How unlikely does an event have to be before chance ceases to be the best explanation?

Suppose I played a game of cards against you. I appear to shuffle the pack, deal the cards out and we start playing. As we start to play you realise that I’ve somehow dealt myself the best hand possible whilst giving you really rubbish cards. You assume I was lucky – after all, any combination of cards is just as likely as any other – and agree to play another round. Again I deal out the cards and somehow end up with the best hand possible. You start to get suspicious however remind yourself that throughout history millions of games of cards have been played and so its hardly suspiring that somebody, somewhere gets a suspiciously good run. You could even factor in the parallel universe theory and so every game of cards will lead to somebody in one possible universe getting the optimum hand. You therefore agree to play a third round of cards and the same thing happens again. How many rounds would we need to play before you accuse me of cheating? Or to put the question another way: how unlikely does an event have to be before a conscious mind becomes a better explanation than chance?

Posted: January 18th 2010

George Locke

When comparing alternative explanations for a given event, you have to compare the likelihood of the explanation itself — not just how likely the event is given the explanation.

Consider a rain of frogs. If an angry god decided to punish people, a rain of frogs might be expected. On the other hand, it’s very unlikely for frogs to be pulled up from the water into the sky naturally. Does this mean that a rain of frogs indicates an angry god? Certainly not.

Even though it’s highly improbable for such a thing to happen naturally, we can imagine such a thing being possible: for instance, a tornado in a swamp could pull frogs into the sky. This is surely a rare event, but it is a rare coincidence of known factors. On the other hand, there are many unlikely assumptions required for the god hypothesis (e.g. the existence of gods, their interest in human affairs, some physical mechanism that allows action at a distance, etc.). Given that these assumptions are purely speculative and contrary to available evidence, the natural explanation is preferable to the supernatural one.

Supernatural explanations always suffer from this exact problem: they only work if you make all sorts of baseless assumptions. What makes them so appealing is that if those assumptions were true, the event in question would be likely, whereas under the naturalistic explanation the event is often very unlikely.

The take home point is that you have to weigh the likelihood of all those assumptions along with the likelihood of the event under those assumptions.

Regarding the card-dealing example you present, it’s not really representative of the arguments theists often make. You offer two possible explanations for your repeated wins: random chance and cheating. The main reason the analogy fails is that the assumptions involved in the cheating hypothesis (the existence of card players, their interest in winning, means by which a player can cheat…) are all readily substantiated by experience. As I have argued above, this asset is exactly what is lacking from supernatural explanations.

I think you can see why I say that a naturalistic explanation would have to be very unlikely in order to suggest that supernatural forces are at work.

Posted: January 27th 2010

See all questions answered by George Locke


There is a whole branch of mathematics devoted to the question of when is it reasonable to conclude that there is something non-random going on. It’s used heavily in epidemiology (sp?) and any double-blind clinical trials of drugs.

Basically, the simple answer is that a) the more trials you do, the more certain you can be, and b) there are far more ways to do such investigations wrong than to do them correctly and therefore c) it’s really easy to get misleading results even if you are honest and trying your hardest.

What that has to do with your example is, however, a bit tenuous, because you are conflating two concepts.

When playing cards, you already know that a) playing cards involves a conscious mind and b) people cheat at cards.

Or, to put it another way, somebody cheating at cards is a very unremarkable occurrence.

I’m presuming you want to apply this to something theological, but a) you actually aren’t really giving an argument there, you only get halfway and b) you’re confused at your analogy.

Oh, and c) the question that you are asking doesn’t mean what you think it means.

It would be a lot easier to answer your question if you just came out and asked the whole question.

Posted: January 25th 2010

See all questions answered by Eric_PK

Blaise www

Unfortunately, your question is predicated on a set of false assumptions, namely: a) it assumes the false dichotomy that every occurrence must be either the result of sentient action or completely random chance; b) it assumes that probability alone could be the determining factor in determining if an occurrence was the result of sentient action; and c) it assumes that the card-player analogy is an unbiased representation of the question. None of these assumptions are true, so the question is difficult to answer. It’s like a lawyer asking a defendant “Have you stopped beating your wife?”, and demanding that the judge restrict answers to “yes” and “no”, never mind that the defendant never started beating his wife in the first place. The question is designed to “incriminate”, regardless of the answer.

Assumption “a” (the false dichotomy) says that things are either caused by random chance, or by sentient action, with no other options available. In reality, there is a spectrum of potential causes of an event, running continuously from pure chance (ala quantum physics) up to solely sentient responsibility (ala man builds a clock). In between the extremes, there are a potentially infinite number of cases that are not pure chance, but still not the result of sentient action. Most things that are thought of as random, i.e. coin-tosses, chance meetings, shuffled cards, natural disasters, etc., are actually anything but. They are the result of complex processes that are set in motion at some point in the past, and would be completely predictable, given sufficient knowledge of the process and its initial conditions. However, the fact that they are not random does not in any way imply that a sentience caused them to happen.

The problem with assumption “b” (probability alone determines) is that statistics says that given enough time and opportunities, anything that can happen, will happen, so its isolated occurrence cannot prove or disprove sentient involvement, by itself. The chances might be 1 in 100,000,000 that on any given day the right number of hydrogen nuclei in the sun’s core will collide in just the right way to fuse. That seems extremely unlikely. Since fusion is ongoing in the sun, this assumption would imply that we know a sentient being made it happen. However, it is obvious that since the sun contains trillions of trillions of hydrogen nuclei, the conditions made it actually pretty likely that at some point during the first few million years of its existence, the nearly impossible would happen, and therefore, fusion started.

Assumption “c” (the “cardplayer” analogy) presupposes a sentient actor, the dealer. This means that it biases the outcome of any logic based upon it to assume the dealer must be responsible for statistical anomalies. Let’s add another layer to the analogy, say the fact that the dealer is a member of a fanatically religious sect that requires utter honesty and fairness from its practitioners, on pain of mandatory suicide and eternal torment. Now the same highly unlikely sequence of cards described comes up. Does cheating on the dealer’s part still seem most likely? What if the dealer is a dumb mechanical robot, pulling cards one at a time from a large rotating drum full of hundreds of new decks of cards that you yourself bought from different stores, guaranteeing no sentient involvement in the dealing process? Statistics says that your example is still completely possible, regardless of how unlikely, so if the stats say it can happen, and the process is certain not to be rigged, how would this support sentient action? Ultimately, this analogy is best at demonstrating the bias of the religious side of the discussion on gods, where if you assume they are there in the first place, then you can make all the evidence point to their existence…

Posted: January 25th 2010

See all questions answered by Blaise


...how unlikely does an event have to be before a conscious mind becomes a better explanation than chance?

Extraordinary evidence for extraordinary claims, please (for your implication that goddidit).

Posted: January 24th 2010

See all questions answered by logicel

SmartLX www

You’re too vague about what specific event you mean. Someone else might take you up on abiogenesis, but I’ll assume your focus is the fine-tuning argument regarding the constants and parameters of the universe. (It doesn’t really work with planet Earth specifically, for instance, because there are so many other planets and therefore our odds are much more plainly decent.) I’ll keep to the card analogy as closely as I can, poker in particular.

We, in this universe, hold one good hand, if you look at each of the universal constants (the speed of light, the gravitational constant, the weak nuclear force, etc.) as one card. It’s like a straight flush, where each card combines with the others to create ideal conditions for victory (life). If you tried to win five hands using each of the cards in turn as the high card, you’d have Buckley’s chance. Each element of our hand is not a great victory in and of itself.

Of course the conditions could be better (heart royal flush) and life could be sustainable on more than the surface of one tiny rock per several hundred cubic light years. Still, we’re fortunate.

The various multiverse models do make it quite likely that a good hand will appear somewhere, especially in versions when infinite hands are dealt. (In fact, an infinite set of multiple hands per player makes good runs inevitable.) If we hold the only hand, however, just how likely was it to be a good one?

The main argument that our hand is impossibly unlikely is that if you change any card, it becomes worthless. 'Tain’t necessarily so; some changes are acceptable.

  • If you change one number in a straight flush, you might get a different straight, or at least you’ll maintain a flush. (The gravitational constant would have to change by a factor of over 3000 to preclude stars.)
  • If you change one suit then you lose the flush, but if you change them all you might get a new one. (Victor Stenger has modelled hypothetical changes to multiple constants instead of one at a time, and come up with other viable combinations.)
  • The right set of changes might even get you the coveted heart royal flush (say, if every star were the same size as the Sun and every planet was the same distance away from its star).

In an ordinary game of poker there are 40 possible varieties of straight flush, including the four royal flushes, and a huge number of other favourable hands which are close to them. Our universe’s big hand is one of a potentially infinite number of winning hands, considering how many different ways the constants can be safely varied. We got one of them, and we’re fortunate in that way. That’s all.

Posted: January 24th 2010

See all questions answered by SmartLX


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