An honest and sincere question deserves an honest and sincere answer:

Gatekeeping: Simply suggesting that others need to read more, or that they need to “look into” one of the largest and most controversial philosophical topics in history is a haughty and disdainful way of saying “I’m right, I’m not going to cite my sources, and anyone who disagrees with me must carry the burden of proof”. Don’t leave the justification for your argument as an “exercise for the reader” involving the entire canon of published thought, since that insinuates that they are simply too uneducated to understand how correct you are. THAT is gatekeeping knowledge.

I didn’t say maths was from Europe: Not directly, but you supported your argument for the statement

“[The scientific] method is predicated on European Enlightenment avowals of what constitutes an acceptable boundary of truth… [etc.]”

with nothing but the statements

“2+2 does equal 4. That doesn’t mean valuing 4 as an answer or valuing the act of valuing of the certainty of 2+2=4 is an objective position.”

as exemplary evidence. You are, quite literally, stating that the “valuing” of 4 as an answer to 2+2 is a question of science (otherwise it’s a non-sequitur), and that this is an example of how the scientific method privileges European Enlightenment ideals over others. That is saying that the precepts of mathematics are based on European enlightenment ideals, Q.E.D.

“Where’s the disdain”: I believe that a reasonable person would read this argument and conclude that the disdain is implied, given that you clearly seem to be complaining that the European enlightenment ideals have somehow “privileged” certain perspectives. Now, I happen to agree with that statement, but clearly in a very different way than you do:

It seems to me that, until the likes of Karl Popper’s contribution of the principle of falsifiability as the chief hallmark of scientific practice, the entrenched belief in strict empiricism was being privileged as a leftover of European Enlightenment traditionalism. Perhaps another will come along soon who similarly unseats Popper. To claim, however, that the scientific method itself is somehow predicated on enlightenment ideals appears, to me, to miss the entire point of this original post: that science changes, just as much as how we do science, because science is all about constantly holding ourselves, and our ideas, to ever-higher standards. Most of the principles of the modern scientific method have been around for more than a thousand years, slowly building on one another. The idea of a strict “scientific method” is as much an illusion as the entirety of reality may be, but that’s just because we are always developing new ways of knowing.

*Edited for readability and clarity.

Gödel’s theorem is a logical proof about any axiomatic system within which multiplication and division are defined.

By nature, every scientific model that uses basic arithmetic relies on those kinds axioms and is therefore incomplete.

Furthermore, the statement “we live in a simulation” is a logical statement with a truth value. Thus it is within the realm of first order logic, part of mathematics.

The reason you cannot prove the statement is because it itself is standalone. The statement tells you nothing about the universe, so you cannot construct any implication that can be proven directly, or by contradiction, or by proving the converse etc.

As for the latter half of your comment, I don’t think I’m the one who hasn’t thought about this enough.

You are the one repeating the line that “science doesn’t prove things” without realizing that is a generalization not an absolute statement. It also largely depends on what you call science.

Many people say that science doesn’t prove things, it disproves things. Technically both are mathematic proof. In fact, the scientific method is simply proving an implication wrong.

You form a hypothesis to test which is actually an implication “if (assumptions hold true), then (hypothesis holds true).” If your hypothesis is not true then it means your assumptions (your model) are not correct.

However, you can prove things directly in science very easily: Say you have a cat in a box and you think it might be dead. You open the box and it isn’t dead. You now have proven that the cat was not dead. You collected evidence and reached a true conclusion and your limited model of the world with regards to the cat is proven correct. QED.

Say you have two clear crystals in front of you and you know one is quartz and one is calcite but you don’t remember which. But you have vinegar with you and you remember that it should cause a reaction with only the calcite. You place a drop of vinegar on the rocks and one starts fizzing slightly. Viola, you have just directly proven that rock is the calcite.

Now you can only do this kind of proof when your axioms (that one rock is calcite, one rock is quartz, and only the calcite will react with the vinegar) hold true.

The quest of science, of philosophy, is to find axioms that hold true enough we can do these proofs to predict and manipulate the world around us.

Just like in mathematics, there are often multiple different sets of axioms that can explain the same things. It doesn’t matter if you have “the right ones” You only need ones that are not wrong in your use case, and that are useful for whatever you want to prove things with.

The laws of thermodynamics have not been proven. They have been proven statistically but I get the feeling that you wouldn’t count statistics as a valid form of proof.

Fortunately, engineers don’t care what you think, and with those laws as axioms, engineers have proven that there cannot be any perpetual motion machines. Furthermore, Carnot was able to prove that there is a maximum efficiency heat engine and he was able to derive the processes needed to create one.

All inventions typically start as proof based on axioms found by science. And often times, science proves a model wrong by trying to do something, assuming the model was right, and then failing.

The point is that if our scientific axioms weren’t true, we would not be able to build things with them. We would not predict the world accurately. (Notice that statement is an implication) When this happens, (when that implication is proven false) science finds the assumption/axiom in our model that was proven wrong and replaces it with one or more assumptions that are more correct.

Science is a single massive logical proof by process of elimination.

The only arguments I’ve ever seen that it isn’t real proof are in the same vein as the “you can’t prove the world isn’t a simulation.” Yep, it’s impossible to be 100% certain that all of science is correct. However, that doesn’t matter.

It is absolutely possible to know/prove if science dealing with a limited scope is a valid model because if it isn’t, you’ll be able to prove it wrong. “Oh but there could be multiple explanations” yep, the same thing happens in mathematics.

You can usually find multiple sets of axioms that prove the same things. Some of them might allow you to prove more than the others. Maybe they even disagree on certain kinds of statements. But if you are dealing with statements in that zone of disagreement, you can prove which set of axioms is wrong, and if you don’t deal with those statements at all, then both are equally valid models.

Science can never prove that only a single model is correct… because it is certain that you can construct multiple models that will be equally correct. The perfect model doesn’t matter because it doesn’t exist. What matters is what models/axioms are true enough that they can be useful, and science is proving what that is and isn’t.

Sorry, the point I was trying to make is that we will be able to know if any statement that is testable is correct.

I just wanted to clarify that your initial comment is only true when you are counting things that don’t actually matter in science. Anything that actually matters can be tested/proven which means that science can be 100% correct for anything that’s actually relevant.

I’d argue that we can’t do a resurrection because that’s really complex, not because we don’t know how.

I’ll also point out that there are people alive today who were declared medically dead that live normal lives because we made their heart beat again.

For me the more important implication of Godel is that mathematics itself is countable and thus measure zero. No matter how much we do, the infinite majority of the unknown will still be left to explore… And that’s just the math, not even talking about the dependent science (also measure zero). The unprovable stuff is just a tiny subset of this.

Nope! Invented by Bangladeshi/brits in England. Its plenty inspired by butter chicken, but made completely differently with British ingredients.