Many discussions end with the statement "you can't prove a negative". This is, of course, silly. I've heard it even from people who are quite expert at physics. People who should know better


Proofs of impossibility abound in mathematics and logic. Reductio ad absurdum is typically the first kind of proof learned when studying such things, and this really is nothing more than assuming the opposite of what one wants to prove, and showing that this cannot be - proving a negative.


I suppose what most people mean by it is that in an open system, such as the universe, which is not constrained by any rules (at least none we are aware of), it is impossible to prove that something does not exist. Showing that no one has ever seen a unicorn is not proof that one won't come down from the stars and eat your cabbages tomorrow.


The problem with this is that in such open systems, it is impossible to prove anything at all, negative or positive. No matter how many times you drop a ball and observe it falling downwards, that still is not proof that it always happens. It is still possible that the next time you try it, the ball will fly up to the ceiling and stay there. Not terribly probable, but also not impossible - at least not provably so. This is why we only have theories in physics, not theorems.


So why am I saying this? Am I arguing that because we can't prove anything, there must be a god? Of course not, don't be silly! I just want to do my bit to improve the argument a bit.


As everyone knows, a theory in physics doesn't mean a guess. But it is still one notch below theorem on the scale of knowledge. Theorems are theories that have been proven, but unfortunately we can only get those in closed, rigid systems such as mathematics (and even there we can't trust them completely, as Gödel showed), but theories are of course still useful. We assign probabilities to hypotheses, based on how well our physical, empirical experiences confirm them, and when the probability exceeds a certain (non-determined) value, we call the hypothesis a theory. I know there is a bit more to the process than that, a theory has to predict previously unobserved phenomena to be considered useful, but basically that is it. The probability has to be high enough to be considered a theory, but it can never be proven.


If the probability climbs high enough we start talking about law instead of theory, but even then it is not a proof (most evident from the fact that everything in physics we call laws were shown in the 20th century to be flat out wrong - but very useful approximations)

So it's not useful to talk about not being able to either prove or disprove god's existence, since we can't prove or disprove anything at all. We can however assign it probabilities based on empirical evidence.

Like Dawkins, I think p(god) is quite close to 0

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Comment by Albert Bakker on February 7, 2011 at 5:03pm
You are correct about the difference between deductive mathematical proofs, syllogistic logic and inductive reasoning in the empirical sciences and the possibility/ impossibility to arrive at absolute proofs.
This is why sophisticated apologists have long ago, since even before Hume, stopped applying deductive reasoning to give proofs of the existence of God. Whenever you encounter this type of thing then you know you deal with someone who either doesn't know enough to be even worth refuting, or someone who isn't interested in proofs at all, but merely in rhetoric.
More amusing, but evenly ill-fated are varieties of cosmological arguments or arguments from design.
Sophisticated apologetics use either inductive arguments within a Bayesian probability construct, like Swinburn. Or they, like Plantinga and his disciples, argue that you can believe and still claim to be entirely rational, because God uploads true knowledge directly into a believers' brain via a "sensus divinitatus" that is implanted in all people (from Aquinas/ Calvin.) That this is very problematic as a model to explain religious diversity is clear. If you believe in the wrong set of dogma's or the wrong God(s) or even worse as atheists then your sensus divinitatus is broken because once upon a time in a not so terribly distant past Adam and Eve ate an apple and suddenly realized they were naked. But if you believe in just the right kind of religion then this is because God in his infinite benevolence has fixed your sensus divinitatus and henceforth then you will be a happy downloader to all eternity.
However attributing probabilities to proposed hypotheses based on how well a certain empirical dataset is explained by it is a sort of verificationism. It's a bit ambiguous how you meant that, but if so, this is not regarded as a very reliable or even useful criterion. Instead falsification-criteria referee between competing hypotheses that - as you say correctly - have to postdict exi
Comment by Albert Bakker on February 7, 2011 at 5:04pm
..sting data, must contain as much as possible strong falsifiers and predict or quantify new, unknown or unobserved phenomena.
Comment by atheist_swede on February 7, 2011 at 5:58pm

Very interesting response, thank you for that. Just to give a quick clarification: what I meant by the probability reasoning was perhaps not so clear. What you say is of course absolutely correct, and was what I meant. I didn't mean the probabilities were assigned based on how well existing data were matched by a hypothesis. I suppose I should have spent a bit more time making that part clearer


What I meant was that as predicted behaviour is tested, and as the tests come in with the right result from different researchers, the probability that the hypothesis is good increases, and at a certain point it gets high enough that people start considering it established, and it gets referred to as a theory. I don't think this step is ever done explicitly of course, but it is there, "under the hood" as it were.


It is also possible to have two or more competing theories that all describe known data fully, where the differences are in areas unreachable by current experimental equipment. In those cases you start hearing scientists talking openly about how likely they consider each to be.


But yes, at some point it has to be decided by failing experiments. I just don't think we're ever going to be able to conduct an experiment to test the God hypothesis, so the best we can do is to assign values to p(god)

Comment by Albert Bakker on February 8, 2011 at 1:26am

I agree. [1] Other considerations come into play also. Elegance, unification, cases in point are for example the Higgs hypothesis and SUSY-needy superstringtheories, M-theory.

We only have to disprove any proposition that says p(god|evidence) > p(~god|evidence), not as some would have it p(god|evidence)>0.


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