Logic will not tell you what is true.
Logic will only tell you what else is true.
Big fan of Randi’s, and I’m sure he’s talking about certain existence claims, (didn’t watch your clip, but familiar with his work). However, we can prove certain negatives with the same amount of certainty as positive claims when certain specific criteria are met.
I think a very large part of Scientific knowledge is proven as ordinary people know it.
Is there a hippo looking over your shoulder right now? A quick peek should prove there isn’t. (Certain Philosophers excepted.)
Is the Earth flat? Photos from space and a ton of other things have proven it isn’t.
Is the mass of an electron vastly less than that of a proton. Provably so.
Is the Andromeda galaxy at least 2 million light years away, you betcha.
And on and on.
It’s only when you get to the edges of things does it get less certain. E.g., what’s up with Dark Matter? Then you have theories.
They are both OK, and they mean exactly the same thing. I’m a scientist and see no difference in nuance between those two sentences.
In my experience, the words “prove” and “proof” are a little bit taboo in science. It’s better to say that you have evidence of something, or that your data show something, or that they support your hypothesis.
I am currently reading the books The Dream of Reason and The Dream of Enlightenment by Anthony Gottlieb. He is the former executive editor at the Economist and held fellowships at Oxford and Harvard. The blurbs on these books are from Big Dog Philosphers and Academics who praise these histories of philosophy as “the new standard” which “supplants Bertrand Russell” (his history of Philosophy).
The fundamental question at issue in the OP is: What are Humans capable perceiving and how should that be described?
In The DofE, about the Enlightenment-era philosophers, Gottlieb spends a lot of time on David Hume. Hume has a thought exercise that is often cited but rarely used correctly. With billiards, when a ball hits another one with a specific velocity, angle, point of impact, etc., we “know” how the target ball will react.
What does “know” mean?
To Hume, it means that, based on observation and experience, Humans have come to the conclusion that, for the most part, certain actions tend to have reactions, and those reactions can be distilled down to mathematical equations. But it means that a Human has “had the idea” to summarize experience and observations - a human noted the repeated correlation between impact and reaction; and a Human worked through the “standard” underlying math.
However:
- When a Human works out the math, they are doing so based on their current ideas about the correlation they have observed.
- Humans are not likely to “observe” EVERYTHING about such events. As they work the math and make more observations, they will sometime detect variations that are not easily explainable.
- That means that a Human will have to update the current “Working Idea” and run experiments to factor in those variations.
So Hume was laying out an Empirical explanation for the Scientific Method. His point, though, is that a Human Agent is always involved, establishing a working theory which explains the actions and reactions in question.
So, to answer the OP: Humans can form theories and collect data to accept or reject those theories. The Human ability to sense and to think is limited because we are limited, frail animals. ** “Prove” is not something Humans really do. ** We are incapable.
Agreed; one of these is when we can search the experimental space exhaustively.
Is there a Bigfoot colony somewhere in the northwestern North American continent? Well, unlikely, but there are places we haven’t searched.
Is there a Bigfoot in the kitchen? Provably not!
Most of the time when I see people bring up scientific proof (not the OP) it is in the context of believing something nutty. The inability of providing them a mathematical type proof gives them what they think is a reason their junk can’t be invalidated.
One doesn’t have to back down when claiming preponderance of evidence.
Within science I agree they are pretty much equivalent.
Another example of a mathematical proof in a physical context is Gauss’s Law. The usual physics statement of the Law is that the net flux of the electric field through any closed surface is proportional to the charge enclosed by that surface. You can mathematically prove that the integral of the flux of any vector field across any closed surface is equal to the integral of the divergence of that field over the interior of the region enclosed by that surface. But that’s still only applicable to physics if you trust that the divergence of the electric field is proportional to the charge (or, if you define charge in terms of the divergence of the electric field, then you have to establish that charge, so defined, is the property that protons and electrons have).
I’m not sure you’re correctly using the bit you’re citing. 
I thought Hume’s point was that, before I first saw one billiard ball hit the other, I wouldn’t have been able to say what was going to happen: maybe it’s going to stop and the second one isn’t going to move; maybe the first will bounce off the second; maybe they’ll both scream in pain, maybe they’ll merge into one, I don’t know.
I can’t really say what’s going to happen, or why.
After seeing what happens, I can start mentioning what I think will happen; but I still don’t perceive the why of it. Adding in experience means I now know what it did before, and so I can – and will – of course start figuring that the next “what” will be like the last few, or the last few hundred; but I’m still the guy who couldn’t deduce that back when (because I didn’t know “why”), and so I’m the guy who can only say “well, this happened and then that happened; and I figure that’ll happen again, since I’m guessing there’s a reason why (but I still don’t know what it is).”
I just snagged your post as an example; I am sure there are others I can use but I found yours first.
But if we shoot that arrow using an Atlas rocket or shoot it into the air from the moon or a seriously low gravity planet? Proof/prove in science is often a case of “in context”. There is also the consideration of when our body of factual evidence expands. The one that always sticks in my mind is how much it was always stressed to us that the speed of light was an absolute speed limit for everything in the universe. Then our knowledge of particles and the universe expanded through research and we leaned that YMMV a little. I use it but more in a guarded sense and I never accept anything as proven in the absolute sense.
Even in math, proofs do not give really 100% certainty. For one thing, the proofs we give are never complete in the sense of symbolic logic. But more fundamentally, no set of axioms sufficient to do arithmetic can be proved consistent. Perhaps proofs in lower predicate calculus (provable using truth tables) are consistent, but it stops there.
My opinion on the OP is that it is correct to say that many things in science (including the effectiveness of vaccines and that they don’t cause autism) have been proved. Anyway, all attempts to refute them have failed.
I’m not sure you’re saying anything different from me. But I strongly believe I am summarizing Hume correctly.
Outside of “existence”, I don’t know that there’s anything provable, and even “existence” is sort of an a priori assumption.
How big is your bow?
Science is the
king of the hill,
you are on top
till you are not.
Interesting that you also nitpicked this, and went with a rocket or low gravity; a lot easier than the solutions I came up with:
As far as the speed of light being an absolute limit for everything in the universe; AFAIK it still is. The data which seemed to show neutrinos traveling slightly faster than light proved to be due tot instrumentation flaws:
However, it still only applies to things in the universe. The fabric of space-time itself can travel faster than light.
I was thinking more in terms of negative matter but still …
One I never thought of before was the Big Bang itself. An interesting look at FTL is a short article at:
I find the *variable speed of light theories fascinating; they go all the way back to Einstein.
A fun science fiction treatment of VSL can be found in Vernor Vinge’s novels A Fire Upon The Deep and A Deepness in the Sky; Earth is buried many lightyears within a “slow-zone” in which the speed of light is incredibly slow, other areas of the galaxy have a higher speed limit.
In reality if VSL really is a thing it is probably only under very special conditions, or a gradual decreasing of the speed of light over time as proposed recently by João Magueijo as an alternative to cosmic inflation in the early universe.
If that is the case, then the Big Bang expansion didn’t happen faster than light; that speed just happened to be higher when the universe was very new. However, it wouldn’t preclude space expanding faster than light; arguably, it still does, since we can observe very distant, very red-shifted objects with an apparent speed faster than light due to their motion added to the motion of the space that expanded between here and there.