WL Craig: The Kalam Cosmological Argument

Craig's arguments for God, Pt 2

Abrahamic religion, you know, the one with the cross...

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Re: WL Craig: The Kalam Cosmological Argument

#2241  Postby Lowpro » Jan 08, 2015 5:30 pm

Thommo wrote:
Lowpro wrote:I have a mostly similar position but one difference. If you do not have data for a position (and I mean data in a strict information stance) then you have NO POSSIBILITY. A probability can be inferred with a sample size of 1, it just will lack meaningful confidence (variation within a sample of 1 is enough). That's mathematics.


Could you elaborate on this? All the likelihood estimation techniques (and similar) I've ever seen have requirements on sample size, 1 is never enough - to say something has a probability of 0.5 ± 0.5 is to say you have no information at all - by definition probability is already in the range 0 ≤ p ≤ 1.


What MLE modelling techniques have you seen? Keep this is mind right now. Probability modeling only cares about variation; more than one measurement. A sample size of 1 would be one coin, two states: Heads or Tails. You can determine likelihood without ever flipping that coin once because you know it's variation, you just will have very little confidence in it (in the case of an unfair coin). That's the point of why probability modeling is easy; the confidence is what matters though.

Now if there's no possibility then we have NO information. Imagine we have a coin with two states, heads and tails, but it is unfair and will NEVER land heads up. You could write a probability of 0.5 for both, but landing heads up is NOT POSSIBLE and if you tested this you'll never have the necessary variation (it will always lands tails up).

The probability works, the possible does not. God has no information, no variation, thus is impossible. Even if we had some sufficient probability of God, it would be impossible.

Fun fact: N of 1 studies happen often and they're definitely modelable.
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Re: WL Craig: The Kalam Cosmological Argument

#2242  Postby Thommo » Jan 08, 2015 6:19 pm

Lowpro wrote:What MLE modelling techniques have you seen? Keep this is mind right now. Probability modeling only cares about variation; more than one measurement. A sample size of 1 would be one coin, two states: Heads or Tails. You can determine likelihood without ever flipping that coin once because you know it's variation, you just will have very little confidence in it (in the case of an unfair coin). That's the point of why probability modeling is easy; the confidence is what matters though.


I'm not sure what you mean by this, yes it's easy to make a probability model with even very restricted data - we know quite a bit about a coin - we know the number of outcomes and how to label each of them, with certainty. But the accurate parts of such a model come from that knowledge, the rest is pure guesswork, we're predisposed to think of coins as fair because we encounter lots of fair coins and know quite a bit about the kinematics of coin tossing. But saying modeling is "easy" just means making any old shit up is "easy", I'm not sure it's accurate to even describe that as modeling.

It's one thing to come up with a no-confidence model where you know the underlying distribution is binomial, but what are you going to do where there's no information about the underlying distribution? You need either that information or a sample size sufficient for the central limit theorem to be applied.

Lowpro wrote:Now if there's no possibility then we have NO information. Imagine we have a coin with two states, heads and tails, but it is unfair and will NEVER land heads up. You could write a probability of 0.5 for both, but landing heads up is NOT POSSIBLE and if you tested this you'll never have the necessary variation (it will always lands tails up).


Right, I agree, the probability is somewhere between 0 and 1. The value of guessing it's 0.5 is nonexistent without wider context (which we do have for a coin, which might make the example misleading for intuitions).

Lowpro wrote:The probability works, the possible does not. God has no information, no variation, thus is impossible. Even if we had some sufficient probability of God, it would be impossible.


I'm sorry, but I don't understand what you're trying to say.

Lowpro wrote:Fun fact: N of 1 studies happen often and they're definitely modelable.


I assume you're talking about medical trials which search for cause and effect with treatments that are known to have some effectiveness. This is not the same thing at all and doesn't rely on statistical techniques in the same way.

If someone is given a treatment and their disease is cured, what can we say about the probability that the treatment was the best possible treatment? Absolutely nothing without wider information - such as whether the disease can get better on its own, and what other treatments are available.
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Re: WL Craig: The Kalam Cosmological Argument

#2243  Postby Lowpro » Jan 08, 2015 8:25 pm

Sorry even after rereading my own post I realized it just...wasn't clear. I was posting during class so I didn't have my full attention to it.

I am almost 100% in agreement with you said except for how you were comparing the coins being face up and its relation to the probability that it was either left face up by an agent or whether it landed face up within a probability of heads or tails. That's beyond testing for a probability because there is no information if there was an agent that left the coin face up; all other states (tails up) are impossible.

We could STILL pretend we're working with a discrete probability of heads or tails and if it's fair then we'd see a 0,1 ( ie heads or tails) in a fair distribution. We could also assume a fair distribution with no flips at all and possibly be correct. That's a probability distribution with no testing. Probabilities can be valid with no confidence, scientifically this is not useful. But it is mathematics.

Again I agree with all the stuff you've posted (mostly). The issue I have is that when you wanted to make a probability of placing the coin heads up or assuming it landed heads up from a flip are independent to the fact it's found face up. Maybe that's what you meant the entire time (and after reading again, it probably was). I just didn't interpret it that way when I read it.

There's a big difference between the sample space of "heads or tails" aka [0,1] from the coin being flipped and NO SAMPLE SPACE, where the agent makes the coin face up. The latter makes the coin impossible, it's nonsensical. So yes this was purely a semantics issue to me, that's all. Have a nice day chap!
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Re: WL Craig: The Kalam Cosmological Argument

#2244  Postby Thommo » Jan 08, 2015 9:13 pm

Lowpro wrote:Again I agree with all the stuff you've posted (mostly). The issue I have is that when you wanted to make a probability of placing the coin heads up or assuming it landed heads up from a flip are independent to the fact it's found face up. Maybe that's what you meant the entire time (and after reading again, it probably was). I just didn't interpret it that way when I read it.

There's a big difference between the sample space of "heads or tails" aka [0,1] from the coin being flipped and NO SAMPLE SPACE, where the agent makes the coin face up. The latter makes the coin impossible, it's nonsensical. So yes this was purely a semantics issue to me, that's all. Have a nice day chap!


As you say I think we agree on almost all of this (which is good, since it's mathematically grounded, so we should expect quite a lot of agreement between informed individuals!), and a little disagreement over the margins which doesn't really matter.

There is a sample space in the latter example - it only has one outcome with nonzero probability though. Clearly there is nothing impossible about the idea of an agent placing a coin heads face up (although in my original example the agent is a fairy creating the coin from nothing, which I agree is impossible). My point was only that even though we can be certain that if an agent has placed the coin heads face up it will be face up (and this I feel as a tautology is about as certain as it gets) it tells us nothing about the distribution of how often coins actually are placed heads face up as opposed to tossed - although again we can be pretty certain that such a distribution actually exists and we could attempt to chart it by observing humans covertly in some location they may fiddle with change, such as a public cafe.
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