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This gets at the heart of the difference between science and math. What is actually science? and what is actually math? You may think you know, but most people
by deltaonefour 5y ago
This gets at the heart of the difference between science and math. What is actually science? and what is actually math? You may think you know, but most people don't.
Did you know? That in Science, and therefore reality as we know it... NOTHING can be proven to be true. Proof is the domain of logic and mathematics, NOT science.
There is a huge difference between science and mathematics.
Math is an imaginary game involving logic. You first recursively assume logic is true then you assume some additional things are true called "axioms." You assume the entire universe only encapsulates Logic and the axioms as part of your theory and that is everything that exists in your theoretical universe. You derive or prove statements that you know must consequently be true in your made up universe based off of logic and the "axioms." These statements are called "theorems." That is math...
For example the "pythagorean theorem" is a statement made about geometry assuming that the axioms of geometry are true and logic is true.
So of course if it's a logical game, there's no real replication crisis. All theorems in mathematics are proven true based off of logic. You can't replicate conflicting results if a result is PROVEN to be true via pure logic.
Science is different. Nothing can ever be proven to be true. There are basically two axioms in science. We assume logic is true, just like in math. And we assume that the mathematical theory of probability is a true model for random events happening in the real world. Then we assume everything else about the universe is completely unknown. This is key.
Because the domain of the universe is unknown... at any point in time we can observe something that contradicts our initial hypothesis. ANY point in time. That means even the theory of gravity is forever open to disproof. This is the reason why NOTHING can be proven. To quote Einstein:
"No amount of experimentation can ever prove me right; a single experiment can prove me wrong."
So sure mathematicians can make mistakes... and I know the author is talking about higher level details.... but at its most fundamental level, assuming all other attributes are ideal... it is fundamentally impossible for math to have a replication crisis while science, on the other hand, is fundamentally forever open to these crisis so long as the universe is unknown.
The most interesting thing to me in all of this however is that within science, probability is a random axiom. We have no idea why probability works... it just does. It's the driver behind another fundamental concept: Entropy and the arrow of time. For some strange reason Logic in our universe exists side by side with probability as a fundamental property.
- mcphage 5y ago> All theorems in mathematics are proven true based off of logic. You can't replicate conflicting results if a result is PROVEN to be true via pure logic. You can publish a paper in mathematics that claims to prove something, but is mistaken. A paper claiming that a theorem is proven, is not the same thing as the theorem being proven. However, that's not often the case—why that is, is an interesting & meaningful question.
- deltaonefour 5y agoYeah I get that. What I'm saying is that outside of mathematics, a proof is fundamentally impossible. It can never happen.
- twobitshifter 5y agoEven math has the problem you describe. https://en.m.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems https://en.m.wikipedia.org/wiki/G%C3%B6del's_incompleteness_...
- deltaonefour 5y agoYeah, but nobody tries to prove anything that can't logically be proven. So not only is there no replicability crisis but such a thing can't exist in the first place.
- morelisp 5y agoPeople try all the time to prove things that can't logically be proven. Probably lifetimes spent on Euclid's parallel postulate alone - over 2000 years of attempts! Before Russell Frege thought his logic was consistent. Before Gödel it was believed we could formalize a complete arithmetic even if Frege's specific design failed. Before Church and Turing the Entscheidungsproblem was considered potentially solvable even if Gödel's work ruled out the resultant proofs wholly capturing powerful theories. It took a very long time to even notice the axiom of choice, and longer to ultimately prove its proof futile.