[TelmoMenezes]

And likewise you can't prove a positive. In fact, you can't prove anything with statistics, and science is not about proof. Mathematics is about proof. Science is doubt. All theories are forever on probation -- or until they are falsified by new experiments.

[awptimus]

Not true. Given a hypothesis "there exists" the first observed instance is proof of the positive. The inverse however, again, requires you to sample the entire population and collect all data.

[duaneb]

Depending on what you're observing, it's only statistical probability you actually observed anything. There is no such thing as an inductive proof; there is no way you can prove anything exists to another person.

I suggest Hume and the writings of the logical positivists. This will wipe the idea of being able to "prove" with science or observation right out of your brain. No matter how much information you have, you don't have enough to predict the future. If our planet collides with some huge energy burst, all the people who said "I know for a fact that the earth will still be moving around the sun at the approximately same rate and mass" will have been PROVEN false. But there is no such trick to prove anything about tomorrow.

[awptimus]

Other people don't factor into this. Proving to them is not necessary. Once an event occurs, it occurred. Your knowledge of what that event or the total state of that event might be uncertain, but the event's occurrence is no longer probabilistic.

[duaneb]

Yea, but you are probably talking about a completely different event than the other person, or whatever happened in your memory, or maybe just a past version of yourself. The world is not naturally quantized into discrete events, causes, and effects, and it is in this disagreement over simple assumptions that "this event happened" that cause people to disagree about "certain" things. Look at how utterly useless witness testimony can be, no matter how hard they swear up and down, if the memory is suspect at all.

So, if you want to lie to yourself, I guess you could "prove" something to yourself. But you know you can't trust your observations for about a billion different reasons.

Why is this important? Because you can always know if a bridge has failed, but you never know if it's not going to fail. Never. No matter how certain you are, unless you can form a deductive proof showing that the structure will NEVER fail (which I suspect is impossible for a computer, let alone a human), you will always have doubt. If you don't recognize the doubt, you are lying to yourself.

Furthermore, once you realize how.... loosely science binds together, you realize that the "laws" we think we "know" are broadly accurate but fall to pieces in the details.

So no, proving a negative is not possible. It's not a proof unless you can show the state of the universe, which is again impossible without consensus, which is itself probabilistic and flawed. If you are 100% certain that an event has happened in any way that you could deductively prove something, that gamma ray burst could easily mess with your plans.

A non-deterministic universe is one of increasing, but always <100%, certainty.

[lisper]

That depends on the claim. For example, I can easily prove the (negative) claim that Bigfoot is not in Times Square. The proof goes something like this:

1. If Bigfoot were in Times Square, someone would notice.

2. No one has noticed.

Therefore it cannot be the case that Bigfoot is in Times Square.

That proof works because of the particular properties of Times Square (e.g. that it's full of people 24x7) and doesn't apply to the forests of the Pacific Northwest.

[awptimus]

What if Bigfoot is dressed in a burka? Under your assumptions your system is logically sound and under the system you can conclude, but in broader context you assume that which you would like to prove. You started with no one saw bigfoot, and add it as a necessary condition for bigfoot's existence. It's not a necessary condition.

If your assumptions are false, then so is your conclusion, in the end.

[lisper]

Bigfoot is seven feet tall so even if he were wearing a burka someone would notice.

Besides, Bigfoot is Jewish.

[danielam]

I know you're being terse, but I hate the way the word "doubt" is used here so I'll take the opportunity to pontificate.

Doubt, too, must be justified as much as certainty. We tend not to doubt something until there is a reason to doubt it and certainty grows with corroborating evidence. Furthermore, if I were to say that I have a coin in my right hand, you would have neither doubt nor certainty about the claim because given your knowledge there is no reason to doubt that I had such a coin but likewise no evidence that I do.

Doubt that does not obey such a process becomes very unproductive and indeed science is most productive when it abides by a falliblistic principle of economy.

[eli_gottlieb]

Claiming that the word "proof" can only be used in the formal sciences is just vocabulary nitpicking.

[TelmoMenezes]

It's conceptual nitpicking, perhaps.

I defend that using the word "proof" in the context of scientific theories is misleading. It invites people to suspend doubt, which is precisely the opposite of the scientific stance. Religions deal in absolute truth. Science is something much better than that, precisely because it is rationally humble.

[eli_gottlieb]

>I defend that using the word "proof" in the context of scientific theories is misleading. It invites people to suspend doubt, which is precisely the opposite of the scientific stance. Religions deal in absolute truth. Science is something much better than that, precisely because it is rationally humble.

Science is fundamentally subject to abductive, statistical reasoning. As such, the whole "doubt" and "humility" shtick wears out once you get to well-tested ideas.

We do not have "some evidence" that "supports", for instance, our conclusion that the Earth orbits the sun. We can simply say that all available evidence supports such a statement. We can imagine some chance, some probability, that the statement is wrong, but that probability involves revoking so very much of our established corpus of scientific observations that it makes no odds. In well-established matters like these, underconfidence in colloquial speech is every bit as misleading as overconfidence in bleeding-edge research.

Note that when you start trying to talk about things anti-scientific people wish to dispute, such as evolution and global warming, all of a sudden it's the enemies of science yacking on about the humility of mere empiricism, as though empiricism is mere.

[shkkmo]

It's not just conceptual nit picking. 'proof' and 'prove' do indeed mean something different in mathematics than they do in science. This semantic difference confuses people (you see a lot evidence of that in this thread). I think it's better to use 'evidence' rather that 'proof' and 'substantially support' rather than 'prove' when talking about science. That doesn't mean that the terms are invalid when used to talk about science, just that they are confusing to people.

[stefantalpalaru]

> [...] science is not about proof. Mathematics is about proof.

Mathematics is a science: https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_sci...

[TelmoMenezes]

The modern meaning of the world science is "natural science". Even the article you cite explains that the claim by Gauss that mathematics is a science implies the old meaning of the word.

Still, if this bothers you, replace "science" by "natural science" in my claim and the relevant aspect of the argument remains unchanged.