a thinking Creator Who does not know everything, He had to figure out how to make this universe from scratch, Awesome work!
But, that, Sir, is not what you are saying. You are saying that He had some energy-stuff with which to work. So, which came first, the chicken or . . .?
I would never presume to suggest that it is work which any human-like mind could ever have done, but I have some positive expectations for the future of human understanding which is not limited by religious doctrine. I’m working for the integration of science and theology, and if that ever happens, the day will come when advanced astrophysics degrees will require courses like, Reverse Engineering Theory— How a Creator might have constructed matter.
I like it. Hope we can help. Is your book finished?

jd

(Didn’t expect that now, did you?)
 
Primary scources that Hawking ever said such a thing.

Your interpretation skills may be what needs to be examined here.
 
Primary scources that Hawking ever said such a thing.

Your interpretation skills may be what needs to be examined here.
Hello there, Strawberry:

Well, if you will read Al Moritz’s two posts, earlier in this thread, and the links he provides, I believe the first link sums up Hawking’s premise pretty nicely.

Here it is, just in case:
firstthings.com/onthesquare/2010/09/much-ado-about-ldquonothingrdquo-stephen-hawking-and-the-self-creating-universe

God bless,
jd
 
Hawking doesn’t understand what creation ex nihilo means, as JDaniel has pointed out.

The doctrine that God created the universe ‘ex nihilo’ is itself a negation of the claim that God created the universe ‘out of’ nothing. There is no ‘out of’. To say that there was ‘nothing except God’ is contradictory, because it takes God to be a ‘thing’ or kind or category of which there was none other. But God is none of these things. The doctrine of creation ‘ex nihilo’ acknowledges the astonishing fact that the world exists, and that therefore it was created by something which, necessarily, is outside the world and outside (at least our univocal) grammar about the world.

The OP says that he finds it difficult to find a place for God in the universe, etc. A good theist is well ahead of you, because he finds it impossible that there should be any place for God in the universe.

I don’t mean to be cryptic; what I’m trying to point out is that you are falling into what is known as onto-theology, and in doing that you wind up worshiping idols, or denying idols.
 
Hawking doesn’t understand what creation ex nihilo means, as JDaniel has pointed out.

The doctrine that God created the universe ‘ex nihilo’ is itself a negation of the claim that God created the universe ‘out of’ nothing. There is no ‘out of’. To say that there was ‘nothing except God’ is contradictory, because it takes God to be a ‘thing’ or kind or category of which there was none other. But God is none of these things. The doctrine of creation ‘ex nihilo’ acknowledges the astonishing fact that the world exists, and that therefore it was created by something which, necessarily, is outside the world and outside (at least our univocal) grammar about the world.

The OP says that he finds it difficult to find a place for God in the universe, etc. A good theist is well ahead of you, because he finds it impossible that there should be any place for God in the universe.

I don’t mean to be cryptic; what I’m trying to point out is that you are falling into what is known as onto-theology, and in doing that you wind up worshiping idols, or denying idols.
I am simply asking the accuser to come up with the evidence of the statement made from a primary source.

I think it is a simple case of misinterpretation of what was said.

God or not, I do not like dishonest apologetics being deployed. That is why I assume there was some misinterpretation first. Then I ask for primary sources.

The same way I do when I put the catholic apologist hat on. And, that is more often than you realize.
 
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