The Incontrovertible Science and Mathematics of God's Existence (1 Viewer)

Rawlings

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The Kalam Cosmological Argument:

1. Whatever begins to exist has a cause of its existence.
2. The Universe (physical world) began to exist.
Argument based on the impossibility of an actual infinite.
2.11. An actual infinite cannot exist.​
2.12. An infinite temporal regress is an actual infinite.​
2.13. An actually infinite temporal regress cannot be traversed to the present.​
2.14 Therefore, an actually infinite temporal regress cannot exist.​
AND
Argument based on the impossibility of the formation of an actual infinite by successive addition.
2.21. A collection formed by successive addition cannot be actually infinite.​
2.22. The temporal series of past events is a collection formed by successive addition.​
2.23. Therefore, the temporal series of past events cannot be actually infinite.​
3. The Universe has a cause of its existence.


Why does the conclusion entail the necessity of God's existence?

The following is my own syllogistic summary of the conclusion regarding the only possible cause of the physical world:

3. The Universe has a cause of its existence.
3.1. If the cause of the universe's existence were impersonal, it would be operationally mechanical.​
3.2. An operationally mechanical cause would be a material existent.​
3.3. The causal conditions for the effect of an operationally mechanical cause would be given from eternity.​
3.4. But a material existent is a contingent entity of continuous change and causality!​
3.5. An infinite temporal series of past causal events cannot be traversed to the present.​
3.6. Indeed, an actual infinite cannot exist.​
3.7. Hence, a temporal existent cannot have a beginningless past.​
3.8. Hence, time began to exist.​
3.9. A material existent is a temporal existent.​
3.10. Hence, materiality began to exist.​
3.11. The universe is a material existent.​
3.12. Hence, the universe began to exist.​
3.13. Hence, the cause of the universe's existence cannot be material (per 3.10.).​
3.14. Hence, the cause of the universe's existence cannot be operationally mechanical (per 3.2., 3.10.).​
3.15. Hence, the eternally self-subsistent cause of the universe's existence is wholly transcendent: timeless, immaterial and immutable (3.13.).​
3.16. The only kind of timeless entity that could cause the beginning of time sans any external, predetermining causal conditions would be a personal agent of free will (per 3.3., 3.14.).​
3.17. Hence, the eternally self-subsistent cause of the universe's existence is a personal agent of free will.​

Broadly summarized: the eternally self-subsistent cause cannot be natural (or material), as no continuously changing entity of causality can be beginningless. The latter would entail an infinite regress of causal events, which cannot go on in the past forever. There must be a first event, before which there is no change or event. In short, given that an infinite regress of causal events is impossible, the physical world cannot be the eternally self-subsistent ground of existence. The eternally self-subsistent cause cannot be abstract either. An abstract object has no causal force, and, in any event, abstractions contingently exist in minds. Hence, the uncaused cause is a wholly transcendent, unembodied mind.
 
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Rawlings

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Whether our universe is the one and only to have ever existed, one large spacetime continuum, albeit, with localized areas of activity, one in a cyclical series of universes, or a multiverse: the cosmological configuration at large cannot be past eternal.

We cannot scientifically preclude the former potentialities in bold, but we can logically, mathematically and scientifically preclude the possibility that the latter is past eternal!

Science has recently caught up with what logic and mathematics have told us all along about entities of space, time, matter and energy. The physical world cannot be an actual infinite.

From an excerpt of an article I wrote a few years ago:
Our theorem shows that null and timelike geodesics are past-incomplete in inflationary models, whether or not energy conditions hold, provided only that the averaged expansion condition H av > 0 holds along these past-directed geodesics. This is a stronger conclusion than the one arrived at in previous work in that we have shown under reasonable assumptions that almost all causal geodesics [i.e., as distinguished from those of higher dimensions], when extended to the past of an arbitrary point, reach the boundary of the inflating region of spacetime in a finite proper time (Borde-Guth-Vilenkin Theorem: Inflationary spacetimes are not past-complete).​
This theorem extends to cyclical inflationary models and the inflationary models of multiverse as well. The physical universe at large, regardless of the chronological or the cosmological order of its structure, cannot overcome the thermodynamics of entropy.​
Joined by others, Vilenkin summarizes the matter as follows:​
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past eternal universe. There is no escape, they have to face the problem of a cosmic beginning (Many World in One; New York: Hill and Wang, 2006, pg. 176).​
 
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Grasping the essence of the Kalam Cosmological Argument entails an appreciation of the distinction between potential and actual infinities. The following is an excerpt from an article I wrote regarding that distinction:

. . . Just as more than a few atheists have argued on their blogs, Morriston inexplicably argues potential infinities in refutation of Craig's observation regarding the existential impossibility of a quantitatively definite actual infinity. How is it possible that a professor of philosophy doesn't grasp the difference between potential infinities and actual infinities? As every serious calculus student should know, actual infinities only exist in minds and only as they're intuitively understood to entail a boundlessly large, indeterminable number of things or a boundlessly large, indeterminable amount of something.​
It's impossible for actual infinities to exist outside of minds precisely because there's no limit, and the only sense in which they exist inside minds is strictly conceptual. There's never a point in time or being outside of minds when there isn't still more and more. . . . One might as well ask what the numeric value of Beauty is as ask what the numeric value of Infinity is. From this we see that the existential impossibility of an actual infinity outside of minds goes to quantity, not to essential qualities of being.​
A common mistake is to point to the set of real numbers, for example, as its cardinality is an actual infinity, albeit, conceptually. Indeed, the set of all real numbers arguably entails an infinite number of actual infinities, each of which is an actual infinity within an actual infinity. The infinite set of real numbers is an example of an uncountable infinity, wherein the actually infinite amount of real numbers between the integers 0 and 1, for example, is as infinity great as the actually infinite amount of real numbers between all of the other adjacently sequential ±integers from 0 to ±∞ combined (see Cantor's diagonal proof)! Mind blowing to be sure, but, once again, the infinite set of real numbers only exists in minds and only as intuitively understood to entail a boundlessly large, indeterminable number of infinities.​
Which brings us to the realization that no number actually exists, in and of itself, outside of minds either. When we talk about a real number like ±1 as opposed to a surreal number like ±∞, what we actually mean is that a real number has a definitive, finite value, while a surreal number has some indeterminate value. The only things that actually exist outside of minds in this wise are the symbols (or numerals) scribbled on paper, for example, to represent numbers.​
Infinity is also used to denote the quality of God’s attributes. When the classical theist says that God is infinite, he means that God is incomparably perfect in all ways. There’s no divine attribute of infinity as such. God’s omniscience, omnipotence and eternality are routinely confounded as being actual infinities, but once again these are inherent qualities, not external quantities of things. I’ve written on the actual nature of these attributes elsewhere and Craig addresses their nature quite handily in his articles "Is God Actually Infinite" and "God, Time and Eternity", so I need not repeat him or myself here, except to point out that the key to understanding their actual nature is to keep in mind that God is wholly transcendent—having no temporal extension (or magnitude). God is the Eternal Now who stands and stays, as it were, with no beginning or end.​
While Morriston seems to grasp the key that unlocks the door to the understanding of the nature of the pertinent attributes of divinity, at one point in his critique he smugly argues that God could create a hotel with an actual infinite number of rooms, as if to say that this is so obviously possible that even a child could understand why Craig's argument is false.​
But it's Morriston who's befuddled.​
That's akin to wondering if God could create a rock so heavy that even He couldn't lift it. God can't do that either. Divine omnipotence is not the power to do anything at all; rather, it's the power to do all things possible. This is not a limit on God's power. On the contrary, it's precisely because God is omnipotent that no rock too heavy for Him to lift could possibly exist in the first place, just like a hotel with an actually infinite number of rooms couldn't possibly exist in the first place. An actual infinity is a set containing an infinite number of elements, and in general, it's the set containing all possible quantity that's forever growing toward Infinity but never reaching Infinity. The distinction between potential infinities and actual infinities is ultimately a misnomer, as the "distinction" is actually the definition of the only kind of infinity that can exist outside of minds, namely, a potential infinity, which is a set with a finite number of elements at any given moment in time or being that is always increasing toward Infinity as the limit.​
It's impossible to traverse an actual infinity!​
In any event, God couldn't logically do anything contrary to His nature. Objectively speaking, according to the first principles of metaphysics, if God exists, our logic is God's eternally uncreated logic bestowed on us. For God to do something contrary to His nature is for God to deny Himself. God = God. God cannot be God and not-God simultaneously. How did this guy Morriston get a doctorate in religious philosophy? Clearly, he's one of these leftist kooks turning out imbeciles from our universities.​
Now on to the mathematical treatment of Infinity.​
 

SystemShock

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The Kalam Cosmological Argument:
Have to say, I find it ironic when Christians use Islamic arguments. Anyway, you could've stopped right there. I can grant you the original Kalam argument, and you still cannot get to the Christian god, or any god really.

Of course, you throw in William Craig, who added a couple bullets to the argument, including the god of the gaps fallacy: that the cause of the universe must be a god, and once you hit that fallacy, there goes Craig's argument.

Actually, Craig's arguments sound really good, if you want to believe in them or are not familiar with the concepts he talks about. But in the end, they fail, because he always reaches a point when god of the gaps has to make the jump from whatever he's talking about to Jesus, lack of evidence and all.
 
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Rawlings

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Have to say, I find it ironic when Christians use Islamic arguments. Anyway, you could've stopped right there. I can grant you the original Kalam argument, and you still cannot get to the Christian god, or any god really.

I find it ironic that you believe the universal imperatives of logic and mathematics are inherently Christian or Islamic. :hahar:

But, then, that's not the historical order of things. The Kalam Cosmological Argument is historically predicated on the work of Philoponus. Another except from my article "A Refutation of Cosmic Skeptic's Sophomoric Critique of the Kalam Cosmological Argument":

The Christian theologian and early empiricist philosopher John Philoponus of the 5th Century was actually the first to argue from the impossibility of an infinite regress in Against Aristotle, wherein he not only refuted a temporally infinite universe, but the credibility of Aristotelian cosmology concerning the composition of the lower heavens and celestial spheres. Following the arguments of Philoponus, Al-Kindi (801–873 A.D.) composed the first formal version of the horizontal cosmological: "Every being which begins has a cause for its beginning; now the world is a being which begins; therefore, it possesses a cause for its beginning."​
Aristotle himself understood that an actual infinity is impossible; i.e., the physical universe couldn't be spatially infinite. Philoponus and Al-Kindi argued that precisely because the universe is divisible magnitude as Aristotle points out, nothing about the universe could be infinite. An infinite past would be an actual infinity. Absurdity! Hence, the universe necessarily began to exist in the finite past. Philoponus and Al-Kindi's primary interest was to evince why no divisible entity could possibly be the necessary existent and invited one to conclude that only an indivisible and, therefore, timelessly immaterial entity could be the necessary existent.​
While Al-Ghazali (1058–1111 A.D.) wholeheartedly agreed, he was dissatisfied with the unnecessary ambiguity of the argument. Like Philoponus and Al-Kindi before him, he argued that the universe is composed of temporal phenomena preceded by other temporally-ordered phenomena, and given that an actual infinite is impossible, such a series of temporal phenomena cannot continue to infinity. Then Al-Ghazali brilliantly observed that not only must the universe have a timeless cause of its existence, but this timeless cause must be a personal free agent; for if the cause of the universe's existence were impersonal, it would be operationally mechanical. This would mean that the cause could never exist sans its effect, as from eternity the sufficient causal conditions for the effect to occur are given.​
As explained by Craig:​
The only way for the cause to be timeless but for its effect to begin in time is for the cause to be a personal agent who freely chooses to bring about an effect without any antecedent determining conditions. Philosophers call this type of causation 'agent causation,' and because the agent is free, he can initiate new effects by freely bringing about conditions which were not previously present. . . . Similarly, a finite time ago a Creator endowed with free will could have freely brought the world into being at that moment. In this way, the Creator could exist changelessly and eternally but choose to create the world in time. So the cause is eternal, but the effect is not. Thus, we are brought, not merely to a transcendent cause of the universe, but to a Personal Creator.​
Hence, Al-Ghazali appends the syllogism per his ontological analysis of the properties of the cause.​
Known today as the Kalam, it's this version of the argument that came to the medieval Christian tradition through Bonaventure (1221–74 A.D.), and it's this version that's championed by Craig et al. today with the very same philosophical supports for the second (or pivotal) premise, albeit, as decisively supplemented by Al-Ghazali's personal-impersonal distinction. Craig et al. have since mathematically and analogously elaborated on the philosophical supports and formulated a syllogistic expression of Al-Ghazali's ontological analysis.​
Of course, you throw in William Craig, who added a couple bullets to the argument, including the god of the gaps fallacy: that the cause of the universe must be a god, and once you hit that fallacy, there goes Craig's argument.

Well, presumably, at sometime, you're going to stop spouting slogans and directly refute the argument. In the meantime, your invocation of the atheist in the gaps fallacy, which apparently holds that the physical world just popped into existence out of an ontological nothingness, is the baby talk of magic.

Actually, Craig's arguments sound really good, if you want to believe in them or are not familiar with the concepts he talks about.

Actually, the logical, mathematical and scientific imperatives of the matter stand and stay. As for your unfamiliarity with the pertinent concepts, I'll be happy to lace you up.

But in the end, they fail, because he always reaches a point when god of the gaps has to make the jump from whatever he's talking about to Jesus, lack of evidence and all.

If you want to start a thread on whether or not the God of the Bible is in fact the God of Creation, have at it, sport. The topic of this thread regards the God of Creation.

Now on to the mathematical treatment of Infinity.
 
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Rawlings

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Excerpt from my article:

But, once again, what do we do with any given integer divided by Infinity? The quotient would obviously not equal ±∞. Nor would it equal 0. If we were to divide ±1 by , for example, and say that the quotient were 0, then what happened to ±1? Calculus entails the analysis of algebraic expressions in terms of limits, so in calculus the expression n ÷ ∞ = 0 doesn't mean the quotient literally equals 0. Rather, 0 is the value to which the quotient converges (or approaches). Again, Infinity is a concept, not a number. We can approach Infinity if we count higher and higher, but we can't ever actually reach it. Though not an indeterminate form proper, n ÷ ∞, like any other calculation with Infinity, is technically undefined. Notwithstanding, we intuitively understand that ±1 ÷ ∞ equals an infinitesimally small positive or negative number. Hence, we could intuitively say that ±1 ÷ ∞ = ±0.000 . . . 1, and we would be correct.​
For the proof, let the input variable = x, and let the integer = 1:​
x
1 ÷ x
1​
1​
2​
0.5​
4​
0.25​
10​
0.1​
100​
0.01​
1,000​
0.001​
10,000​
0.0001​
100,000​
0.00001​
1,000,000 . . .​
0.000001 . . .​
Note that as x gets larger and larger, approaching Infinity, 1 ÷ x gets smaller and smaller, approaching 0. The latter is the limit, and because we can't get a final value for 1 ÷ ∞, the limit of 1 ÷ x as x approaches Infinity is as close to any definitive value as we're going to get. The limit of a function in calculus tells us what value the function approaches as the x of the function (or, in shorthand, the x of the f ) approaches a certain value:​
lim f(x)
xa
We know that we're proving the limit for 1 ÷ ∞; hence, the following reads "the limit of the function f(x) is 1 ÷ x as x approaches Infinity":​
f(x) = lim 1 ÷ x
x→∞
Additionally, the output values of function f depend on the input values for the variable x. In the expression f(x), f is the name of the function and (x) denotes that x is the variable of the function. The function itself is "the limit of 1 ÷ x as the inputs for x approach Infinity." When we solve for the limit of more than one function in an algebraic combination, we typically call the first of the functions f for "function." It really doesn't matter what we call any of them as long as we distinguish them from one another. The names given to the others typically follow f in alphabetical order merely as a matter of aesthetics: g, h, i, j and so on.​
Hence, as we can see from the table above, the function proves out that the limit of 1 ÷ x as x approaches Infinity is 0. That is, as x approaches Infinity, 1 ÷ x approaches 0.​
lim 1 ÷ x = 0
x→∞
Altogether then:​
lim f(x) =
x→a
lim 1 ÷ x = 0 (i.e., 0.000 . . . 1)
x→∞
x
1 ÷ x
1​
1​
2​
0.5​
4​
0.25​
10​
0.1​
100​
0.01​
1,000​
0.001​
10,000​
0.0001​
100,000​
0.00001​
1,000,000 . . .​
0.000001 . . .​

In nature t = 0 is never reached via an infinite regress into the past. Hence, an infinite regression can never be traversed to the present.
 

SystemShock

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I find it ironic that you believe the universal imperatives of logic and mathematics are inherently Christian or Islamic. :hahar:
And how exactly did you get that from what I posted?

Ilm al-Kalām.

Now on to the mathematical treatment of Infinity.
And what exactly is it that you are trying to prove here? Are you going to try to make me dizzy with mathematics (like Craig does), then tell me that because infinity is a concept and not a number, therefore Yahweh?
 
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Rawlings

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And how exactly did you get that from what I posted?

Ilm al-Kalām.


And what exactly is it that you are trying to prove here? Are you going to try to make me dizzy with mathematics (like Craig does), then tell me that because infinity is a concept and not a number, therefore Yahweh?

You said: "Have to say, I find it ironic when Christians use Islamic arguments."

It's not an Islamic argument as such, and it's historically predicated on a Christian's work. But, ultimately, it's a universally self-evident, logical and mathematical observation relative to the existential distinction between potential and actual infinites. An actual infinity only exists as a mathematical concept in minds, namely, as a boundlessly large, indeterminable number of things or a boundlessly large, indeterminable amount of something. A potential infinity, on the other hand, has existentiality in both minds and nature as a finite quantity of something at any given moment in time or being, albeit, tending toward infinity as the limit. That is the existential distinction between the two. Grasping that is the key to understanding why the Argument is incontrovertible.

And what exactly is it that you are trying to prove here? Are you going to try to make me dizzy with mathematics (like Craig does), then tell me that because infinity is a concept and not a number, therefore Yahweh?

Well, that's a silly takeaway, isn't it? Do you routinely "straw man" that which you don't understand? I've now given the reader everything he needs to grasp the argument. Study to show thyself approved. It's free to read. No charge.
 

SystemShock

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You said: "Have to say, I find it ironic when Christians use Islamic arguments."

It's not an Islamic argument as such, and it's historically predicated on a Christian's work. But, ultimately, it's a universally self-evident, logical and mathematical observation relative to the existential distinction between potential and actual infinites. An actual infinity only exists as a mathematical concept in minds, namely, as a boundlessly large, indeterminable number of things or a boundlessly large, indeterminable amount of something. A potential infinity, on the other hand, has existentiality in both minds and nature as a finite quantity of something at any given moment in time or being, albeit, tending toward infinity as the limit. That is the existential distinction between the two. Grasping that is the key to understanding why the Argument is incontrovertible.



Well, that's a silly takeaway, isn't it? Do you routinely "straw man" that which you don't understand? I've now given the reader everything he needs to grasp the argument. Study to show thyself approved. It's free to read. No charge.

Attacking me is not going to get you anywhere. Neither is posting walls of text.

Again, I'll concede the original Kalam. I'll concede whatever you want me to concede about infinity mathematically speaking. And still, you cannot get from there to Yahweh.
 

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Just some thoughts.
1. Whatever begins to exist has a cause of its existence.
What caused God to exist?
3. The Universe has a cause of its existence.

3.1. If the cause of the universe's existence were impersonal, it would be operationally mechanical.
3.2. An operationally mechanical cause would be a material existent.
Can you clarify your premise a bit here? I don’t follow.
3.3. The causal conditions for the effect of an operationally mechanical cause would be given from eternity.
I don’t understand how this conclusion follows your premise. It seems like you’re stating this as a premise, but this is not universally accepted and you haven’t yet established that this is an immutable fact.
3.5. An infinite temporal series of past causal events cannot be traversed to the present.
Why not?
3.6. Indeed, an actual infinite cannot exist.
Again, I’m not sure this conclusion follows the premises you have attempted to establish.
3.7. Hence, a temporal existent cannot have a beginningless past.
3.8. Hence, time began to exist.
Same.

That sure is a lot of big words, though.
 

SystemShock

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Just some thoughts.

What caused God to exist?

Can you clarify your premise a bit here? I don’t follow.

I don’t understand how this conclusion follows your premise. It seems like you’re stating this as a premise, but this is not universally accepted and you haven’t yet established that this is an immutable fact.

Why not?

Again, I’m not sure this conclusion follows the premises you have attempted to establish.

Same.

That sure is a lot of big words, though.

Those arguments come from William Lane Craig's "updated version" of the Kalam cosmological argument. Craig has PhD's in philosophy and theology, so his arguments can be confusing for us mere mortals and heretics. In the end, Craig's arguments cannot make the logical or mathematical leap to any god, much less a specific god, without god of the gaps. It's either "this cannot be, therefore god", or "this is, therefore god". That is where all of these arguments end.
 

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God didn't begin to exist. God has always existed. Let's start there.

The old special pleading fallacy. Even if someone were to concede both the argument and the special exemption, you still run into the obvious problem SystemShock pointed out. It doesn't get you to god.
 
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Rawlings

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Attacking me is not going to get you anywhere. Neither is posting walls of text.

Again, I'll concede the original Kalam. I'll concede whatever you want me to concede about infinity mathematically speaking. And still, you cannot get from there to Yahweh.

I didn't attack you. I humorously deconstructed your obfuscations in order to clarify things for the reader of your post (post #5), and the pertinent takeaway is the emboldened below and Craig's explication:

While Al-Ghazali (1058–1111 A.D.) wholeheartedly agreed, he was dissatisfied with the unnecessary ambiguity of the argument. Like Philoponus and Al-Kindi before him, he argued that the universe is composed of temporal phenomena preceded by other temporally-ordered phenomena, and given that an actual infinite is impossible, such a series of temporal phenomena cannot continue to infinity. Then Al-Ghazali brilliantly observed that not only must the universe have a timeless cause of its existence, but this timeless cause must be a personal free agent; for if the cause of the universe's existence were impersonal, it would be operationally mechanical. This would mean that the cause could never exist sans its effect, as from eternity the sufficient causal conditions for the effect to occur are given.
As explained by Craig:​
The only way for the cause to be timeless but for its effect to begin in time is for the cause to be a personal agent who freely chooses to bring about an effect without any antecedent determining conditions. Philosophers call this type of causation 'agent causation,' and because the agent is free, he can initiate new effects by freely bringing about conditions which were not previously present. . . . Similarly, a finite time ago a Creator endowed with free will could have freely brought the world into being at that moment. In this way, the Creator could exist changelessly and eternally but choose to create the world in time. So the cause is eternal, but the effect is not. Thus, we are brought, not merely to a transcendent cause of the universe, but to a Personal Creator.​
What you call walls of text as succinctly as possible summarize the essence of the argument. Certain details are very important. The matter is relatively simple once one grasps the facts of the pertinent science (post #2) and the existential distinction between potential infinities and actual infinities. Hence, the mathematical discourse (post #3) and treatment (post #6) on infinity. Not everyone is as familiar as you apparently are with these things. That's all. One has to read and think. I'll be happy to answer any questions you might have, but I would suggest that we deal with one question at a time for the sake of clarity.

Again, the OP does not directly pertain to the God of the Bible.
 

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Again, the OP does not directly pertain to the God of the Bible.

It doesn't matter. Kalam doesn't get you to any god, period. You have to make a special exception to shove a god in because you've already logic'ed the bastage out.
 
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Rawlings

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It doesn't matter. Kalam doesn't get you to any god, period. You have to make a special exception to shove a god in because you've already logic'ed the bastage out.

Nonsense. See above. Nuh uh is not an argument.
 

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Nonsense. See above. Nuh uh is not an argument.

As opposed to the eloquent "Yeah huh, because I said so" argument you are putting forth...

1. Whatever begins to exist has a cause of its existence.

Your argument is that god did not begin to exist, that god has always existed. How can you demonstrate this?
 
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Rawlings

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As opposed to the eloquent "Yeah huh, because I said so" argument you are putting forth...

1. Whatever begins to exist has a cause of its existence.

Your argument is that god did not begin to exist, that god has always existed. How can you demonstrate this?

Are you suggesting that something has not always existed? Something does exist, after all, rather than nothing. The physical world has not always existed. See above.
 

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