I'm thinking about posting this to a few more religious forums, but I'd just like to hear what people have to say on here.

So, playing Devil's Advocate, and hopefully without a bunch of straw man replies, what is the best argument for God you've heard? And, if you really can't stand it, why is that argument not good enough?

My favorite is Descartes' Ontological argument- but since I don't have a clear and distinct perception of God, this one still isn't enough for me.

Excited to hear replies!

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We're done here.

FALSE. We are most certainly NOT done. 

In due course I will address each and every point you have made. But in this post I am focusing narrowly on your FAILURE to respond to my question:

And yet, if I'm not mistaken, you DO BELIEVE the square root of 2 exists, right?

You and others in this forum seem to be saying in your writings (screaming actually), that you are unwilling to believe anything unless there is empirical evidence for it. You say you want "data."

Accordingly, I am right now, via this post and its follow up posts, conducting a scientific experiment that will produce empirical data. The witnesses of my experiment are all the readers of this discussion. And the subject of the experiment (i.e. the "guinea pig") is YOU. I shall state my hypothesis, make a prediction concerning YOUR behavior to test my hypothesis, and the witnesses will see if my prediction comes out right. However, before I get to my experiment, I must first make several salient points about arithmetic, measurement accuracy and right triangles.

When teaching children arithmetic, it is good practice to use blocks or other tangible objects to show them how it works. For example, to demonstrate that 5+8=13, we can put 5 blocks in one pile, 8 blocks in another pile, and count each pile to confirm (yes, 5 in the first, 8 in the second). Then we can move them all together into a single pile, and count it. Lo and behold, the count is 13. This constitutes empirical, scientific evidence that 5+8=13. Anyone who memorizes the arithmetic facts without seeing (or at least imagining) such a demonstration is unlikely to comprehend arithmetic (and tragically, there are millions out there in this category, but I digress). We could use this same method to confirm, scientifically, that the SUM of 5 and 8 does indeed EXIST... its existence is shown and is precisely measured in the pile of 13.

I'm not certain what the present limit of accuracy is, as expressed in number of decimal places, of the most advanced scientific instruments. A quick check here shows the speed of light at about 9 decimal places, the gravitation constant at 8, the reduced Plank constant at 12, the electron charge at 12. And so, it would appear to me that (say) 15 decimal places is an "outer limit" on what is currently the most precise empirical data. 

The Pythagorean Theorem states an algebraic relationship between the sides of a triangle, where one of the angles is PRECISELY 90 degrees. If we were to construct a triangle out of metal (or out of something more exotic such using optics or nano technology or some such), then how precisely could the angle and sides be measured? 15 decimal places appear to be the current outer limit, but nevertheless, let's allow 100 decimal places.

(As an aside, I will note that we can count discrete, observable things with accuracy far greater than 15 decimal places, such as counting the number of bytes in a computer file, although 100-decimal-place counts are a stretch even for the best computers. However, such measurements are not pertinent for measuring angles or side-lengths of triangles.)

If we could construct a right triangle with the two legs of length 1, then, per the Pythagorean Theorem, the hypotenuse would have length square root of 2. We will ignore, for the sake of discussion, a severe limitation with this scenario (namely, that the Pythagorean Theorem cannot be proven without assuming an axiom for which their is NO scientific evidence from either classical geometry, or from real analysis, or from set theory). Now, how precisely could we measure the length of the hypotenuse? Certainly, we cannot measure it any more accurately than 100 decimal places, which is wildly beyond anything science can do today. And of course, such an extraordinarily precise measurement of the hypotenuse would be useless unless we likewise measure the angle as equal to 90, within 100 decimal places of accuracy, and, as well, the 2 legs to be 1, within 100 decimal places of accuracy.

Here is the difficulty. Whatever number our measurement returns for the hypotenuse, accurate to 100 decimal places, it's square is guaranteed NOT to equal 2. Hence, there is NO WAY to produce empirical data that confirms the existence of the square root of 2. Indeed, for much of mathematical history, it was believed that the square root of 2 did not exist. Similarly, it was believed that you cannot "square the circle" which is more or less equivalent to saying pi does not exist.

And so, I shall now turn to my present experiment of which YOU are my subject. Your task is simple: either answer my two questions set forth below within a time limit, or don't answer them within that time (either by failing to respond to this post, or responding with a rant that fails to answer the questions). Here we go....

MY HYPOTHESIS: You are harboring inconsistent beliefs to support your atheism, and you lack the emotional maturity to admit you are doing so.


Question 1 (Multiple Choice): Do you believe the square root of 2 exists?
(a) No.
(b) Yes, because I have empirical evidence that the square root of 2 exists.
(c) Yes, but I admit I have no empirical evidence that the square root of 2 exists.

Question 2 has three alternative forms, depending on your answer to Question 1:

Question 2(a), to be answered only if your answer to Question 1 is (a). Justify your position as a so-called "scientist" when you reject the existence of a number, the square root of 2, the existence of which is universally believed by mathematicians, scientists and engineers today, and without which much of the mathematics developed after about 1650 (on which science firmly rests today) would collapse.

Question 2(b), to be answered only if your answer to Question 1 is (b). What is your EMPIRICAL evidence that the square root of 2 exists? Explain how the experiment was done, including what instruments were used to make the measurements. And, most importantly, produce the measured hypotenuse length, within 100 decimal places, that squares to equal exactly 2 (NOT, e.g., 1.999999999999998 or 2.00000000000001).

Question 2(c), to be answered only if your answer to Question 1 is (c). Justify your inconsistent position, wherein you defend your atheism by requiring empirical evidence before believing anything to exist, and yet you believe the square root of 2 exists WITHOUT empirical evidence.

TIME LIMIT: Post your answers to my two questions on this forum, in reply to this post, NO LATER THAN 10:00 p.m. Pacific Daylight Time on June 30, 2013.

I note that you have been very quick to respond to most of my posts here, so it would appear that three days is ample time. However, if you need additional time (e.g. because you are going on vacation), I will gladly extend the deadline by a reasonable number of days upon receiving your polite request that includes the requested new deadline.

This is GOOD SCIENCE to test my hypothesis. Your posts in reply to this post constitute empirical data. And I can't falsify the data because everyone reading this discussion is a witness!


Prediction 1. You will fail to answer my two questions before the deadline.

Prediction 2. You will post a rant in reply to this post that EVADES answering my two questions (and does NOT answer them), and instead attacks my questions (without answering them), and/or addresses other material I have posted that is unrelated to my two questions, and/or assassinates my character, and/or ridicules me or my website, and/or poses another experiment.

Okay, Gallop's Mirror, let the scientific experiment begin! I'm wearing my white lab coat, clipboard in hand, listening to the clock tick and watching to see what the guinea pig does. (Hint: look in the mirror... there's a red spot painted on your forehead.) We shall all see if my Predictions come out correct.

Good luck! :)


I apologize for misspelling Gallup at the end of my post.  Just caught it after the 15 minutes to edit expired.

Interesting read, Mark.  I was reminded of Zeno's paradoxes, in particular the dichotomy one - perhaps because your suppositions were based on Pythagoras's theory. 

I was also reminded of the ghastly 'logarithm' tables we had to use in school, that, much to our childish hilarity, failed to produce accurate results to certain apparently simple calculations.

I realise you are a mathematician, and as such, the subject must be close to your heart, so to speak.  But is it not possible that there are certain mathematical conundrums that simply cannot be resolved to a logical answer?

This is in reply to Strega's post above, which appears be at the limit of indentation on this forum, as there was no reply button.

Interesting read, Mark.

Thank you.

I was reminded of Zeno's paradoxes, in particular the dichotomy one - perhaps because your suppositions were based on Pythagoras's theory.

You hit the nail on the head. The struggle over the millennia to resolve Zeno's paradoxes is really what this is all about. In my view, the paradoxes have all been beautifully resolved by the development of continuum methods, using epsilons and deltas with predicate logic. When I comprehended this as a student at UCLA, my atheism dissolved, and there was no going back. Forget the Bible and all of that stuff. Look at the profoundly ingenious, staggeringly beautiful, awesomely inspiring mathematical methods developed in the 20th century that transcend the limitations posed by Zeno. But in doing so, you must DROP the requirement of empirical evidence in favor of transcendent intellectual beauty.


I was also reminded of the ghastly 'logarithm' tables we had to use in school, that, much to our childish hilarity, failed to produce accurate results to certain apparently simple calculations.


Well, the square root of 2 is only the beginning of an infinity vastly larger than the infinity of the ordinals, to wit: the infinity of the real numbers (a.k.a. continuum). This includes most logarithms. Flipping the coin from your school memory, I was a student at UCLA before the days of calculators. We used slide rules, but they were only accurate to 3 decimal places. Unfortunately, in my freshman chemistry lab, 4 decimal places were required, so our slide rules were useless. As my classmates laboriously did hundreds of 4-place multiplication and division problems by hand, I purchased a good log table, and reduced all that labor to addition and subtraction!

I realise you are a mathematician, and as such, the subject must be close to your heart, so to speak. But is it not possible that there are certain mathematical conundrums that simply cannot be resolved to a logical answer?


The breathtaking mathematical results from about 1880 to the present, virtually all of which rest on predicate logic, provide encouragement, to say the least. On the other hand, Godel's First Incompleteness Theorem roughly states that, in any axiomatic system sufficient to describe the natural numbers, there exist true statements that have no proof. So you might be right that THAT conundrum will never be resolved, to wit: identifying such unprovable truths... how will we know they are true if we can't logically prove them? Even Fermat's Last Theorem, which resisted both proof and counterexample for several centuries, was finally proven by Andrew Wiles, as published in 1995. Not that I understand Wiles' proof... it's way over MY head! :)

Significantly, our proof that God exists rests on five axioms NONE of which requires continuum or other infinite methods.  We use predicate logic.  But we do NOT use, for example, the axiom of infinity from set theory, or Peano's successor axiom, or the completeness axiom from real analysis.  Nor do we do any mathematical induction.  And yet, we prove a unique, self-causing, omnipotent phenomenon exists.  Blew me away when I first read Hatcher's paper!


Cheers, Mark

"my atheism dissolved, and there was no going back"

You have my deepest sympathies --

Thank you, Mark.  

Are you saying that your proof calculations demonstrate a cosmic cause or prime mover, as opposed to affirming the religions' specific versions of god?

In other words, are you evidencing Deism or Theism?

This is in reply to Strega's post above.

Thank you, Mark. 

You're welcome.

Are you saying that your proof calculations demonstrate a cosmic cause or prime mover, as opposed to affirming the religions' specific versions of god?

Yes. Precisely. However, I don't care for the wording "proof calculations." It's simply a proof. If you watch my Videos 2 and 3, I think you will agree that "calculation" is not appropriate. 

In other words, are you evidencing Deism or Theism?

As I found Deism defined here (but without an in-depth examination of the definition), it appears we have proven the Deity exists, per such definition, which I am calling God. As for Theism, the definition here is vague, to say the least, and is certainly broader. ALL we have proven at my website is that a unique, self-causing, omnipotent phenomenon exists, which, in your words, is "a cosmic cause or prime mover."

Nevertheless, it is my opinion, based on empirical data not easily shared as well as intellectual insight, that this same God has numerous additional qualities beyond what we have proven, and our result is forward compatible. Thus, for example, if there is an omnipotent God that LOVES us and/or is GOOD, then it is necessarily the SAME unique God that we have already proven exists. Such investigation is for the future (some interesting ideas are in formation), and I cannot predict the results. However, I have no interest in exploring, either with mathematics or with science, the doctrines, scriptures, allegorical tales or myths from Christianity or any other religion.

Cheers, Mark :)

@Mark - you've tossed the word, "omnipotent" about on numerous occasions, I'd love to hear your definition of it.

Mark, am not a mathematician so I will not go into asking you what this or that axiom means. I have read your last comment where you talk about maths having proved that god exist and looked at the link you have provided. 

In it I found this short synopsis, maybe there is more

  • The G Proof — how the Axioms and Predicate Logic are used to rigorously prove a phenomenon exists that:
    1. creates itself — i.e. it causes itself,
    2. is omnipotent — i.e. it causes everything else, and
    3. is unique — i.e. it is the one and only such phenomenon.

Such a phenomenon can only be what is commonly known as “God.”

My first question is why must this be god and not the universe or rather matter? The universe is unique, I mean tell me if there is any other thing you know as unique as the universe?

It is omnipotent and I will add omnipresent. I want you to tell me where Nature is not present at all times and where it's laws doesn't apply?

Creates itself- am waiting for you to show me how to annihilate matter. When you do that, maybe you can then show me how to create matter.

As a general comment, I don't think there is anything new in this argument that is different from the Ontological argument which it tries to prove. The mistake this does is you define god into existence and then continue to insist that god exists. I don't know if you like philosophy, maybe you should read Kant's critique of pure reason where he shows the weakness of this proofs for god though at the end he says he believes in god which I don't know how he gets there.

I strongly suspect that, as a professional mathematician, Mark is aware of a number of mathematical paradoxes, Gordian knots, so to speak, and he has chosen one that can only result in one of the three responses he has predicted. When it comes to bar bets, never play another man's game.


My experiment is GOOD SCIENCE, not a "bar bet"! I'm not "inviting" Gallup's Mirror into a "bet." He (or perhaps she, but probably he) has no choice here, rather like the guinea pigs in a lab cage... they are IN the experiment, period. The data we all see from my experiment will be very real, empirical and legitimate, and my predictions stand.  If he chooses not to "play" (as you say) by remaining silent, then his LACK of response is good data that makes my Prediction 1 come out true, although not my Prediction 2. :)

Cheers, Mark

archaeopteryx, I'm replying here to your omnipotence question above, as we are at the limit of the intent levels.

@Mark - you've tossed the word, "omnipotent" about on numerous occasions, I'd love to hear your definition of it.

Phenomenon is an undefined term, and all variables (e.g. x, y, z) are phenomena.  Causes is also an undefined term, and is a two-place predicate that joins two phenomena, e.g. "x causes y".

We define O as a one-place predicate, that takes a single variable, such as Ox, which means "phenomenon x is omnipotent."  O is formally defined as follows (using English here in lieu of predicate logic symbols not available in this text editor, at least to my knowledge):

For all x (Ox if-and-only-if, for-all y( x causes y ))




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