Miracles

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On the contrary, I would prefer to feel dumber than anyone else but despite all my efforts it's beyond my capabilities. Your own posted comments are a Mt.Everest in this enterprise and I'll never get to the top.

Sand, you are far from being the most intelligent person here.

Thanks. I really appreciate your encouragement, but my efforts to accept that encounter great difficulties. My humble efforts have uncovered a few very bright people here and the general intelligence of the people on this site outweighs by far most sites on the web but we all have a great distance to go (some more than others) before the hubris about human intellect is in any way justified.
The very few very bright people in human history have lifted human capabilities hugely and I have no illusions as to how far below this standard I exist but humanity, in general, has a powerful motivation to take these great advances and use them to employ the basest animal impulses so that the great powers provided by the greatest intellects have been almost totally corrupted towards, not only the destruction of humanity, but the destruction of a huge bulk of all other life on this most unique and fragile planet. I am deeply in love with all the forces and creatures of this world and the huge tragedy of this destruction will undoubtedly be undone over the course of a few million years (which is a mere geological moment) but my possibility of witnessing the resurgence is, of course, totally non-existent. In my ignorance I have this feeling that this tragedy need not take place if humanity could muster its intellect properly but, who knows? Perhaps this is merely an unavoidable incident in the progression of events.

Aside from your being thoroughly infected with the most peculiar memes that encourage you in the weirdest inclinations, Magnus, what is most impressive is your almost total lack of a sense of humor. If only you could appreciate how howling funny your ideas about spirits and odd gods and miracles and aliens and multiple lives is your life would be endlessly entertaining to yourself. Admittedly what most people do is very funny indeed, if you can divorce it from the idiotic and major brutal tragedy, but the hilarious nonsense that religion and superstition imposes on it is the delicious icing on the cake.

i think what this thread comes down to is the rupture between faith and knowledge. i view this as a symptom of a split consciousness, which is characteristic of mental disorders.humans luv their miracles but as long as the principles and docrines of miracles are not quantifyed in an individual reasoning faculty, they quite simply will never exist for that individual consciousness

Faith, after all, is the basis of actions and it exists in science as well. Science has the faith that all observed phenomena can eventually be fitted into a self consistent comprehensive set of rules and it proceeds on that basis. So far that faith has been justified. Religious faith has been around for thousands of years with many unjustified beliefs that nevertheless persist because it is useful for social manipulators and is pervasive because of the massive lack of understanding and education in the world in general and also because it comforts many who are afraid to face the brutal realities of life.

I disagree of your characterization of science having said faith. My objection is that faith is "belief without evidence", and science does not believe without evidence. Indeed, science doesn't believe anything -- even the most well-established scientific concepts are always, 100% of the time, up for review and scrutiny, in order to find the spot that we, as imperfect humans with a lack of knowledge, have screwed up.

Although if you use a castrated and distorted version of the word faith or belief to merely mean "dependent upon", then you are pretty much spot on. Science is definitely dependent upon the concept that observed phenomena can be explained -- science is the striving to explain that phenomena in the most accurate way possible.

I think I just prefer to use the most accurate words possible.

in my simple perception, "miracles" are the same as "accidents".

there is no such thing as an accident i believe.

a "miracle" or an "accident" is the conclusion of a mind that has exhausted it's investigatory power, and believes that because no definitive "cause" for what they witnessed could be established before their mental power was exhausted, it must be a miracle.

in some ways it seems conceited to assert that something is a miracle. it means that one concludes that if something were less than a miracle, their minds would be able to define a cause for it.

And that presumption is unjustified. Take the set of all possible explanations for an event. If you allow the probability of the event being a miracle to be > 0, you include a miracle in the set of all possible events. You find evidence that make one of the non miraculous explanations less likely. To keep things simple, let us say the evidence is relevant only to that explanation and is irrelevant to all other explanations. The sum of all probabilities in the set of possible explanations must be 1. Therefore if the probability of one explanation decreases, the probability of all other explanations unrelated to the evidence must increase. so if you progressively exclude one non miraculous explanation after the other, eventually the miracle can be the most likely explanation. Hume's premise 3, as you describe it, is simply wrong.

You can rescue Hume's argument if you replace premise 3 by something better grounded in probability theory. Include in your set of explanations the possibility that the event is the result of natural forces, but we are ignorant because either we do not have a theory of everything, or we lack data, or we lack computing power. Set the prior probability of ignorance higher than the prior probability of a miracle. If evidence that makes identifiable natural causes less likely is irrelevant to both ignorance and miracles, then as the posterior probability of both ignorance and miracle grows, the probability of ignorance will remain larger. If you like, you can take that as a reformulation of premise 3. I am only saying that premise 3, as you presented it, is not justified.

There is also Spinoza's argument:

1) A "miracle" is phenomena we can't explain explain with our current understanding of laws of nature.
2) Our current understanding of law of nature is far from being perfect
3) Therefore we can't establish that a phenomena is not caused by natural laws or is outside those
4) Therefore we can't prove a "miracle"

Umm.... yeah, that does not really clash with anything, certainly not premise 3. Premise 3 states that natural explanations are more valid than non-natural ones, so yes, if you found a way to exclude all natural explanations, then the miracle could be the only explanation, this, however, is pretty difficult to do. Thus, I do not see anything close to the problem you promote.


I don't see a problem with premise 3, and I do not think you have actually presented a problem.

Here's what I put as premise 3:
"non-violations of natural laws are more probable than violations"

I don't see how you have found a problem in your first or second paragraph, I mean, perhaps you can argue that ignorance should be included in a list of probabilistic explanations, but obviously this kind of argument applies to a single unknown occurrence rather than a daily miracle that can be studied in depth. I might be missing something, but here's how I see the argument:

a) Anything fit to call a miracle violates our natural laws to an extreme extent
b) Therefore any explanation of a miracle without this violation makes more sense
c) Ergo, we cannot trust miracles even if one occurred(implicitly assumes that at least one natural explanation exists in any circumstance, not a large assumption at all given that the known world is natural)

Could this rule theoretically exclude some true instances? Sure, but the question is epistemology, so the judgment is partially on it's ability to exclude false positives. In any case, I do not see what the problem actually is, because b) is not invalidated by decreasing natural explanations, because each natural explanation will grow more than the probability of the miracle, and thus the miracle can only be allowed if it is the *only* explanation, because it cannot be larger than a natural explanation.

Now, we can argue that adding in a bit of Spinoza's argument makes Hume's stronger, however, I do not see the need, because there would even be reason to doubt an extreme "natural" miracle's existence.

Go through the calculations yourself. Set up a set of explanations, one of them is "miracle". Set the probability of that as low as you like, but still > 0. Use Bayes' theorem to see what happens if you have evidence that makes one of your naturalistic explanations less likely. Keep doing that, and show me how you prevent the probability of a miracle ever exceeding 0.5. Your statement was

You need premise 3 for that, which is begging the question because it presumes the answer. The odds of a miracle are to be established. Premise 3 already presumes those odds. You need a justification for that premise, and either Hume or you forgot.


Do the calculation, show me your numbers.


Is that a prior or posterior probability? If it's a prior, the conclusion doesn't follow. If it's supposed to be a posterior, it's begging the question because it presumes the answer.


Does that mean those we know? Then "miracle" is just another name for ignorance. I would be happier if we say a miracle violates all natural laws, including those we haven't yet discovered. What we know and what we don't know is then important.


That's again begging the question. It confuses prior and posterior probabilities.


Please demonstrate that by an example calculation, so that I can see what your assumptions are. I just did. Applying Bayes' theorem, you get the same priors and posteriors when p(evidence|explanation X is true) is the same for every explanation. A miracle, violating every natural law it pleases, can produce any evidence. The simplest assumption about the evidence is that p(evidence|a miracle occurred) = p(evidence). Let's say p(evidence) = 0.001. Take a set of 10 possible explanations, one of them being a miracle. Set the prior p(miracle) = 0.001. By my calculation, if the likelihood of each of the nine naturalistic explanations producing the evidence is p(evidence|naturalistic explanation X is true) = 0.00001, the posterior probability of the miracle, p(miracle|evidence) = 0.50251. For this set of priors, that's the level of evidence against naturalistic explanations that makes the miracle the most likely explanation.

If you want to set a smaller prior probability of a miracle, you will need lower probabilities of the naturalistic explanations producing the observed evidence. That's all. There's still nothing in there to prevent the miracle from becoming the most likely explanation.

The only way I see to make sure that "each natural explanation will grow more than the probability of the miracle" is to have some explanation in there that is consistent with the event having happened according to natural law, but also being equally or more consistent with any evidence than the miracle, meaning having a likelihood ratio p(evidence|explanation X is true) >= p(evidence|miracle), for any evidence whatsoever. The only thing I know that fits is ignorance.

I see two ways for you to counter the argument. Show me that I misunderstand Bayes' theorem. Or suggest another naturalistic explanation that is compatible with any evidence at all.


Unless I am mistaken (always possible), that does not follow from Bayes' theorem. If I am mistaken, please show me how.

Gromit, I think you are missing something. The supernatural is ridiculously unlikely, the natural is thus a priori a *lot* more likely, the only way for it to become less likely, is for our natural explanations to essentially all become supernatural explanations, because there is not a probability lower than the supernatural. Thus, a Bayesian calculation becomes almost absurd, as it obscures the logical point about relative probability being hammered.

I do need premise 3 for that, and I think that was in acceptance of premise 3. Premise 3 does not need justification given that it is based upon premises 1 & 2.


Ain't a matter of calculation, it's a matter of logic in relationship to comparative probabilities.

I mean, I can cite Bayes' theory right here:
P(A|B)=(P(B|A)*P(A))/P(B)

But, really, the problem is just that the probability of a miracle vs a non-miracle is still liable to be absurdly low, unless the non-miracle proves to demand a miracle to make it happen. Thus, the notion that all other probabilities have to be excluded makes sense.


This is P(A), a statement of extremely low probability. The notion is that P(A) is so small only unrealistic values of P(B|A) and P(B) can establish P(A), the issue is that if P(B) is unrealistic, then it will involve it's own re-valuation on the matter of validity, and somewhere within the probabilistic chain, viability will fail to be established. Thus, it is not arguing based upon pure Bayesian statistics.

Is it correct that this argument cannot outright say that miracles cannot happen if miracles were part of our background? Yes. But, this argument is making some background assumptions on how the world is, and it is not just strictly mathematical, as it is not expressing something that is purely a logical possibility but a realistic one.


That's Spinoza's argument, however, the issue is that claims of strange occurrence appear all of the time, not all of them are actual violations or changes in anything.


The argument includes both prior and posterior possibilities, as it says the prior is very low, and that other better explanations likely exist, thus the posterior is low. I do not see how this just begs the question though.


The issue is that the probability of a miracle is taken to be absurdly low, almost below the point where rational calculation is possible. Basically the instance is that Hume is basically trying to make it assuredly put forward that P(natural)>>>>P(supernatural) by the nature of both probabilities. This is without appealing to the probability of a particular instance, but rather a general statement about the probability of something natural to something supernatural. You can argue that this is begging the question, but arguing that a priori P(natural)>>>>P(supernatural) does not seem problematic, and I think it can establish everything that is desired to be established. After all, one of the things I believe Hume invokes against miracles, is that lying is non-miraculous and can account for the same facts, this is not just a statement about miracles, this is a statement about the probability of a simple natural thing, and a simple supernatural thing

I am avoiding calculations simply because the issue is not one of calculation, but rather the problem is purely logical. The argument is also not perfectly airtight, but rather it could be argued as also being probabilistic, but it is solid enough that an analytical variant, while not absolutely true, is still better than just a probabilistic variant.


There are naturalistic explanations compatible with any evidence though. You or the person who is telling you something went crazy, was high, was dreaming, etc. Natural, happens more often than miracles, accounts for anything. Or how about this, the data you saw in favor of X was heavily doctored and this was done well, this is plausible, it can happen, etc. Such possibilities can work for almost any instance of a miracle. In fact, I think a common argument is that mass hysteria would be a naturalist explanation that would be compatible with most evidence, and that it would also be more probable than the miracle, given that a coin landing on heads 10000 times in a row is considered more probable than a miracle by the standard given by Hume that miracles are such because they essentially *never* happen.

Have I been missing something? I think your focus on Bayes theorem ends up being problematic, as the real issue is still relative probabilities, and the extensive possibility of naturalist explanations.

Anything can be rationalized.

http://en.wikipedia.org/wiki/Confirmation_bias

But Not everything can be made logically valid and consistent!


Hey BY THE WAY Awesomelyglorious: Although I studied prob-stat all that much so my knowledge is minimal I DO happen to know and would like to remind you all that You CanNOT prove anything with probability and statistics! Even if you can assign a high likelyhood to an effect having no apparent cause that does NOT mean that you have proven it to be inexplicable! It might have a natural cause that is not yet understood by science but if miracles exist than one has an effect with no cause. Causality is an axiom that has yet to be demonstrated false.

Last edited by Haliphron on 02 Mar 2009, 12:33 am, edited 1 time in total.

Human behavior will never be consistently logical.

If we are talking about miracles, human nature probably plays a big part in it as well as whatever natural laws we are unaware of. There are way too many variables that come into play.