GotG arguments rely on gaps in scientific knowledge as evidence of the existence of the numinous.
This argument isn't about gaps in scientific knowledge. It's about gaps in scientific knowability. The argument is Godelian in nature.
The set of natural laws is a logical axiomatic system. It cannot be both consistent and complete. Therefore, either the scientific method is fundamentally unreliable for determining the truth, or there are true propositions about reality that cannot be proven within the axiomatic system of the natural laws. In short, unless the natural sciences are inherently bunk, it's a logical necessity that there exists something outside their scope, literally super-natural.
It's an imperfect analogy but I always come back to the idea of CPU privilege rings. We run up against a hard limit of what is observable/provable - a privilege boundary, if you will. That suggests we are in Ring > 0, and therefore there is something in Ring 0.
What's in Ring 0? Nobody knows. Whatever it is, we call it God.
It’s not this mystical thing that people make it out to be online.
However I do wonder if it’ll turn out that these higher dimensional geometric problems turn out to have the same structure as Godel’s proof. That the higher dimensional geometric structure is complex enough to represent their own foundation.
Although now I’m committing the same fallacy I was arguing against i.e. an equivalence between unknowns
Can you explain why?
In other words, there are two ways to talk about the laws of nature: (1) some set of Platonic ideal laws existing outside of human experience, that actually govern the universe and (2) the set of approximations of these ideal laws that could possibly be discovered by a logic-based science. The GGP's mentioning of axioms means they're clearly talking about (2), but your statement makes much more sense if meant about (1).
Everything below is based on my original understanding of what you wrote, which I believe is a misunderstanding on my part.
I'm not sure what you're getting at with regard to Godel's incompleteness theorem not applying to modern science.
Are you arguing that Godel's incompleteness theorem doesn't apply to the mathematical logic model(s) at the heart of the modern scientific method, because a scientific model is an approximation of reality? The match between the models and reality has no bearing on the limits of the structure of the models themselves.
The original statement was about the limits of the logical structure of the models underlying modern science, having nothing to do with how well they actually fit reality.
Are you perhaps saying something along the lines that because scientific models don't precisely match reality, it's okay to introduce axioms that make them complete (able to prove all true statements in their domain) but inconsistent (and therefore able to construct proofs that false statements are true)?
Gödel's work was concerned with formally defined abstract systems, and his results demonstrate the limits of mathematical proof within such systems.
But science never proves anything. Science often uses the language of mathematics to express and to quantify ideas, but the core of science is observation, hypothesis-forming, and experimentation. Scientists apply logic to rule out theories, but it's an informal application of logic, not a formal one, because you can never precisely define a theory the way you can precisely define a mathematical object.
Science may appear to be a rigorous discipline, but it is at best diligent, not rigorous - not in the sense that a proof of a mathematical theorem is rigorous. A proven theorem must necessarily be true - that's what the proof demonstrates. Meanwhile, a scientific theory is only conditionally true, inferred from the evidence and hypotheses about the underlying mechanisms of the universe. All scientific truth is subject to revision if contradictory evidence arises.
Science is a system of best guesses based on what we have observed. Some of those guesses have proven very useful, and very reliable at predicting the future. But none of those guesses are fundamentally based on, or necessarily limited by, formal axiomatic systems of logic.
For all we know, there is a low upper bound on the complexity of the universe, and it might be completely explainable and understandable through the lens of science, without getting anywhere near the towering near-infinities of abstract mathematical thought.
Alternatively, if the universe was a formal system about which there were unprovable truths, one could simply add that unprovable truth as an axiom, to form a larger formal system, which itself would have unprovable truths, but as long as the universe was entirely contained within that larger system, you could prove every truth relevant to it, without being limited by Gödel.
If someone is seeking unknowables in the real world, something like the uncertainty principle could be a closer match.
Q: How many oranges are there in the kitchen? A: 2.
Not so fast. Addition is a mathematical model and doesn't necessarily reflect the physical universe.
Nobody knows if it is or not. It could also be that the physical universe is a reflection of mathematical truth.
> It can be, in cases like addition, but it doesn't necessarily need to be. Which was the parent's point.
Again, nobody knows if it what you claim is true or not. What we do know is that all scientific models are based on math, and if there is something wrong at the foundations of math, then all science is pseudoscience. Gödel's theorems are at the foundations of math. You can't just decide that you are skeptical about that part of math being applicable to physical models but addition is fine.
The real problem with Gödel is that it says something that a lot of people don't like to be true.
This is your personal belief, unless you can justify it. I won't hold my breath, because this discussion has been raging for centuries with no end in sight.
> For example, infinite numbers exist, but the natural world cannot have an infinite or infinitessimal amount of things, there are upper and lower limits.
Nobody knows if the natural world is finite or not. Consider for example the many worlds interpretation of quantum mechanics. We just don't know enough to assert such as thing.
Although, some would argue the universe would cease to exist without humans to observe it (and initiate collapse :))
I certainly have faith in physics...
"God, that is, Nature..."
Here's a good quote, wherein he's criticizing people's conception of God as the 'first cause' -
"So they will not cease to ask for the causes of causes, until you take refuge in the will of God, that is, the asylum of ignorance."
But I don't believe that our universe is neither unique, neverending, or cyclical.
I believe that our universe is just one of many, that exists on a super-dimensional plane (or substrate - not sure what word to use), where 'universes' continously appear and disappear, like bubbles in boiling water.
Every one of these universes will have different sets of laws, or rather, the laws will be tweaked differently, depending on the exact conditions of how they form.
Most will not be valid. They will 'pop' or implode near instantaneously. Some will not have the right values for constants like gravity and speed of light.
But every once in a while, there will be a universe where the laws are just perfect for what we see in our universe. A place where stars and planets can form. Where the right elements appear, and life as we know it is possible.
I wasn't trying to answer that.
I'm aware that my comment merely added an additional layer, between us and "the creator"/creation, (however you define that).
My point was more, that I don't believe our universe is unique, as in "alone". But rather that it is just one of many.
That some "God", or event, didn't create a single universe, perfect for (human) life. That's way too antropocentric for me.
Instead I believe that they are plentiful, and by chance one of them happened to be suitable for life as we know it.
We are not here because a universe _was created for us_.
We are here because a universe _could produce us_.
But of course it’s unfortunately impossible to know due to space time limits.
The community thrives by following guidelines, among them:
* be kind
* do not sneer
* do not call names
* respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize
But can we at least recognise that there's an enormous distinction between criticism of people and criticism of ideas? In my estimation, when someone is calling for an idea to be protected from unkindness, or name-calling, or sneering, it's probably deserving of it.
However, by labelling the idea as nonsense, by extension I must be someone whose ideas are nonsense.
This lowers the level of discourse. To what end? What did labelling my idea as nonsense accomplish? Did it help your argument? Or was it to make me feel bad, or to make you feel good?
I certainly wouldn't say labelling an idea as "dumb" would be unethical, though. It's just not productive to having a conversation: name calling begets more name calling. It puts people on the defensive where they are not receptive to new ideas.
They're both? But agree with everything else
And with that you've just demonstrated my point. By focusing on an aesthetic component of my rhetoric rather than the substantive, you have chosen to steer this entire discussion away from the underlying topic.
> by extension I must be someone whose ideas are nonsense
That is nonsense. It does not follow.
> What did labelling my idea as nonsense accomplish?
It's my opinion. And while you're welcome to call that idea yours, I only consider it an idea. You shouldn't be so quick to tie your ideas to your identity. Everyone has lots of opinions and a good number of them are certain to be wrong.
But you are not someone who makes ill conceived, pedantic, or desperate arguments to save face. That would be nonsense. It does not follow. Don't be so quick to tie your identity to the pedantic arguments you've made.
* do not sneer
* do not call names
* respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize
[0] https://en.wikipedia.org/wiki/God_of_the_gaps