# Proofs and facts in science, math and life

1. Oct 25, 2017

### Greg Bernhardt

I've long heard that in science nothing is proven. That proof is a mathematical term. So what exactly do you call a certifiably known fact? An example is that the earth is round or at least that the earth is not flat. What do you call that? Can we not say it's proven or that we have proof that the earth is round? If not technically, what then do we call that fact? Is it really a fact if we can't prove it? Also at what amount of evidence do we call something a fact even if we can't technically prove it?

2. Oct 25, 2017

### Staff: Mentor

The round earth can be proven by inspection, so it reduces the validity of that of our perception. In the end it might always end there and the entire question is the same as Do we live in a simulation? Both won't make much sense to debate here (again).

Let me give another example: The famous apple. Do we know that it must fall, or did it simply happen that we didn't observe the alternative, yet?

And if this is still too obvious for some to doubt about the truth content of the must fall, let's take the proton decay. Does it or does it not? And if not, how can we ever know for sure?

To me, a proof has necessarily a framework of assumptions considered true and then a precise chain of conclusions based on them. This means in return, that we may conclude that under the assumption that the quadratic law of gravitation is rght, the apple has to fall. Unfortunately this law is wrong. It is substituted by GR, in which case the apple still has to fall. But GR isn't correct either. At least not complete. So when are we allowed to assume anything in nature to be actually true? In my opinion, never. There will always be a potential margin of error, as small as it might ever get.

3. Oct 25, 2017

### Tio Barnabe

I think this way, too.

Hey, why do you think we will never reach a perfect theory? Note that I'm not saying perfect in the metric sense, because indeed we will probably not be able to construct perfect measuring devices (that's one of the things undergraduate students realise during their lab classes), but I'm saying perfect in the sense that it's the ultimate theory.

4. Oct 25, 2017

### Staff: Mentor

That's not what I'm saying. I think we can never be sure. On the other hand, experience tells that there is always something left on another scale, so at least I doubt that there is a TOE possible. But this is not what I've said here. I think there cannot be proven facts about nature, as the experiments regardless how often we will have performed them are always only a measure of likelihoods per definition. They might be as close to $1$ as one might wish they were, but not equal to $1$ from a theoretical point of view.

5. Oct 25, 2017

### Tio Barnabe

You're likely regarding the question from the math point of view. A theory is more than math.

Never the less, the question raised on this thread is far more deeper than it looks, if one consider that a theory even tell us how a given experiment should be performed! This means that even what we measure is in a sense dependent on the theory in question. Sounds remarkable, no?