I composed the first draft of this post a few weeks back, and, curiously, not long after (a few days), I saw David B make a similar albeit much briefer argument in the middle of a thread on Skeptiko... David, I haven't cribbed your notes!

Here, I am using "paranormal" as a shorthand for everything that a "skeptic" would deny: psi, UFOs, mediumship, etc etc.

So, here's the (very informally expressed) argument, which in the end is very simple, but I'll explain it via a narrative which hopefully isn't too tedious.

Let's say you show a denier of the paranormal a potential paranormal case - something very strange which is hard to explain - and ask him/her, "What do you think? Could that be a case of a genuine paranormal phenomenon?" - and s/he says, "Very probably not!" Let's say you then ask him/her to quantify that: "How probably not? Would you give it, say, odds of one in ten thousand of being a genuine paranormal phenomenon?"

Let's say the denier of the paranormal agrees: "Yes, odds something like one in ten thousand sound about right".

So far, so good.

Let's say you then come back to this particular denier of the paranormal with another potentially paranormal case, and s/he again agrees that the odds that it really is paranormal are only about one in ten thousand.

What are the odds that neither case is woo given the woo denier's odds for each? Simple probability tells us that those odds are 0.9999 (the odds of each against woo, 9,999 in ten thousand) to the power of 2 (because there are two cases), i.e. about 0.99980001. Thus, the probability that at least one of the two cases is genuine is about 0.00019999 (i.e. 1 - 0.99980001).

Not very hopeful for us proponents. But here's the interesting question: how many similar cases would we need to present to the denier of the paranormal for the odds that none of them are genuinely paranormal to drop (by his/her own admission) below 50%, i.e., for it to be more probable than not that at least one case is genuine, home-spun "woo"?

The answer is log 0.5 with a base of 0.9999, which, on rounding up to the nearest whole case, is 6,932.

Is it that hard to find 6,932 potentially paranormal cases, each of which has odds in favour that a reasonable denier of the paranormal would have to concede were at least one in ten thousand? I think alone on Skeptiko (and hopefully, eventually, this forum) we probably have considered and linked to a number of resources which comes close to that count, many of which an honest denier of the paranormal would have to give better odds than one in ten thousand for.

OK, but not all deniers of the paranormal are going to go that far. So, how about we consider odds of one million to one against: how many cases would we need for the probability that at least one of those million-to-one cases was genuine woo?

The answer rounded up to the nearest whole case is 693,147. Do that many cases, at odds of at least one million to one in favour of being genuine paranormal phenomenon, exist? Given that almost every person I've spoken to has had at least one "weird" thing happen to them, and that this seems to have been going for as long as humans have existed, I think they most certainly do, and that a genuine skeptic would have to admit as much.

But back to the deniers. What's my point, then? That a denier, to maintain his/her denial, cannot realistically give any reasonable odds that any individual case is genuine woo, because to do this consistently, given the number of reports of "strange" things out there, would ultimately undermine his/her position: s/he would be bound to admit that the probability of at least one genuine case of the paranormal is greater than 50%, even given his/her exceedingly low odds for individual cases. And once there is one genuine case, then the door is permanently open: goodbye blanket denial.

To maintain his/her denial, a denier effectively has to say: the odds of any one case being woo are near enough to zero that it's not worth quantifying them - and this is one part of what separates a denier from a genuine skeptic: a genuine skeptic will allow for some sort of reasonable odds that any given case is genuine.

One consequence, then, of this argument is that a genuine skeptic is almost compelled to grant that "genuine woo" probably exists.

This argument might also be one way of contextualising all of the "debunking" by that goes on: the mere possibility of anything paranormal cannot be allowed in any case, lest this principle (of allowing odds at all) be extended in general to all known cases, and upend via multiplied probabilities the plausibility of the denier's blanket denial.

Well, I hope that that wasn't all too tedious for you guys. I welcome your thoughts. Is this a reasonable argument? Does it have unintended consequences? Would it make any headway with a denier of the paranormal? How about with a genuine skeptic?

The main (probably obvious) objection I can see to it is a skeptic/denier saying, "Wait, I do not grant that such a large number of cases worthy of million-to-one odds exists: not until you show each one to me!" And now I'm wondering whether there is some creative way of using Google to count the number of potential cases of "woo"...

In any case: enough words from me - over to you guys.

Here, I am using "paranormal" as a shorthand for everything that a "skeptic" would deny: psi, UFOs, mediumship, etc etc.

So, here's the (very informally expressed) argument, which in the end is very simple, but I'll explain it via a narrative which hopefully isn't too tedious.

Let's say you show a denier of the paranormal a potential paranormal case - something very strange which is hard to explain - and ask him/her, "What do you think? Could that be a case of a genuine paranormal phenomenon?" - and s/he says, "Very probably not!" Let's say you then ask him/her to quantify that: "How probably not? Would you give it, say, odds of one in ten thousand of being a genuine paranormal phenomenon?"

Let's say the denier of the paranormal agrees: "Yes, odds something like one in ten thousand sound about right".

So far, so good.

Let's say you then come back to this particular denier of the paranormal with another potentially paranormal case, and s/he again agrees that the odds that it really is paranormal are only about one in ten thousand.

What are the odds that neither case is woo given the woo denier's odds for each? Simple probability tells us that those odds are 0.9999 (the odds of each against woo, 9,999 in ten thousand) to the power of 2 (because there are two cases), i.e. about 0.99980001. Thus, the probability that at least one of the two cases is genuine is about 0.00019999 (i.e. 1 - 0.99980001).

Not very hopeful for us proponents. But here's the interesting question: how many similar cases would we need to present to the denier of the paranormal for the odds that none of them are genuinely paranormal to drop (by his/her own admission) below 50%, i.e., for it to be more probable than not that at least one case is genuine, home-spun "woo"?

The answer is log 0.5 with a base of 0.9999, which, on rounding up to the nearest whole case, is 6,932.

Is it that hard to find 6,932 potentially paranormal cases, each of which has odds in favour that a reasonable denier of the paranormal would have to concede were at least one in ten thousand? I think alone on Skeptiko (and hopefully, eventually, this forum) we probably have considered and linked to a number of resources which comes close to that count, many of which an honest denier of the paranormal would have to give better odds than one in ten thousand for.

OK, but not all deniers of the paranormal are going to go that far. So, how about we consider odds of one million to one against: how many cases would we need for the probability that at least one of those million-to-one cases was genuine woo?

The answer rounded up to the nearest whole case is 693,147. Do that many cases, at odds of at least one million to one in favour of being genuine paranormal phenomenon, exist? Given that almost every person I've spoken to has had at least one "weird" thing happen to them, and that this seems to have been going for as long as humans have existed, I think they most certainly do, and that a genuine skeptic would have to admit as much.

But back to the deniers. What's my point, then? That a denier, to maintain his/her denial, cannot realistically give any reasonable odds that any individual case is genuine woo, because to do this consistently, given the number of reports of "strange" things out there, would ultimately undermine his/her position: s/he would be bound to admit that the probability of at least one genuine case of the paranormal is greater than 50%, even given his/her exceedingly low odds for individual cases. And once there is one genuine case, then the door is permanently open: goodbye blanket denial.

To maintain his/her denial, a denier effectively has to say: the odds of any one case being woo are near enough to zero that it's not worth quantifying them - and this is one part of what separates a denier from a genuine skeptic: a genuine skeptic will allow for some sort of reasonable odds that any given case is genuine.

One consequence, then, of this argument is that a genuine skeptic is almost compelled to grant that "genuine woo" probably exists.

This argument might also be one way of contextualising all of the "debunking" by that goes on: the mere possibility of anything paranormal cannot be allowed in any case, lest this principle (of allowing odds at all) be extended in general to all known cases, and upend via multiplied probabilities the plausibility of the denier's blanket denial.

Well, I hope that that wasn't all too tedious for you guys. I welcome your thoughts. Is this a reasonable argument? Does it have unintended consequences? Would it make any headway with a denier of the paranormal? How about with a genuine skeptic?

The main (probably obvious) objection I can see to it is a skeptic/denier saying, "Wait, I do not grant that such a large number of cases worthy of million-to-one odds exists: not until you show each one to me!" And now I'm wondering whether there is some creative way of using Google to count the number of potential cases of "woo"...

In any case: enough words from me - over to you guys.