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Monthly Archives: April 2012

Why We Are Bad At Probability

From Luke’s (formerly of Common Sense Atheism) Facing The Singularity:

A bank teller?

Meet Linda:

Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

Now, rank these possible descriptions of Linda by how likely they are:

  • Linda is a teacher in elementary school.
  • Linda works in a bookstore and takes yoga classes.
  • Linda is active in the feminist movement.
  • Linda is a psychiatric social worker.
  • Linda is a member of the League of Women Voters.
  • Linda is a bank teller.
  • Linda is an insurance salesperson.
  • Linda is a bank teller and is active in the feminist movement.

When Amos Tversky and Daniel Kahneman gave this test to students, the students ranked the last possibility, “feminist bank teller,” as more likely than the “bank teller” option. But that can’t possibly be correct. The probability of Linda being a bank teller can’t be less than the probability of her being a bank teller and a feminist.

Why is it impossible, from a probability perspective? Being a bank teller is one coin flip. Being a feminist is one coin flip. Being a bank teller and a feminist is two coin flips.

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Posted by on April 11, 2012 in cognitive science

 

My ὑπομνήματα about religion

So what exactly is a ὑπομνήματα? That is, “hypomNEmata”? (the stressed “e” is like the one in beta) The prefix, “hypo-” should be well known (hypothermia, hypodermic [needle], hypothetical, etc.), and the rest of the word, mnemata, should also look familiar. It’s where we get the word “mnemonic” from, meaning that mnemata has something to do with memory.

Justin Martyr, when he speaks of “Memoirs of the Apostles”, actually writes ἀπομνημόνευμα τῶν ἀποστόλων::apomnemoneuma ton aposolon. The “apo” prefix in this case denotes that it is “from” memory, in this case it means something akin to published memoirs.

So it’s my interpretation that ὑπομνήματα is memory aids (the -ατα ending is plural, like the difference between stigma [mark] and stigmata [marks]), sort of like unpublished notes. That’s exactly why many of the ancients refered to their notes and such with a word that has a relationship with memory, since writing was “new” back when people like Plato started associating writing things down with memory and memory aids.

So this blog functions as my “notes about religion”, to help me remember cool or interesting things that I come across that have some relevance to religion.

 
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Posted by on April 10, 2012 in Uncategorized

 

Respecting Religion

I was reading this post over at The Friendly Atheist about respecting religion. Here is what might be the money quote:

The highest respect one can pay to another’s idea is to scrutinize it and explain what might be wrong. This is what “respect” means in the intellectual domain.

Is this an accurate statement? Let me think about it for a second.

If a two year old came up to you trying to explain how the world works (e.g. attempting to explain gravity, sunlight, etc.) would you take the two year old’s explanation seriously and refute his logic point by point? Or would you politely smile and say “Aww, what a cute kid! He’s such an angel; he’s always willing to help people like when he helps mommy with the laundry” ? In other words, completely ignore his contribution to world knowledge and only concentrate on how cute and adorable the kid is.

Actually engaging the kid with his reasoning would be to treat the kid like an adult. As an equal. Completely ignoring the kid’s factual claims and concentrate on his other qualities would be to treat the kid as, well, a kid; someone who is not an equal.

Now imagine an adult, or a peer of yours coming up to you and explaining something that is factually incorrect (e.g. 2 + 2 = 99). Would you have the same reaction to them that you had with the little kid? Or would you attempt to have a rational conversation with them about why they’re wrong?

So by not engaging with religion’s truth claims, and only pointing out other qualities (like it makes people feel better, etc.), is to treat religion like a sensitive little kid. I would think that this is disrespectful. It’s no less disrespectful than outwardly calling religion stupid and ignorant. It’s actually passive-aggressive disrespect. On the other hand, to actually engage in religion’s truth claims, as an equal in the marketplace of ideas, would be the only respectful recourse. Somehow, this is seen as “disrespectful”.

The only way this could be “disrespectful” is if you actually thought of religion as the two year old in the above analogy. It would be equally “disrespectful” — to the poor kid — if you shattered his truth claims about gravity with the more accurate description. Imagine how the little kid would feel if you actually took his assessment of gravity like an adult and corrected him matter of factly. It would probably hurt his feelings. What would be more disrespectful is if you threw in some personal attacks about the kid while correcting his truth claims. Analogously, by not correcting the truth claims of religion because we might hurt religious people’s feelings, is to passively-aggressively call religion the equivalent of a two year old.

So I say respect religion: Challenge their truth claims, without the personal attacks. Like an adult. Don’t passively-aggressively belittle their truth claims by ignoring them, like you would a clueless little kid.

 
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Posted by on April 4, 2012 in atheism

 

Bayes’ Theorem and Falsifiability

The one lesson we should get from Bayes’ theorem is that it is the language of science. If you are thinking like a scientist, you are thinking like a Bayesian. That’s why I was pretty confident that I would end up with the numbers that I did even assuming a high initial probability of the Christian god’s existence for the last three posts on Bayes’ theorem and the existence of the Christian god.

If you notice throughout the last three posts, the conditional probabilities for the Christian god are almost always lower than the alternative. Why is that? Because the Christian god — an all-powerful god — is unfalsifiable. Sure, falsifiability is a good philosophical justification for doing science. But now we know why falsifiability is so important from a purely epistemic (i.e. probabilistic) point of view.

Generally, any hypothesis that is unfalsifiable will always have a lower conditional probability than a hypothesis that is falsifiable.

Falsifiable hypotheses tend to lean towards going all-in probability wise, and will tend to cluster its probability capital in a more bell-curve like way in a class of evidence. Unfalsifiable hypotheses spread their probability capital more evenly across all possible evidence of the same class.

Think of it this way. Say there are 10 possible doors to bet on for winning a prize, and you only have 100 dollars to bet. Someone who is trying not to be “proven wrong” in any sense will spread their money evenly across all 10 doors. Someone who wants a big payout will place the majority of their 100 dollars on very few doors. The unfalsifiable hypothesis is spreading its 100 dollars evenly across all of the doors, while the falsifiable hypothesis goes all in on one door or clusters around very few doors.

The total equation for determining conditional probabilities is P(E | H) + P(~E | H) = 1.00. An unfalsifiable hypothesis is attempting to equally explain everything. And as that equation shows, something that attempts to explain everything equally (i.e. E and everything that entails ~E), explains nothing. The more possible evidence (of the same class) that the unfalsifiable hypothesis attempts to explain equally, the closer the individual conditional probabilities move towards zero.

So, if someone says “You can’t prove that god doesn’t exist!” you know why they’ve already lost the debate: Just by the nature of being unfalsifiable, probability will favor the alternative, falsifiable, hypothesis more.

Besides the Christian god, what are some other unfalsifiable hypotheses? How about Solipsism, or philosophical zombies (P-Zombies). What observations could we see that would falsify solipsism or p-zombies? None. This means that every single possible observation is equal “confirmation” of p-zombies, even mutually exclusive observations. Which means that P(Evidence1 | P-Zombies) + P(Evidence2 | P-Zombies) + P(Evidence3 | P-Zombies) + P(Evidence4 | P-Zombies) + P(Evidencen | P-Zombies) = 1.00. All of the mutually exclusive P(Evidencen | P-Zombies) will be equal to each other; there’s no observation that is less likely than any other observation given p-zombies.

On the other hand, a falsifiable hypothesis would be something like “all swans are white” (from the wiki article). In Bayes’ theorem, the conditional probability is saying that P(E | H) = 1.00, or P(White Swan | All Swans Are White) = 1.00. This, in turn, means that P(Non White Swan | All Swans Are White) = 0 since P(E | H) + P(~E | H) = 1.00. Upon the event of seeing a non-white swan, this drops the prior probability of “all swans are white” to zero, yet seeing another white swan won’t change the prior probability much (depending on the conditionals of the alternative hypothesis).

In short, don’t posit an unfalsifiable hypothesis. If you do:

 
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Posted by on April 3, 2012 in Bayes

 

Bayes’ Theorem and the Existence of God, part 3

This is part 3 of my attempt at using Bayes’ theorem to see what adding up all of the evidence usually presented in favor of the Christian god does to an assumed high prior probability of the Christian god. Over the course of the last two posts, I went from the starting point of .977 probability to .8235 probability when factoring in things like the existence of morality, the likelihood of life arising on Earth, evolution, religious experiences, and cultural language.

What is some of the other evidence that people usually appeal to for the existence of the Christian god?

Mind  Body Dualism

This will be another tricky one to express with the current assumptions I’ve made over the last two posts. Certainly, if mind body dualism is true, then this supports the existence of the Christian god. But it could also support any other god as well, and even some flavors of atheism. As I wrote as a note in part 2, there are many atheists who believe in psi or ghosts which is mind body dualism. Psi, then, counts as a sort of “natural supernaturalism”. Thus, while mind body dualism – i.e. supernaturalism — supports the existence of the Christian god, it could also support some flavors of atheism.

So we have two paths to go on. One, if supernaturalism (i.e. mind body dualism) is true, then of course the existence of the Christian god makes sense of this proposition being true. Thus P(Supernaturalism | Christian God) = .9999. If supernaturalism is not true, then the existence of the Christian god does not make sense of this. P(No Supernaturalism | Christian God) = .0001. On the other hand, P(Supernaturalism | Non Christian God, Atheism) really depends on your flavor of god or atheism. This would be a bit less necessary than the Christian god because the Christian god might not exist but supernaturalism could still be true. It could really be that the Mayan gods have been perpetuating all supernatural encounters for all of human history and not the Christian god. And then P(No Supernaturalism | Non Christian God, Atheism) is also less extreme than the formula for the Christian god.

Like so:

P(Supernaturalism | Christian God) + P(No Supernaturalism | Christian God) = 1.00
P(Supernaturalism | Non Christian God, Atheism) + P(No Supernaturalism | Non Christian God, Atheism) = 1.00

The Likelihood Ratio would have to favor Christianity in the event of supernaturalism being true. I’m not sure by how much, so I’ll assume that P(Supernaturalism | Non Christian God, Atheism) is .5 since I don’t have any other way of splitting up the probability capital. Now I figure out what numbers I get assuming both the existence and non-existence of the supernatural.

Assuming Supernaturalism:

P(Christian God | Supernaturalism) = P(Supernaturalism | Christian God) * P(Christian God) / [P(Supernaturalism | Christian God) * P(Christian God)] + [P(Supernaturalism | Non Christian God, Atheism) * P(Non Christian God, Atheism)]

P(Christian God | Supernaturalism) = .9999 * .8235 / [.9999 * .8235] + [.5 * .1765]
P(Christian God | Supernaturalism) = .8234 / .8234 + .0833
P(Christian God | Supernaturalism) = .8234 / .9117
P(Christian God | Supernaturalism) = .9032

Assuming no Supernaturalism:

P(Christian God | No Supernaturalism) = P(No Supernaturalism | Christian God) * P(Christian God) / [P(No Supernaturalism | Christian God) * P(Christian God)] + [P(No Supernaturalism | Non Christian God, Atheism) * P(Non Christian God, Atheism)]

P(Christian God | No Supernaturalism) = .0001 * .8235 / [.0001 * .8235] + [.5 * .1765]
P(Christian God | No Supernaturalism) = .0001 / .0001 + .0883
P(Christian God | No Supernaturalism) = .0001 / .0884
P(Christian God | No Supernaturalism) = .0009

So the non existence of the supernatural (i.e. mind body dualism) deals a huge blow to the probability that the Christian god exists. Which makes sense. But the existence of the supernatural is a separate hypothesis altogether. Since the probability of Christianity depends on the probability that the supernatural exists, they rise and fall together.

The supernatural is another hypothesis without 100% confirmation or disconfirmation like the coin flips. So just like the prior uncertainty of the coin flips, we would multiply the probability of the supernatural with the probability of Christianity, like multiplying the probability of getting heads with the probability of getting the second heads. Which is not Bayes’ theorem per se but general probability theory. So for example, if there is an 80% or .8 chance that the supernatural exists, we would multiply that .8 by the .8235 that I arrived at, and end up with .66. If there was a 100% chance that the supernatural exists, then there is no uncertainty and multiplying wouldn’t apply. I would just use Bayes’ as I did when I assumed 100% chance (i.e. it happened) of getting heads in the coin flip example.

To me, it seems that it is highly unlikely that the supernatural exists at all. I guess I could run through all of the evidence for or against the supernatural using Bayes’, but these posts are getting log enough as it is. Maybe some other time :). But I’ll privilege the supernatural hypothesis a bit and say that there’s a 90% or .9 probability that the supernatural exists. This then means that the probability of the Christian god is .8235 * .9 = .7412

Fine Tuning of the Universe

Another major argument that people use for the Christian god is the fine-tuning of the universe. I already went over this argument before, so I’ll rehash it here again.

Our two conditional probabilities are now P(Current Universal Constants | Christian God) and P(Current Universal Constants | Non Christian God, Atheism). Expanding on these conditionals further, we have:

P(Current Universal Constants | Christian God) + P(Other Universal Constants | Christian God) = 1.00
P(Current Universal Constants | Non Christian God, Atheism) + P(Other Universal Constants | Non Christian God, Atheism) = 1.00

According to this apologetics website the probability of the current arrangement of our universe’s constants is the equivalent of picking one red dime out of a pile of 1037 dimes. Or, P(Current Universal Constants) = 0.0000000000000000000000000000000000001.

This problem is similar to the Privileged Earth observation I wrote about in part 2. So our P(Current Universal Constants) is 0.00000000000000000000000000000000000001. This means that, expanding on the Total Probability Theorem, P(Current Universal Constants | Christian God) * P(Christian God) + P(Current Universal Constants | Non Christian God, Atheism) * P(Non Christian God, Atheism)  = 0.0000000000000000000000000000000000001.

0.0000000000000000000000000000000000001 = P(Current Universal Constants | Christian God) * .7412 + P(Current Universal Constants | Non Christian God, Atheism) * .2588.

So we have to see how each hypothesis splits up its probability capital between our current universal constants and some other universal constants.

Is the Christian god limited to our current universal constants in order to make universes? This is what we would mean if we said that P(Universal Constants | Christian God) was high. It is in effect saying that P(Other Universal Constants | Christian God) is low. A similar question is posed to the alternative hypothesis. Is a non Christian god or even atheism limited to our current universal constants to create universes? From the above link, I’ll take one of the proposed fine tuning observations and see what limits are placed on them.

Fine Tuning Parameters for the Universe

Strong Nuclear Force (SNF) constant

if larger: no hydrogen would form; atomic nuclei for most life-essential elements would be unstable; thus, no life chemistry
if smaller: no elements heavier than hydrogen would form: again, no life chemistry”

So for example, the strong nuclear force constant is 10,000 Newtons.

Given that the Christian god created the universe is there any reason why a universe with larger or smaller strong nuclear force constants would be impossible? Why couldn’t the (all powerful) Christian god make the strong nuclear force larger but make chemistry possible anyway? Or why couldn’t he make it smaller and yet still have heavier elements than hydrogen form? Imagine how much more of a miracle it would be if we observed that strong nuclear force was too large to create hydrogen but hydrogen formed anyway.

So for this small sample, we have P(Larger Strong Nuclear Force | Christian God) + (Current Strong Nuclear Force | Christian God) + P(Smaller Strong Nuclear Force | Christian God) = 1.00. It seems to me that all three are equally possible assuming the all powerful Christian god. Another problem is what constitutes the comparatives “larger” and “smaller”. Is the Christian god restricted from having strong nuclear force be 1 Newton? Or 1 billion Newtons? What are the limits of an all powerful supernatural being when creating a universe? It looks like in reality we have:

P(1 Newton SNF | Christian God) + P(2 Newton SNF | Christian God) + P(Current SNF minus n Newton SNF | Christian God) + P(Current SNF | Christian God) + P(Current SNF plus n Newton SNF | Christian God) + P(Current SNF plus n + 1 Newton SNF | Christian God) + P(… | Christian God) = 1.00.

Since we have no a priori reason for restricting how the Christian god would go about selecting which constants to use, since he in reality isn’t restricted at all, we have no a priori reason to pick just one P(n Newton SNF | Christian God) over any other. It looks like there are an infinite amount of Newtons that the Christian god could choose from and still make a universe teeming with life if he really wanted. What’s stopping him? So P(Current SNF | Christian God) would be 1 / billion? 1 / 1 trillion? 1 / 1 quintillion? 1 / infinity?

This problem of restriction of the Christian god hypothesis applies to every single fine-tuned constant on that page. So if P(Current Universal Constants | Christian God) were say 1 / 1 quintillion, then P(Other Universal Constants | Christian God) would be the remainder; 1 quintillion – 1 / 1 quintillion. This means that there is a higher probability of every other universal constant compared to our current universal constants given the all-powerful Christian god. Or, P(Other Universal Constants | Christian God) = .9999 making P(Current Universal Constants | Christian God) = .0001. Though these numbers would have to be a lot more extreme in order to make the Total Probability equal to 1 / 1037, or that P(Current Universal Constants | Christian God) is basically zero.

As I wrote in that previous post, the fine tuning argument assumes a god that had to look up what type of universe life, or even humans, could live in and designed a universe against those requirements. This is not the all powerful god of Christianity. This is some other, non-all powerful being. Just like a Goldilocks Zone planet is evidence against the all powerful Christian god, and evolution is evidence against the all powerful Christian god, so it is with a fine-tuned universe. In other words, a Likelihood Ratio would favor the hypothesis P(Non Christian God, Atheism) in some fashion. Or that P(Current Universal Constants | Non Christian God, Atheism) > P(Current Universal Constants | Christian God).

Back to our Total Probability formula:

0.0000000000000000000000000000000000001 = P(Current Universal Constants | Christian God) * .7412 + P(Current Universal Constants | Non Christian God, Atheism) * .2588.

0.0000000000000000000000000000000000001 = ???? * .7412 + P(Current Universal Constants | Naturalism, Atheism) * . 2588.

It looks like the equation has to be P(Current Universal Constants | Non Christian God, Atheism) > P(Current Universal Constants | Christian God) in such a manner that makes the Total Probability equal to 0.0000000000000000000000000000000000001. Since P(Current Universal Constants | Christian God) is basically zero — the majority of the probability capital goes into P(Other Universal Constants | Christian God) — this means that P(Current Universal Constants | Non Christian God, Atheism) is equal to a miniscule amount more than P(Current Universal Constants). At this point, it might as well be equal to P(Current Universal Constants).

Since P(Current Universal Constants | Christian God) is basically, zero, this means that the probability of the Christian god’s existence given the current universal constants is also basically zero. It’s not actually zero because zero isn’t a probability. I’d like to say that I’m the first one to make that argument, but it already looks like other people have come to a similar conclusion about the fine-tuning argument.

Conclusion

So my final conclusion is that there is almost a zero percent chance that the Judeo-Christian god exists, and an almost 99% chance that either some non-Christian god exists or no god exists at all. I started off assuming a high probability that he exists (.977). I looked at the evidence of cultural language and personal religious experiences and found that those two can neither be used for nor against the existence of the Christian god so given those, the probability stayed at .977. Next, I looked at evolution and the probability of life arising on Earth. Both of those knocked down the probability of the Christian god’s existence from .977 to .7487. However, looking at morality bumped up the probability of the Christian god’s existence a bit up to .8235. And then in this post I looked at how the existence of the supernatural favors the Christian god’s existence; since I didn’t look into any confirmation or disconfirmation of the supernatural, I simply privileged that a bit by assuming that the probability of the existence of the supernatural is .9 and wound up with a bit lower probability of the Christian god’s existence at .7412.

Lastly, I looked at the evidence for fine-tuning, which dealt the strongest blow to the existence of the all powerful Christian god. While it’s still possible that some other god exists, we have no epistemic warrant for using the supposed fine tuning of the universe to argue for the Christian god’s existence. On the contrary, the fine tuning argument is one of the strongest arguments against the Christian god. But like I said, this only knocks out the traditional all powerful Christian god. Maybe the Christian god actually isn’t all powerful, or maybe something like Marcionism is true where the Marcionite god — a non-creator god — simply found our universe and subsequently did all of the things that Marcion said he did. In other words, if it is asserted that the Christian god is not a creator god, then the fine tuning argument against the existence of the Christian god would not apply.

The next post will be my reasons for why everything worked out the way it did, and why I was confident I would arrive at the conclusion that I did.

 
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Posted by on April 2, 2012 in Bayes

 
 
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