Exactly. And this was my basis for objecting to the word "conclude." I would accept "suspect" as a better choice. My suspicions increase, I cannot conclude, based on this happenstance alone.
But you can conclude a few things, when extremely long odds come up. Many cosmologists (Max Tegmark, a member here) have concluded a multiverse of universes exist, precisely to explain the fantastic coincidences we keep discovering wrt to the fine-tuning problem in cosmology.
To go back to dice (groan!), if we rolled a bunch of ten sided dice, and we got 31415926535897932384626433832795028 (Pi), there are a couple things we would conclude (not just suspect):
1. The dice aren't fair
2. Someone with a knowledge of mathematics have rigged the dice.
I mean, if that happened, wouldn't you believe (1) and (2)? Not just suspect but believe it to be the case?
So I disagree that we can't make conclusions based on probabilities. Drug trials are concluded based on probabilities, court cases are often determined based on DNA evidence (which is just probability) and it happens in science, in the case of the fine-tuning problem.
Here's what I think you're trying to say: if someone got 10 out of 10 on a Zener card test, you would suspect something is going on...and if they got another 10 out of 10, you would still suspect something is going on...the problem is, you reach a point (or you should) where suspicion turns into certainty (or near-certainty).
This is where we part ways. To make progress on which hypothesis to accept, it isn't enough to identify which explanation is more probable. Probability alone doesn't have explanatory power. If, on the other hand, we take the die apart and find out how it's been altered, that is a good explanation. Probability can influence our suspicions and lead us to look for one explanation over another, but that's it.
I would agree with this: probability can knock out competing hypotheses, but it often can't tell us the whole story (although in the case of the multiverse, probability alone is behind asserting a huge number of other universes exist).
So to go back to the person who gets 100 out of 100 on the Zener test, we can conclusively say it wasn't chance, but you would say, well, maybe they're cheating in a way we don't know about. More testing has to be done with this person. I would agree.
But here's my point: if we succeed in totally isolating the person so that cheating isn't a live hypothesis, and they still get all the cards right, we are now able to conclude a few things, wouldn't you agree? That it's not chance, it's not cheating, so what's left? That some unknown power/causal mechanism is at work.
The lack of confidence (unwillingness to bet) is akin to an opinion. And you are right - I am a cautious bettor and would avoid it. However, when we wish to make assertions about the world, this should go beyond suspicion and opinion - we need to check and demonstrate to provide a positive explanation, not one built on whether something was improbable or not.
True, positive explanations (those that lay a foundation for cause and effect- tiny germs cause disease) are always preferred, but they're not always available. We know, for example, that something is increasing the expansion of the universe. Yet we have no positive explanation of what it is or how it works. Yet we know something is out there, otherwise how do we explain our results?
So the absence of a positive explanation doesn't mean there's no explanation that can be given. Quite the contrary. We may never know why the murderer killed Jane Doe, but his blood is at the scene, and he gets put away for life.
I generally see this type of argument used in a similar fashion - to show some intelligent interference behind an improbable phenomenon. We are saying the dice are "fixed" - meaning there is purpose and intent. So too does the creationist, stunned by the improbable outcome of a world with them in it, say the situation is "fixed" and designed. But it's the explanation behind the different ideas that holds sway - not merely the unlikelihood I should be here to comment.
Except when there is no explanation, as in the case of Dark Energy. What is Dark Energy? We have no explanation. Does it exist? Certainly. Either it exists, or all our measurements are totally off (which is possible).
Again, I disagree. The chance explanation is always in play until some other explanation is settled upon.
This is wrong. Go back to Zener Cards: John Doe gets 1,000 out of 1,000 right. The chance explanation cannot rationally be considered to be a viable explanation at this point, even though we're not entirely sure John isn't cheating in some way. There are ways to explain an event like what John did, but chance is not one of them.
Or take Dark Energy. The chance explanation for Dark Energy is that every observation we've made has been screwed up in some way. There is no Dark Energy, we just can't get the observations right. That's the chance hypothesis, and it could be true, but no one takes it seriously, even though there is no explanation for why our observations are what they are. It's just this mysterious thing called dark energy.
Consider a deeper question. Suppose I grant that Obama's prediction couldn't have been a chance event and was based on some secret ability of the President. I can then ask, even without knowing what that ability is, what the chances are that he should have the ability itself? And, receiving an answer to that, I can ask what the further chances are for the next level.
In other words, what are the chances of people having precognitive dreams? Sure, you would have to look at that to figure out what happened. If you believe it's simply not possible, then you would believe Obama just happened to get it right by chance.
If that's where you are, that's where you are, but I don't think that's being very skeptical. What if Obama had dreamed about 20 earthquakes and got them all right? There comes a time when our most fundamental beliefs have to be gotten rid of, in the face of overwhelming evidence.
So long as we accept our universe is fundamentally built from random quantum events, no matter how improbable anything may be, we already know, deep down, chance rules the game. I see no escape from this.
And yet, if Obama correctly predicted a whole day's worth of earthquakes from a dream, I think you would see an escape from that. There's always a competing theory, no matter how sure one is. Maybe it has a .0000001% chance of being true, but all it takes is one white raven to invalidate "All Ravens are Black".