I reviewed the book Why? on the Popular Science website, but I wanted to pick out one example of where taking what you might call a mathematically philosophical view neatly disposes of a piece of cosmological sophistry that has always got on my nerves.
I have often seen the fine tuning of the universe used an argument for the multiverse existing. Many variables of nature have to have values very close to the ones we observe if life is to exist. It's not generally considered scientific to attribute this fine tuning to some sort of divine or panpsychic cause, so it is used as evidence for the existence of a multiverse.
The argument goes something like this. The fine tuning is incredibly unlikely. It's a bit like winning the lottery with a single ticket. But people do win lotteries every week, because there are very many tickets sold, making it much more likely that at least one of those tickets will be drawn. If we lived in a multiverse, where our universe is just one of a vast number, each with different potential settings for the physical constants, then it's not particularly unlikely that at least one universe has the right settings for life. We then invoke the anthropic principle to say that this has to include our universe, otherwise we wouldn't be here to observe it.
This argument has always felt specious to me. It seems to be misusing probability, but I could put my finger on exactly why it was. Goff, though, has a beautifully clear description of why the argument simply doesn't hold up.
We are asked to envisage a casino (it's no coincidence I used a gambling analogy above too - gambling and probability are, of course, intimately linked). This is not a direct quote, but puts across Goff's approach. Imagine you walk into this casino with your friend who is a cosmologist, and the first person you see is winning time after time. Your friend says 'Look at that, the casino must be full!' This seems a bit of an odd assertion, so you ask her why she thinks this. She says 'If the casino were empty, it would be really unlikely that this person would keep winning like that. But if the place is packed, it's a lot less improbable that someone would be on a winning streak.'
Unfortunately, the cosmologist's argument, which is exactly the same as that used to suggest there should be a multiverse, is just as wrong as the traditional gambler's fallacy: the idea that if you toss a lot of heads in a row, the next toss is likely to come up with a tail. The coin has no memory. Each time, you are observing a single throw, unconnected to all the others. Similarly, you have only observed one person's success. Players at the casino are not probabilistically connected. You can't deduce anything about other players from what is happening to that single individual. In the same way, cosmologists have only observed a single universe that is fine tuned - they can't use this to deduce anything about other universes.
Just in case the cosmologists resort to the anthropic principle, Goff has an answer to this too. The principle might incline them to say 'Ah, but we are bound to see a universe that is fine tuned, because that's necessary for life to exist.' True, but again, how can it tell us anything about other universes? As Goff points out, all you need do is add in a sniper to the casino scenario, aiming at the lucky player; the sniper will kill the player if he doesn't win. You can only observe the player if he is alive to still be playing. But it still doesn't allow you to deduce whether or not the casino is busy.
I agree there are plenty of philosophers talking tosh. But, personally, I'm very happy to disagree with the late Stephen Hawking and Leonard Mlodinow. We certainly still need philosophy.
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