Sunday, November 12, 2006

Sources of Knowledge

In the course of a debate I've been having at Thinking Christian, a theist produced a link to Alvin Plantinga's critique of Daniel Dennett's Darwin's Dangerous Idea:
Here Dennett seems to assume that if you can't show by reason that a given proposed source of truth is in fact reliable, then it is improper to accept the deliverances of that source. This assumption goes back to the Lockean, Enlightenment claim that, while there could indeed be such a thing as divine revelation, it would be irrational to accept any belief as divinely revealed unless we could give a good argument from reason that it was. But again, why think a thing like that? Take other sources of knowledge: rational intuition, memory, and perception, for example. Can we show by the first two that the third is in fact reliable--that is, without relying in anyway on the deliverances of the third? No, we can't; nor can we show by the first and third that memory is reliable, nor (of course) by perception and memory that rational intuition is. Nor can we give a decent, non-question-begging rational argument that reason itself is indeed reliable. Does it follow that there is something irrational in trusting these alleged sources, in accepting their deliverances? Certainly not. So why insist that it is irrational to accept, say, the Internal Testimony of the Holy Spirit unless we can give a rationally conclusive argument for the conclusion that there is indeed such a thing, and that what it delivers is the truth? Why treat these alleged sources differently? Is there anything but arbitrariness in insisting that any alleged source of truth must justify itself at the bar of rational intuition, perception and memory? Perhaps God has given us several different sources of knowledge about the world, and none of them can be shown to be reliable using only the resources of the others.
My first observation was that Plantinga sees that reason relies on certain unprovable axioms, without all of which, no reasoned conclusion can be reached. This is a good start. Plantinga claims the axioms are logic, memory, and perception, but I suspect these equate to my axioms of logic, regularity, and the axiomatic nature of experience (that experiences need to be explained).

Plantinga then argues that, since we are comfortable accepting these axioms without proof, why not accept additional axioms (e.g., that there are non-rational sources of knowledge)? Maybe "Internal Testimony" (whatever that is supposed to mean), is just an extra-rational assumption, rather than an irrational one.

Alternate Sources of Knowledge
Assuming that knowledge is defined as justified true belief, what does rationality say about sources of knowledge?

If I have some source of knowledge, S, then I am saying that there is some associated test, TS, I can apply to a proposition, P, to test its truth:
S: Truth(P) = TS(P)

I am also saying that there is some (potentially different) form of justification for belief in P:
S: Justification(P) = JS(P)

In the case of science, justification and test are one. The truth of a scientific belief is fixed by the test of its truth.

If I have multiple sources of knowledge, then I may have multiple definitions of the truth:
S1: Truth(P) = TS1(P)
S1: Justification(P) = JS1(P)

S2: Truth(P) = TS2(P)
S2: Justification(P) = JS2(P)

At this point, I'm going to assume that S1 is science and S2 is supernaturalism. This means I can write:
S1: Truth(P) = Justification(P) = TS1(P)

S2: Truth(P) = TS2(P)
S2: Justification(P) = JS2(P)

There's no guarantee that a truth from one source of knowledge is a truth in the other. An intuitive personal truth (one tested by asking a person for his opinion) may not be a scientific truth. Thus, in general, the "truth" of a proposition has no fixed meaning when there is no preferred source of knowledge.

There are three ways to avoid the problem of propositions having no truth values:

1) Assume that there is only one source of knowledge. In this case, most of us would likely choose science.

2) Assume that there are multiple sources of knowledge, but that they should all agree on the truth of any applicable proposition. This means that:
TS1(P) = TS2(P)

3) Assume that no single proposition can be evaluated by every source. That no truth value revealed by S1 can be revealed by S2, and vice versa. This might be akin to Stephen Jay Gould's Non-overlapping Magisteria.

I'm pretty sure theists would reject (1). I won't entertain the claim that science is not the preferred source of knowledge where available because no one reading this blog could consistently make that claim.

This means that either (2) or (3) is the case.

Overlapping Magisteria
Case (2) is ruled out because supernatural knowledge sources are broadly inconsistent with scientific ones where they overlap. Psychics and miracles are routinely shown to be fraudulent, and supernatural sensation isn't any better than guessing. Thus, we have ample evidence that supernatural knowledge sources fail to give the same truth values as scientific methods, as would be expected in case (2).

Non-Overlapping Magisteria
Case (3) is problematic for the theist because it means that any question that can potentially be settled by predictive means cannot be answered by a supernatural source. Indeed, it means that any phenomenon that one claims to know through supernatural methods must be unknowable through natural methods. I think this is one reason why theists assert that the mind cannot be purely physical, for otherwise, there would be no meaningful truth claims about supernatural souls.

As is well known, history's trash heap is littered with supernatural beliefs that were displaced by scientific truths, and the boundary of the supernatural domain has been in monotonic retreat for centuries. Still, the inductive inference that all supernatural claims are rot isn't deductive proof that they are rot. So, let's suppose that there is a domain, non-overlapping with science, in which supernatural sensation does reveal the truth (at least, most of the time). It is implicit in a knowledge claim (supernatural or otherwise) that the knowledge will be true as well as justified. Can we not then ask science to assess the efficacy of the supernatural knowledge source?

Symbolically, what we're evaluating is this:
S1: Truth(S2 is effective) = TS1(S2 is effective)

If it were possible for S1 to find S2 to be ineffective, then the space of truths of S2 would overlap (and potentially conflict) with those of S1 because S2 also implicitly asserts that it is effective. This would violate the premise that S1 and S2 don't overlap.

Therefore, S2 cannot give an answer that S1 might later determine to have been wrong. Thus, a fortune-teller cannot tell me that I'll be a millionaire by age 30 because I could use scientific means to know that he was wrong, and the fortune-teller implicitly claims he is right (i.e., he claims that his knowledge is not just supernaturally justified, but true). Unfortunately, this principle also negates all knowledge about future experience derived by S2 because such knowledge could be falsified by S1.

The practical upshot of all this is that S2 is unable to tell me anything about future experience. So why should I care what S2 has to say?

I might care about what S2 says if the execution of the method of S2 is a source of amusement. Is this why TV commercials for psychic hotlines display a "for entertainment only" disclaimer?

Science and Rationality
The beautiful thing about science (apart from the fact that it works) is that it is derived from rationality itself. In assuming that science is a source of knowledge, what am I assuming? I am assuming that I can make inductive inferences from past experience to predict future experience. Can I drop this assumption without destroying rationality itself?

If I assume that past experience is no guide to future experience, why should I assume that a theorem that I have just deductively proven true won't be false before I perform the next step in a proof? I cannot. I must assume that past experience, whether mental or physical, is a guide to future experience. Once I make this assumption for purposes of rationality, science automatically follows.

Conclusion
I have shown that supernatural sources of knowledge are either totally unreliable, or can only tell me about things that are irrelevant to experience. I have shown that science as a source of knowledge follows from the assumed axioms of rationality.

If science is accepted as the primary source of knowledge in any domain, it is the only relevant source knowledge about experience.

Nov 14 2006 Clarification: Science here refers to methods of deductive and inductive inference. It could be mathematics as easily as it is physics or linguistics.

8 comments:

Wedge said...

doc,
(2) is definitely the way to go (if you mean "partially overlapping" instead of "fully overlapping"), and the route most theists would take.
I think that you dismiss it too easily.

Case (2) is ruled out because supernatural knowledge sources are broadly inconsistent with scientific ones where they overlap. Psychics and miracles are routinely shown to be fraudulent, and supernatural sensation isn't any better than guessing. Thus, we have ample evidence that supernatural knowledge sources fail to give the same truth values as scientific methods, as would be expected in case (2).

Two Points:

First of all, Christianity is primarily about salvation from sin and inner transformation, and it has always invited empirical testing of this claim. Most Christians feel they have abundant first- and second-hand verification that it delivers on its offer of new life.

Secondly, about miracles: the existence of frauds and charlatans does not really prove the point. Scientific and supernatural explanations are broadly inconsistent because science is usually defined so that they are impossible, not because science has disproved them. Frauds count as evidence against the supernatural, while anything not obviously fraudulent is attributed to chance or as-yet-unknown physical causes. This methodology does not provide a way to disprove the supernatural.

But, again, most Christians feel they do have empirical evidence of the supernatural. Here is an experiment: gather together a group of several devout Christians, and ask them for examples of miracles, healing, and answered prayer for specific low-probability events. Limit them to verifiable first- and second-hand accounts. I am confident you'll find many more examples than can reasonably be attributed to chance. Good luck publishing your findings in Nature, though.

As to monotonic retreat, the big bang is a perfect counterexample. Christianity has always asserted that God created the universe, which implies that the universe has a finite age. The science of the early part of last century held to an infinite, steady-state universe in direct contradiction to this claim. However, the big bang (first proposed by a Catholic priest, btw) in combination with the quite recent discovery that expansion is accelerating (ruling out an infinite bang/crunch cycle) supports the Christian claim.

Doctor Logic said...

Wedge,

I think that choice (2) is an extremely difficult road for the supernaturalist to take. You seem to agree with me that if we travel road (2), there has to be strong scientific verification of supernatural claims. Where we differ is in our interpretation of what science says about supernatural intuition.

First, you say:

Christianity is primarily about salvation from sin and inner transformation, and it has always invited empirical testing of this claim.

How would you go about objectively measuring salvation and inner transformation? It certainly sounds tautological because we are talking about transformation to a Christian worldview. Needless to say, the more Christian one's worldview, the more transformed to a Christian worldview one becomes. Without metrics, don't expect to see scientific evidence of this anytime soon. Indeed, this sort of claim is intended to make Christianity look verifiable when it isn't even remotely so.

Second, you say that frauds and charlatans don't count against you. However, they very much do. Among the frauds are people who truly believe in their supernatural intuitions. For example, I expect that most psychics who report the locations of evidence to authories actually believe in their own powers. Such supernatural claims counts as noise in your scientific data. For example, if we search for instances where a person says astrology accurately predicted an event, I have no doubt that we will find accurate predictions. However, that's not the test. The test is whether accurate predictions outnumber the inaccurate ones by a controlled, statistically significant margin. They don't and never have.

So your proposed experiment is useless because Christians only remember the times when their prayers were answered. I recently heard about the story of a woman who prayed her father, suffering from a chronic illness, would be taken into heaven as soon as possible. After three years, her "prayers were answered." This is typical of the kind of anecdote you hear as evidence for Christian faith. I hope you can see what's wrong with it.

So, prayer and intuition about low probability events are ineffective, because no attention is payed to failures, and you can't determine the effectiveness of the method without looking at failures.

As for the Big Bang, you say:

Christianity has always asserted that God created the universe, which implies that the universe has a finite age.

Yes, but not only was there no description of the mechanism or evolution of that universe, but the timescale of the evolution was claimed to be around 6,000 years. It doesn't matter whether the scientists formally described the universe as being in a steady state for infinite time. That was for purposes of the model. Christians could easily assume God created the universe in its steady state.

Had the Bible said that the universe had existed forever, do you think Christians would have dropped their faith when the Big Bang models was verified? No. As with the claims that the Earth was 6,000 years old, or that humans were made sans evolution, etc., Christians would adapt their faith to the facts (not the creationists, they adapt the facts to their beliefs). For example, Christians might claim that the universe wasn't around forever and that "the word 'forever' meant a long time like 13bn years." Or else they might argue that the Big Bang doesn't exclude the possibility of an infinite age universe.

I really don't think that monotonic retreat was too strong a term.

Wedge said...

So your proposed experiment is useless because Christians only remember the times when their prayers were answered.

If the evidence for prayer were this flimsy, you'd be right. But I'm not talking about the “I prayed for a parking spot and God gave me one!” sort of prayers. Here is an example of the sort of thing I am talking about: a few years ago, a friend of mine heard a lecture in which the speaker urged his audience to test prayer by praying consistently for specific, low-probability events. So he prayed for a piano. A month or two later, he had one (and it wasn't given to him by someone who knew he wanted it).

Of course this one example doesn't prove anything. But suppose this is not an uncommon occurrence. Enough examples with similarly low probability would make a case which a lot of “God gave me a parking spot” anecdotes wouldn't. You may not have an accurate idea of the unanswered-to-answered prayers ratio, but you can certainly bound it. If the number of unanswered prayers needed to make a series of answered prayers explainable by chance is unreasonably high, then chance is not a satisfactory explanation.


It doesn't matter whether the scientists formally described the universe as being in a steady state for infinite time. That was for purposes of the model. Christians could easily assume God created the universe in its steady state.

I think you need to distinguish between the core claims of Christianity, and claims made by people who are Christian. The core claims of Christianity (as exposited in, for example, the Nicene Creed) are the ones on which it stands or falls. The 7-day creation and 6,000-year figure are based on specific assumptions about the genre of the first few chapters of genesis, the exhaustiveness of the genealogies, etc. Many of the early church fathers (cf. St. Augustine, 4th century) interpreted the days in Genesis 1 metaphorically for reasons that had nothing to do with evolution. And some of today's prominent Hebrew scholars think Genesis 1 ought not to be interpreted literally on grammatical grounds.

All that to say, young-earth creationism and most other specific claims about the natural sciences are in a separate category from the claim about creation (which is in the creeds). I do not think it involves creative re-interpretation to keep Christianity compatible with science.

Now, about the big bang: you claimed that the boundary of the supernatural was in monotonic retreat. A steady-state universe is fairly easy to explain on naturalistic terms by assuming the universe is eternal. It seems to me that , though, that a universe with a finite age that began in a specific moment raises questions of causality that theism has a ready answer for but which naturalism has a harder time explaining. It isn't a coincidence that a Christian was the first one to propose it. Many of the scientists of the day found the idea that the universe had a beginning distasteful on (naturalistic) philosophical grounds.

Doctor Logic said...

Wedge,

You may not have an accurate idea of the unanswered-to-answered prayers ratio, but you can certainly bound it. If the number of unanswered prayers needed to make a series of answered prayers explainable by chance is unreasonably high, then chance is not a satisfactory explanation.

You have to have per-person controls or else you'll just be deluding yourself. I expect that most theists claim to have had prayers answered with low-probability events. However, each person is making their own assessment of what is low-probability and what isn't.

Furthermore, it's certainly subjective as to whether or not a given low probability event fulfills a prayer. For example, suppose I pray that the chronic suffering of an elderly relative is relieved. Well, there are many low-probability events that would fulfill this wish, from full remission, to death by rare cause, to brain death by rare cause, to chance discovery of new painkillers. Any one of these events would be considered fulfillment, and many specific ways in which this occurs would be considered low-probability. The decision as to whether the wish is fulfilled integrates over many low-probability events.

For example, suppose a man is injured in a car accident. The individual circumstances leading to the accident might each be rare. The drunk driver just happened to run out of money at the bar at the right time. The man just happened to stop to pick up a quarter on the sidewalk before entering his car. The drunk just happened to throw up before getting behind the wheel. If any one of these low-probability events had been different, the man would not have collided with the drunk. However, none of this low-probability stuff tells us anything about the chances of getting into an accident with a drunk driver. Something that's not so low a probability after all.

You would think that, if this prayer research could be done, the Vatican and the mega-churches would sell some of their lavish riches pay for the research to scientifically prove that wishful prayers work. I don't see that happening.

I think you need to distinguish between the core claims of Christianity, and claims made by people who are Christian. The core claims of Christianity (as exposited in, for example, the Nicene Creed) are the ones on which it stands or falls.

I had no idea that the Creed was so short. Well, let's look at what it says:

WE BELIEVE in one God,
the Father, the Almighty,
maker of heaven and earth,
of all that is, seen and unseen.


That's pretty vague. Worse yet, there's no implication here that the universe doesn't have infinite extent in time. After all, the Big Bang is not only the beginning of space, but of time. If so, then God is outside of both space and time, and creating an infinitely large time is no different from creating an infinitely large space.

And I haven't even begun to ask what the verb "to create" might mean when there's no time coordinate in which the created thing doesn't exist.

It seems to me that , though, that a universe with a finite age that began in a specific moment raises questions of causality that theism has a ready answer for but which naturalism has a harder time explaining.

It is not possible to find an explanation for the totality of the universe, and theism is no exception. Theism is more fine-tuned than the universe itself, and specifies no predictive mechanism that would show up in, say, the microwave background. The creation story is a poetic restatement of the data its trying to explain. It's not an explanation for it. Read my next post for the the details.

It isn't a coincidence that a Christian was the first one to propose it.

Do you think there might have been any theists advocating for the other side?

Wedge said...

Doc,

You have to have per-person controls or else you'll just be deluding yourself.
Could you explain why this is? I'm not following.

With regard to low-probability events: you are right that (depending on the prayer, of course) there are many individual low-probability ways in which it might be answered – but not usually, I think, very many relative to the number of ways it could not be fulfilled. There are certainly many ways that one might come across a free piano, but that has relatively little effect on the probability of being offered one, I think. Another example: take a series of 10,000 English letters. An incredibly large amount of coherent English text can be made that consist of 10,000 letters, but that doesn't make it likely that a random string of 10,000 letters will be coherent English. I think the same reasoning applies to the number of experiences that would fulfill a low-probability request as compared to the number of possible experiences.

What would make these events possibly significant statistically is the fact that you need to multiply the probability of the event by the probability that you were praying for it when it occured (factoring in, of course, how long you have been praying for it).

If you have time and interest, listen to this interview with J.P. Moreland (1:05:20 to 1:55:00, the meat is in 1:12:20 - 1:31:20) where he describes miracles/healings/etc. he knows of. Most of the things he recounts are specific and verifiable (except for the fact that I am not at liberty to go flying all over the world to do so :-). I think there are only two options: these accounts are blatantly false (or at least wildly exagerated), or Christianity is true. In fact, I would be willing to bet my Christianity on the empyrical verification of a significant number of these sorts of stories. Would you bet your naturalism?

You would think that, if this prayer research could be done, the Vatican and the mega-churches would sell some of their lavish riches pay for the research to scientifically prove that wishful prayers work. I don't see that happening.
I hear that the Vatican is actually pretty rigorous about documenting miracles. You need at least 2 to be considered for sainthood. Not being Catholic, though, I don't know the details. I doubt it is possible to gather enough evidence to convince the skeptics.

I had no idea that the Creed was so short.
Well, there are a whole lot of them. I picked this one because it's early and fairly basic.

Do you think there might have been any theists advocating for the other side?
I don't know how to verify whether there were or not, but I doubt there were very many (Einstein was some vague sort of Deist, not sure if he counts); as it follows from relativity that the universe is either expanding or contracting. Einstein had to throw in an extra constant in order to maintain his commitment to steady-state.

Doctor Logic said...

Wedge,

Sorry for taking so long to get back to your comment...

You have to have per-person controls or else you'll just be deluding yourself.
Could you explain why this is? I'm not following.


I mean that you can't let each subject decide after the fact what he was really praying for, what counts as fulfillment, what counts as low probability, and so on. That has to be laid out in advance, and there have to be controls, e.g., people who don't pray, but are observed to see if they do as well or better.

For example, I'm going to go out on a limb here and guess that the guy who wanted a piano was... a musician! In that case, it wouldn't matter whether you knew he was looking for a piano because, if you had an old piano you were getting rid of, you would likely offer him the piano. Unless these things are factored into the study (using blind trials), you're just selectively interpreting what happens as being the result of prayer because you're ignoring all the low (or high) probability events that aren't the result of prayer.

I think there are only two options: these accounts are blatantly false (or at least wildly exagerated), or Christianity is true. In fact, I would be willing to bet my Christianity on the empyrical verification of a significant number of these sorts of stories.

This is interesting. So, if it is found that there's no statistically significant evidence to support claims that prayer works, you'll renounce Christianity?

Would you bet your naturalism?

If you're right, I wouldn't have to. A predictable benefit of prayer would make prayer material. The benefits of prayer would be as lawful as gravity.

I hear that the Vatican is actually pretty rigorous about documenting miracles. You need at least 2 to be considered for sainthood. Not being Catholic, though, I don't know the details. I doubt it is possible to gather enough evidence to convince the skeptics.

You are right. Miracles are claims of events that have such low probability that the events are far less probable than low-probability alternatives. It's more likely that people faked the events or suffer group delusion than it is that the miracle actually occurred. In such cases, it's not impossible for the miracle to have occurred, it's just not rational to believe that it did.

Wedge said...

Doc,
I had been hoping to be able to come to an agreement with you on some specific claims which, if true, would provide evidence for Christianity. But apparently there is no evidence that would convince you.

For example, I'm going to go out on a limb here and guess that the guy who wanted a piano was... a musician! In that case, it wouldn't matter whether you knew he was looking for a piano because, if you had an old piano you were getting rid of, you would likely offer him the piano.

In this particular case, my friend got his piano when we were attending a summer-school session in Berkeley. The place we were staying happened to be very old and scheduled for destruction. Everything in it was basically free for the taking. That included a lot of furniture, and a old piano. So no, the piano isn't explainable by someone knowing that my friend might like to have one.

This is interesting. So, if it is found that there's no statistically significant evidence to support claims that prayer works, you'll renounce Christianity?

If I could be convinced that Christian claims of the supernatural (answered prayer, miracles, etc.) were sufficiently explainable by chance and wishful thinking, then yes I would. I think one of the weaknesses of your view is that it forces you to make the assumption that if only Christians understood statistics and psychology, like you do, they would see that they've been deluding themselves all this time.

If you're right, I wouldn't have to. A predictable benefit of prayer would make prayer material. The benefits of prayer would be as lawful as gravity.

Oooh, now you're not playing fair. My claims about the efficacy of prayer weren't intended to imply that it was some sort of a lawlike process. God is a person, and person's don't obey laws. I simply mean to suggest that chance is a provably unsatisfactory explanation for answered prayer.

You are right. Miracles are claims of events that have such low probability that the events are far less probable than low-probability alternatives.

Hume's argument against miracles is not so good. I've often wondered, though... even if Hume's argument is successful in proving we aren't rationally justified in believing that a particular event is miraculous, couldn't one argue that the large number of accounts of miracles is evidence that they do occur?

Doctor Logic said...

The place we were staying happened to be very old and scheduled for destruction. Everything in it was basically free for the taking. That included a lot of furniture, and a old piano. So no, the piano isn't explainable by someone knowing that my friend might like to have one.

Doesn't that mean he scrounged/self-selected the piano? Most people would not see this as a miracle.

I think one of the weaknesses of your view is that it forces you to make the assumption that if only Christians understood statistics and psychology, like you do, they would see that they've been deluding themselves all this time.

It's only a weakness if Christians have a scientific case for their beliefs. They categorically do not. If they had, they would either have produced it, or would stop denying the possibility.

Oooh, now you're not playing fair. My claims about the efficacy of prayer weren't intended to imply that it was some sort of a lawlike process. God is a person, and person's don't obey laws. I simply mean to suggest that chance is a provably unsatisfactory explanation for answered prayer.

Wedge, you don't get to play both sides of the fence. If you mean that unexplained events occur with no statistically significant bias one way or the other, then you'll get total agreement from me. Random stuff happens, and we cannot always divine the conditions or rule that caused it to occur.

However, if you're trying to say there's a definite bias between a cause (prayer) and an effect (granted wishes), then that's a firmly scientific hypothesis.

Hume's argument against miracles is not so good. I've often wondered, though... even if Hume's argument is successful in proving we aren't rationally justified in believing that a particular event is miraculous, couldn't one argue that the large number of accounts of miracles is evidence that they do occur?

Actually, I did not know this particular argument was due to Hume. Damn, he was a clever man. In any time period.

Here's a professional review of the book you cite. What the book says is that miracles can be shown to be true, if there's sufficient evidence. This doesn't change my point at all. Yes, if the odds of the Bible being false were lower than one in 10 billion, the story would be believable. However, this is not the case in reality. That's where your question comes in. The answer is that, yes, people will regularly report miracles where none have occurred, and 99% of holy books are untrustworthy by your own estimates. The odds of the Bible being fiction are therefore much closer to 10^-1 than 10^-10.

When I was about 12, I so much wanted to believe in UFO's that I hypersensitized myself to anything that remotely looked like an alien spaceship. Not surprisingly, I saw something unusual, and I convinced myself had seen a UFO. A couple of years later, I realized that I had deluded myself with wishful thinking. It was a clear illustration of how untrustworthy we are when we interpret our facts as evidence for the granting of wishes.

In the case of prayer, a person is hyper-sensitizing themselves to the occurrence of events that meet a certain criteria. There are many individual events that would meet those criteria, and each individual event is improbable. When the person finds an event meeting the criteria, he focuses on that individual event as if it were the only way the prayer could have been answered. Clearly, this methodology is broken. In the case of the piano, what would have happened if the person had scratched a lottery ticket and won $300? If he used that money to buy a piano, they would have attributed it to prayer.

I expect that similarly improbable individual events occur to people who don't pray, but such events are never interpreted as meaningful. I'm pretty sure I've randomly received stuff I wanted, but since I didn't focus on my wishes as if they would result in their being granted, the receiving wasn't particularly significant for me.

So you have several questions you need to answer to prove prayer is effective. First, what are the true odds of random events occurring? This is very hard to establish, so you will need to control for it. Compare the event rate for two groups, one praying for the event, the other not. You also need to be specific about what is prayed for. What counts as an answered prayer has to be rigorously defined, and praying participants should not be praying for other things. Personal anecdotes are wholly inadequate for this sort of study.

Finally, there's a question of whether this effect is restricted to Christianity. Are you under the impression that Jewish, Muslim, and Hindu prayers are not answered with equally apparent miraculousness?