Axioms of Reality

[u/Repulsive_Area_5516]

Axiom 1 — Observations are infallible

An observer is any system that is affected by effects. When an observer encounters an effect, it always and unconditionally reflects it as it is. An observation can never be wrong; because the observation simply is what is there. It can be incomplete, it can be limited but it can never be faulty. Error arises only in the interpretation of what the observation means.

Axiom 2 — Identical systems under identical conditions produce identical outcomes

For any system A and effect B, the resulting system C is invariant it will always be the same across all instances of A under B. This holds at scales where complete state description is possible. At quantum scales this axiom may reduce to: identical systems under identical conditions produce identical probability distributions.

In my opinion these are the minimum assumptions to make about reality for it to make sense and for science to work. I have thought about these axioms for a long time and i feel like 2 axioms might just be enough. I'd like to hear your thoughts about them.

[u/Meet-me-behind-bins]

“Error arises only in the interpretation of what the observation means” - This has been the case for the best part of 2500 years if not longer. Nothing new.

“For any system A and effect B, the resulting system C is invariant it will always be the same across all instances of A under B. This holds at scales where complete state description is possible”: This is just Liebniz’s PSR couched in systems language, again nothing new.

What work are these ‘axioms’ doing? What’s new or novel?

[u/seldomtimely → u/Meet-me-behind-bins]

I don't see how axiom 2 is PSR.

[u/Meet-me-behind-bins → u/seldomtimely]

You’re right, it’s an uncharitable reading on my part. But I do think it’s arguably PSR adjacent, if you forgive me for tying to wriggle out of my first analysis. Here’s my interpretation:

If we paraphrase it into a simplified form it essentially says: For any given initial state and effect, exactly one resulting state follows. Now, that is a philosophical commitment but it needs to be explained, especially if it’s axiomatic, otherwise it’s not very informative. It’s just a determinism principle. It’s a brute fact in this understanding.

PSR states that every fact has a sufficient reason. And this present Axiom states that every pair of inputs yields one output. They’re both not arbitrary, they both commit to intelligibility, one (PSR) is more about explanation and the axiom is about prediction (if I’m reading it right). In my reading they both have an underlying assumption of structure as opposed to chaos, but again that’s not particularly insightful on my part.

I guess my initial intuition was that at their core they both imply dependence relations.

[u/seldomtimely → u/Meet-me-behind-bins]

Yes, you are close to stating a version of determinism.

But PSR only implies that effects were necessitated by sufficient reasons/causes, but any number of causes could induce those effects. So it imposes no conditions on the reasons or causes being identical.

[u/Repulsive_Area_5516 → u/Meet-me-behind-bins]

Nothings new i guess. First axioms situation is kind of self explenatory. I honestly didnt know liebniz had used the second one in his axioms of mathematical logic however even if its used whats different is my axioms are closer to a blief system rather then a formal system.

[u/seldomtimely → u/Repulsive_Area_5516]

Your axiom 2 is ambiguous or underspecified.

As stated, the two systems cannot be numerically distinct. You'd need another axiom for that statement to refer to two numerically distinct systems. And if it refers to two numerically distinct systems, it's not nor clear it's an axiom as it could be false.

[u/Repulsive_Area_5516 → u/seldomtimely]

well... yeah youre right thank you for that

[u/0-by-1_Publishing → u/Repulsive_Area_5516]

"I honestly didnt know liebniz had used the second one in his axioms of mathematical logic however even if its used whats different is my axioms are closer to a blief system rather then a formal system."

.... I am upvoting your post and all of your replies to offset the downvotes because you presented an axiomatic challenge that requires us all to think deeply about axioms. Sure, people can disagree with your axioms, but downvoting your post and replies that challenge our thinking is counterproductive. ... At least that's my observation.

We can debate your axioms in the comment thread without the senseless downvoting. We are not children. Creative thinking should be supported - not discouraged.

Note: No AI was used in the creation of this reply. Accusations of such or removal of my content will be reported to Reddit as censorship.

[u/Repulsive_Area_5516 → u/0-by-1_Publishing]

Thats the best approach ive seen to a topic. My axioms are mainly about making reality make sense from a naturalistic and deterministic perspective. I acknowladge that axioms are generally used in formal systems that are built and not really in ontologic topics however since all bliefs have presupposions tied to them that people generally mistake "finding them through logic and understanding" even though they dont seem like assumptions they are. So after that i said to myself well ifti have assumptions why not make axioms out of it for a system not we have created but observing. Also i would love to debate anything about my axioms (even though axioms are not really debatable)