Recently I've noticed that some apologists like William Lane Craig are using mathematicsbased arguments to assure us that the Christian god exists. I would like to explain why those arguments use poor logic.
A very broad argument is that mathematics in general seems to explain the cosmos in a way that seems to work unreasonably well. An intelligent designer like Yahweh is then required to explain this apparent mathematical basis for the universe. He is "the great mathematician in the sky."
Not really. The reason math works so well to explain the worldin at least some casesis because we humans created math to describe the cosmos. There is no mystery here. We are the mathematicians describing the universe.
Also, many apologists like to wow us with enormously improbable events that they say cannot be attributed to chance. Since chance is ruled out, "God musta done it."
Wrong again. The only probability that rules out an event happening by chance is an event with a probability of zero. Extremely improbable eventslike the conception of any of ushappen all the time.
Also, to state how improbable a natural event might be doesn't say much if you don't know the probability of an alternate event. So if apologists wish to argue that an event like the apparent finetuning of the universe by chance is only one out a a gazillion, they must compare that probability to the probability that "God musta done it." If they cannot say that the probability of God finetuning the cosmos is greater than chance, then they haven't proved anything.
Finally, a really laughable argument is that the universe cannot be infinitely old because if it was infinitely we could never have reached the present! Such apologists must have slept through their highschool algebra. Consider the number line with numbers increasing infinitely with positive numbers to the right and negative numbers to the left. All you need to do is have any point on that line represent a moment in time with zero being the present, points on the positive direction are the future, and points on the negative direction are the past. See that? You're at 0 (the present), but the past is infinite. You can go back as far as you want to with no limit.
I can go on, but for now let me ask the...
Question for Debate: Are apologists sloppy mathematicians, or are they deliberately trying to deceive people with numbers?
Bad Math Used in Apologetics
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Re: Bad Math Used in Apologetics
Post #61Greetings, Don Don McIntosh wrote:
A naturalistic universe might be expected to be much more chaotic, much less held together by a large number of mathematically welldefined natural laws. Yet here we are.
In the trillions of trials prior to our forming universe, disorder may have disintegrated into the chaos you speak of many times. It may be that one random hit was what generated the order that we apparently see, and this lucky sequence will continue for a bit until the luck runs out. In generating random numbers we can come across the sequence 1,2,3,4,5,6,7,8,9 â€¦.. even irrational numbers expressed decimally will have in their non repetitive sequences some semblance of order. Our assumption is to see the present order, that lets us breathe, as a part of permanence. And yet vast galaxies come and go; stars explode.
Rather than a linear explanation, which seems to replicate human thought, we can follow Einstein with his double cone where either apex meets at a point and the cones divide space into absolute future, absolute past and swirling around, the present. I believe that mysteriously a Lorenz transformation can take a point from one region to another, whatever that might mean in practice.
Mathematics fascinates but I don't think it performs acts of worship. When we try to find God mathematically, we bump against our finite brains and the limitations of our reasoning. Go well.

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Re: Bad Math Used in Apologetics
Post #62Wait a minute, humans "created" math? News to me.Jagella wrote: Recently I've noticed that some apologists like William Lane Craig are using mathematicsbased arguments to assure us that the Christian god exists. I would like to explain why those arguments use poor logic.
A very broad argument is that mathematics in general seems to explain the cosmos in a way that seems to work unreasonably well. An intelligent designer like Yahweh is then required to explain this apparent mathematical basis for the universe. He is "the great mathematician in the sky."
Not really. The reason math works so well to explain the worldin at least some casesis because we humans created math to describe the cosmos. There is no mystery here. We are the mathematicians describing the universe.
Bruh, there are only two games in town..either..Jagella wrote: Also, many apologists like to wow us with enormously improbable events that they say cannot be attributed to chance. Since chance is ruled out, "God musta done it."
1. Nature created the event by random chance
2. Intelligence created the event by...intelligence
If 1 is ruled out, then yeah..."God musta done it".
Right, and with the same token, the only probability that rules out the existence of God is if the existence of God has a probability of zero.Jagella wrote: Wrong again. The only probability that rules out an event happening by chance is an event with a probability of zero.
See what I did there?
Let me see if I can break it down for you; You see, atheists always want to make it seem as if when apologists talk about the improbability of life (or whatever) existing without God is similar to other improbable events in nature, such as winning the lottery, or as you put it; the conception of any of us.Jagella wrote: Extremely improbable eventslike the conception of any of ushappen all the time.
Well yeah, true...someone has to win the lottery, right? Regardless of how improbable it is. However, for the atheistic side of things, the improbability of the universe/life existing is even MORE improbable than the odds of a person winning the lottery.
Again, let me break it down for you; suppose every single person in the USA played the lottery. Now, since AfroAmericans are a minority, the chances of an AfroAmerican winning the lottery is considerable low compared to any other ethnicity, right? (not necessarily, but follow me here).
But wait, there is more; suppose by some unknown fate that the person that wins the lottery will have to be an AfroAmerican who has the occupation of a lawyer. The probability of an AfroAmerican winning the lottery has gotten lower.
But wait, there is more; suppose by some unknown fate that the person that wins the lottery will have to be an AfroAmerican who has the occupation of a lawyer, that lives on the West Coast. Well, the probability of an AfroAmerican winning the lottery has gotten even lower.
But wait, there is more; suppose by some unknown fate that the person that wins the lottery will have to be an AfroAmerican who has the occupation of a lawyer, lives on the West coast, and is under 5'8 in height. Well, the probability of an AfroAmerican winning the lottery has gotten even lower.
So, it is already improbable for an AfroAmerican to win the lottery, generally speaking..but it is even MORE improbable for an AfroAmerican to win the lottery based on those other specified parameters.
It is the improbability of an AfroAmerican winning the lottery in general, PLUS the improbability of an AfroAmerican meeting those other "improbable" parameters...which means that improbability+improbability+improbability+improbability= improbability.
Hell, the probability of a Caucasian winning the lottery would even drop under those specified parameters.
And btw, work as already been done to demonstrate the improbability of our universe being life permitting by random chance alone...and the number as it relates to the improbability of it occurring is so incomprehensible, that to think that we are here based on random chance alone is to actually believe in a miracle.
You may as well just say "Goddidit" at that point.
What do you mean "if"? Not only can we say the probability of God finetuning the cosmos is greater than chance...but we DO say it.Jagella wrote: Also, to state how improbable a natural event might be doesn't say much if you don't know the probability of an alternate event. So if apologists wish to argue that an event like the apparent finetuning of the universe by chance is only one out a a gazillion, they must compare that probability to the probability that "God musta done it." If they cannot say that the probability of God finetuning the cosmos is greater than chance, then they haven't proved anything.
LOL ok, so here is your task...I want you to count DOWN from ALL of the negative numbers, in numerical order...and let me know when you've successfully counted all of the numbers in the negative set of infinite numbers leading to zero on the numbers line.Jagella wrote: Finally, a really laughable argument is that the universe cannot be infinitely old because if it was infinitely we could never have reached the present! Such apologists must have slept through their highschool algebra. Consider the number line with numbers increasing infinitely with positive numbers to the right and negative numbers to the left. All you need to do is have any point on that line represent a moment in time with zero being the present, points on the positive direction are the future, and points on the negative direction are the past. See that? You're at 0 (the present), but the past is infinite. You can go back as far as you want to with no limit.
Go ahead. I will wait. But long story short; if you can't successfully count all of the negative numbers on the infinite set to arrive at zero on the numbers line...then how in the heck can you successfully traverse all of the days on a pasteternal timeline and arrive at the present day?
Can't be done. This is an inescapable problem for atheists...and no amount of science can help you. No amount of mathematical equations can help you...and no amount of philosophical thought can help you.
It is the GESTAPO for atheists.
So only atheists are good mathematicians, and they never deceive people?Jagella wrote: I can go on, but for now let me ask the...
Question for Debate: Are apologists sloppy mathematicians, or are they deliberately trying to deceive people with numbers?

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Post #63
Moderator WarningJagella wrote:
Either post your concession that the apologists' arguments in the OP are exactly what apologists argue, or admit that you are lying here.
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My theological positions:
God created us in His image, not the other way around.
The Bible is redeemed by it's good parts.
Pure monotheism, simple repentance.
YHVH is LORD
The real Jesus is not God, the real YHVH is not a monster.
Eternal life is a gift from the Living God.
Keep the Commandments, keep your salvation.
I have accepted YHVH as my Heavenly Father, LORD and Savior.
I am inspired by Jesus to worship none but YHVH, and to serve only Him.
God created us in His image, not the other way around.
The Bible is redeemed by it's good parts.
Pure monotheism, simple repentance.
YHVH is LORD
The real Jesus is not God, the real YHVH is not a monster.
Eternal life is a gift from the Living God.
Keep the Commandments, keep your salvation.
I have accepted YHVH as my Heavenly Father, LORD and Savior.
I am inspired by Jesus to worship none but YHVH, and to serve only Him.
Re: Bad Math Used in Apologetics
Post #64For_The_Kingdom wrote:
Bruh, there are only two games in town..either..
1. Nature created the event by random chance
2. Intelligence created the event by...intelligence
And another one is one we haven't the ability to access.
As for (1): Nature may have created an event that initiated nonrandomness.
(2) is simply the human way of explaining the inexplicable. Primitive but it does explain, just as Thor explains thunder.
For_The_Kingdom wrote:
And btw, work as already been done to demonstrate the improbability of our universe being life permitting by random chance alone...and the number as it relates to the improbability of it occurring is so incomprehensible, that to think that we are here based on random chance alone is to actually believe in a miracle.
Well the first problem area in this type of reasoning is the assumption of independence which allows the multiplication of probabilities. It may be that the appearance of some rare event makes other events more probable.
The second problem is that we can argue from events on Earth that some event with probability 0.00000000000000000000000000000001 won't happen, unless miraculously. This is because we are dealing with finite sample populations. When we extend our reasoning to the creation of the universe, we move towards the infinite and so an event with nonzero probability will be expected to happen at least once.
Re: Bad Math Used in Apologetics
Post #65Of course people created math. The Greeks, for example, were very important in the invention and development of mathematics. You may wish to look up great mathematicians like Archimedes, Pythagoras, Euler, and Newton to see how they invented mathematical techniques.For_The_Kingdom wrote:Wait a minute, humans "created" math? News to me.
Your mistake here is to limit the number of "games in town" to two. A third possibility is that events can happen with some combination of chance and necessity. For example, a volcanic eruption results from pressure under the surface of the earth. So such eruptions happen all the time with no god involved. There's little if any role chance might play, too. So apologists are mistaken when they claim an event results from either chance or a god. Natural events can and do result from physical necessity.Bruh, there are only two games in town..either..
1. Nature created the event by random chance
2. Intelligence created the event by...intelligence
If 1 is ruled out, then yeah..."God musta done it".
Yes. I see that you've posted a strongman argument. Nowhere did I post that the probability of the existence of gods is zero....the only probability that rules out the existence of God is if the existence of God has a probability of zero.
See what I did there?
What is the probability of the universe existing with no gods, and what is the probability of a god creating the universe? We need these numbers to compare them to see which probability is greater....the improbability of the universe/life existing is even MORE improbable than the odds of a person winning the lottery.
Right so far.Again, let me break it down for you; suppose every single person in the USA played the lottery. Now, since AfroAmericans are a minority, the chances of an AfroAmerican winning the lottery is considerable low compared to any other ethnicity, right?
You're making a lot of mistakes. Here, for instance, you don't add these "improbabilities." If you wish to calculate the probability of an AfricanAmerican lawyer winning the lottery, for example, then divide the number of AfricanAmerican lawyers playing the lottery by the total number of people playing the lottery (assuming that each person playing the lottery has an equal chance of winning).It is the improbability of an AfroAmerican winning the lottery in general, PLUS the improbability of an AfroAmerican meeting those other "improbable" parameters...which means that improbability+improbability+improbability+improbability= improbability.
But go on.
Again, what is that probability?And btw, work as already been done to demonstrate the improbability of our universe being life permitting by random chance alone...and the number as it relates to the improbability of it occurring is so incomprehensible, that to think that we are here based on random chance alone is to actually believe in a miracle.
Besides, we aren't here by random chance alone. Natural selection plays a major role in our evolution.
Which if? I posted more than one here.What do you mean "if"?Also, to state how improbable a natural event might be doesn't say much if you don't know the probability of an alternate event. So if apologists wish to argue that an event like the apparent finetuning of the universe by chance is only one out a a gazillion, they must compare that probability to the probability that "God musta done it." If they cannot say that the probability of God finetuning the cosmos is greater than chance, then they haven't proved anything.
Sure, you say that the Bible god's finetuning of the universe is greater than the probability without him, but I need to see some actual numbers.Not only can we say the probability of God finetuning the cosmos is greater than chance...but we DO say it.
Well, obviously it is impossible to count all the negative numbers (I assume you mean negative integers). But we don't need to count all the negative integers to know that there is a zero that divides the negative integers from the positive integers. So despite an infinite number of negative integers, we can get to the number zero.I want you to count DOWN from ALL of the negative numbers, in numerical order...and let me know when you've successfully counted all of the numbers in the negative set of infinite numbers leading to zero on the numbers line.
Well, you don't "traverse" all the days in an infinite past to get to the present. We are already at the present, and there is no logical limit to how far back we can go into the past....how in the heck can you successfully traverse all of the days on a pasteternal timeline and arrive at the present day?
But, I might be wrong. If the past cannot be infinite, then of course there is a limit to how far back we can go. What is that limit? Why is it a limit? Apologists neglect to tell us what this limit is.
I think it's fair to say that some atheists are poor mathematicians and deceive people. I don't know how that exculpates apologists and their sloppy math, though.So only atheists are good mathematicians, and they never deceive people?

 Apprentice
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Re: Bad Math Used in Apologetics
Post #66Trillions of trials frankly sounds like the work of either an intelligent agent or a program created by an intelligent agent. I alluded to this same basic thought somewhere else on the board, but it's not as if, say, a mindless preuniverse quantum vacuum could really be expected to endlessly try out different combinations of natural laws and initial conditions to see which one might produce a lifepermitting universe.marco wrote:Greetings, Don Don McIntosh wrote:
A naturalistic universe might be expected to be much more chaotic, much less held together by a large number of mathematically welldefined natural laws. Yet here we are.
In the trillions of trials prior to our forming universe, disorder may have disintegrated into the chaos you speak of many times. It may be that one random hit was what generated the order that we apparently see, and this lucky sequence will continue for a bit until the luck runs out.
In generating random numbers we can come across the sequence 1,2,3,4,5,6,7,8,9 â€¦.. even irrational numbers expressed decimally will have in their non repetitive sequences some semblance of order. Our assumption is to see the present order, that lets us breathe, as a part of permanence. And yet vast galaxies come and go; stars explode.
I think that's right in principle, again given trillions of trials. Yet it seems to undermine everything to which we currently attach meaning. By the same principle, it may be that you, Marco, have not actually said anything here. That's because, given the sheer number of login and keystroke errors committed by billions of sleepy, exhausted, drunk, drugged, and otherwise mentally impaired human beings over decades of online activity, someone was bound to eventually, and by sheer accident, log in to your account and type the message attributed to Marco above. But of course that's really nonsense and would literally be an insult to your remarkable intelligence.
That's fair. I agree that we should not read too much theology into our equations. But there is a certain ordered rationality to mathematical systems, and when they map onto physical reality the way they do it does seem to suggest a divine hand at work in the creation.Rather than a linear explanation, which seems to replicate human thought, we can follow Einstein with his double cone where either apex meets at a point and the cones divide space into absolute future, absolute past and swirling around, the present. I believe that mysteriously a Lorenz transformation can take a point from one region to another, whatever that might mean in practice.
Mathematics fascinates but I don't think it performs acts of worship. When we try to find God mathematically, we bump against our finite brains and the limitations of our reasoning.
Extraordinary evidence requires extraordinary claims.
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Re: Bad Math Used in Apologetics
Post #67Well, when you tell me what the other one is I will add it to the list.marco wrote:For_The_Kingdom wrote:
Bruh, there are only two games in town..either..
1. Nature created the event by random chance
2. Intelligence created the event by...intelligence
And another one is one we haven't the ability to access.
Randomness will only get you more randomness, and nothing contrary to this FACT has ever been demonstrated in nature. So to believe it is to believe in the unseen...which is...faith. Not reasonable faith, but blind faith.marco wrote: As for (1): Nature may have created an event that initiated nonrandomness.
Wait a minute, you are a human, right? Well, didn't you just explain the "inexplicable" with nature?? Hmm.marco wrote: (2) is simply the human way of explaining the inexplicable.
Sure, the rare event of me winning the lottery makes it more probable for me to buy a mansion with my lottery winnings.marco wrote:Well the first problem area in this type of reasoning is the assumption of independence which allows the multiplication of probabilities. It may be that the appearance of some rare event makes other events more probable.For_The_Kingdom wrote: And btw, work as already been done to demonstrate the improbability of our universe being life permitting by random chance alone...and the number as it relates to the improbability of it occurring is so incomprehensible, that to think that we are here based on random chance alone is to actually believe in a miracle.
So what? How does that negate what I said?
But there wasn't an infinite amount of possibilities. The big bang event was just a one time event...and to get all of the parameters for a lifepermitting universe just right based on complete randomness/chaos the very first time is like standing on Mars and randomly throwing a dart towards the rotating Earth and hitting the bullseye on a target somewhere in Montana.marco wrote: The second problem is that we can argue from events on Earth that some event with probability 0.00000000000000000000000000000001 won't happen, unless miraculously. This is because we are dealing with finite sample populations. When we extend our reasoning to the creation of the universe, we move towards the infinite and so an event with nonzero probability will be expected to happen at least once.
Do you think you will hit the mark with just one try?

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Re: Bad Math Used in Apologetics
Post #68Oh, so I guess 2+2 didn't = 4 prior to the times of Archimedes, Pythagoras, Euler, and Newton.Jagella wrote:Of course people created math. The Greeks, for example, were very important in the invention and development of mathematics. You may wish to look up great mathematicians like Archimedes, Pythagoras, Euler, and Newton to see how they invented mathematical techniques.For_The_Kingdom wrote:Wait a minute, humans "created" math? News to me.
Jagella wrote:Your mistake here is to limit the number of "games in town" to two. A third possibility is that events can happen with some combination of chance and necessity. For example, a volcanic eruption results from pressure under the surface of the earth. So such eruptions happen all the time with no god involved. There's little if any role chance might play, too. So apologists are mistaken when they claim an event results from either chance or a god. Natural events can and do result from physical necessity.Bruh, there are only two games in town..either..
1. Nature created the event by random chance
2. Intelligence created the event by...intelligence
If 1 is ruled out, then yeah..."God musta done it".
"Nature events can and do result from physical necessity" < #1 has already taken care of this one.
As I said, 1 and 2 are the only games in town.
Yeah but the problem is, once you've admitted the possibility of God (a necessary being) existing, then you are simultaneously concluding that God actually exists (see Modal Ontological Argument).Jagella wrote:Yes. I see that you've posted a strongman argument. Nowhere did I post that the probability of the existence of gods is zero....the only probability that rules out the existence of God is if the existence of God has a probability of zero.
See what I did there?
Impossible.Jagella wrote: What is the probability of the universe existing with no gods
We don't need to know the probability of something that has actually occurred. That is like asking what is the probability of Michael Jordan winning 6 championships.Jagella wrote: , and what is the probability of a god creating the universe?
Well, the fact that the universe exists would mean that the probability of God creating the universe is high. And since the physical world cannot be pasteternal, that would make the probability of the universe existing without God impossible.Jagella wrote: We need these numbers to compare them to see which probability is greater.
The point is; the more parameters you add to the mix, the more improbable the task will become...and that is a parallel to the physical constants which govern our universe, with each constant being so mathematically precise that if the value of each one was either decreased or increased, life would have never have began to exist.Jagella wrote:You're making a lot of mistakes. Here, for instance, you don't add these "improbabilities." If you wish to calculate the probability of an AfricanAmerican lawyer winning the lottery, for example, then divide the number of AfricanAmerican lawyers playing the lottery by the total number of people playing the lottery (assuming that each person playing the lottery has an equal chance of winning).It is the improbability of an AfroAmerican winning the lottery in general, PLUS the improbability of an AfroAmerican meeting those other "improbable" parameters...which means that improbability+improbability+improbability+improbability= improbability.
You don't get that kind of mathematical precision from a mindless/blind process...you get it from an engineer..a cosmic engineer.
https://evolutionnews.org/2010/04/roger ... ic_finetu/Jagella wrote:
Again, what is that probability?
Do you see that? The probability is 1/10^10^123. Do the math on that one.
Natural selection selects, it doesn't create anything...and it is something that happens AFTER life had already originated...but we are talking about the probability of life occurring in the first place with no intelligence at all.Jagella wrote: Besides, we aren't here by random chance alone. Natural selection plays a major role in our evolution.
Does science help us here? No.
A temporal universe existing without God (or any First Cause) is logically impossible..so the probability is zero.Jagella wrote: Sure, you say that the Bible god's finetuning of the universe is greater than the probability without him, but I need to see some actual numbers.
Splitting hairs..Jagella wrote:
Well, obviously it is impossible to count all the negative numbers (I assume you mean negative integers).
That is the point; it is all conceptual...but when you apply the "concept" to reality, you wind up with absurdities...which is precisely why, in the real world, you can't count "down" from infinity to zero.Jagella wrote: But we don't need to count all the negative integers to know that there is a zero that divides the negative integers from the positive integers.
And if you can't count down from infinity to zero, then how can you traverse an infinite number of past days to arrive at today? You can't do it.
So why can't you get to the number zero by counting (one by one) all of the negative numbers down to zero?Jagella wrote: So despite an infinite number of negative integers, we can get to the number zero.
Oh, so yesterday wasn't traversed to arrive at today?Jagella wrote:
Well, you don't "traverse" all the days in an infinite past to get to the present.
Dude, you just said that we don't traverse all days in an infinite past to get to the present. Now you are saying there is no logical limit to how far we can go into the past...which implies that we can traverse an infinite amount of days in the past as far back as we can go.Jagella wrote: We are already at the present, and there is no logical limit to how far back we can go into the past.
Well, I am an apologist, and I will tell you what the limit is...the limit is; the beginning of time.Jagella wrote: But, I might be wrong. If the past cannot be infinite, then of course there is a limit to how far back we can go. What is that limit? Why is it a limit? Apologists neglect to tell us what this limit is.
The beginning of time is the furthest you can go back in time.
So the pot is calling the kettle black?Jagella wrote:I think it's fair to say that some atheists are poor mathematicians and deceive people. I don't know how that exculpates apologists and their sloppy math, though.So only atheists are good mathematicians, and they never deceive people?
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Re: Bad Math Used in Apologetics
Post #69[Replying to post 68 by For_The_Kingdom]
Geez louise...
...you still haven't learned? Even after going through two H2Hs, you're still throwing out the MOA as though it just works?Yeah but the problem is, once you've admitted the possibility of God (a necessary being) existing, then you are simultaneously concluding that God actually exists (see Modal Ontological Argument).
Geez louise...
Your life is your own. Rise up and live it  Richard Rahl, Sword of Truth Book 6 "Faith of the Fallen"
I condemn all gods who dare demand my fealty, who won't look me in the face so's I know who it is I gotta fealty to.  JoeyKnotHead
Some force seems to restrict me from buying into the apparent nonsense that others find so easy to buy into. Having no religious or supernatural beliefs of my own, I just call that force reason.  Tired of the Nonsense
Re: Bad Math Used in Apologetics
Post #70Do you suppose that declaring there are only two possibilities makes for a truth?
(a) What we see is illusion (b) We are in a repetitive process (c) Order is a freak occurrence in chaos. And there will be others the ingenuity of which is as yet beyond the boundaries of Marco's brainpower.
Is this Schrodinger's Law? Random trials can bring solutions. Mathematics students know this.
For_The_Kingdom wrote:
Wait a minute, you are a human, right? Well, didn't you just explain the "inexplicable" with nature?? Hmm.
I think perhaps you missed the point being made. In any event I haven't "explained" the inexplicable. God is a simplistic explanation of what we see. I have no idea how events combined to give what we've got.
For_The_Kingdom wrote:
Sure, the rare event of me winning the lottery makes it more probable for me to buy a mansion with my lottery winnings.
So what? How does that negate what I said?
I see no connection between this and anything that has been said. The point I was putting across is that given a sufficiency of possible trials, we can expect a rare event to happen. What applies in the limitations of, say, a lottery draw with a fixed set of numbers, differs from what happens in the vast aeons of time in an emerging universe.
For_The_Kingdom wrote:
But there wasn't an infinite amount of possibilities. The big bang event was just a one time event...
That was the successful outcome. Do you know how many failed events there were?
If we are talking of combinations and results with minuscule probabilities, then for these events to occur we would need a sufficiency of time. For me it seems we have close to an infinite amount of that resource, before success took place. This view negates the proposition that minute probabilities can be discarded as impossibly unlikely.
For_The_Kingdom wrote:
is like standing on Mars and randomly throwing a dart towards the rotating Earth and hitting the bullseye on a target somewhere in Montana.
Do you think you will hit the mark with just one try?
No. But this bears no resemblance to anything I've said. I have never argued about ONE trial producing a rare event. I am saying that in a copious quantity of time, events will conspire to produce a rarity.