[deltasixeight]

No. You are both wrong.

Logic is one of the fundamental axioms of the universe. We assume logic is true and consistently applies everywhere throughout the universe. This "rewriting expressions" thing is just a symbolic representation of logic. It is not logic in itself. The symbolic representation of logic by writing down "expressions" works because logic is a inherit property of our universe and since you are writing those "expressions" in that same universe, it works.

There is no way to prove or verify logic is consistently real. We just recursively assume logic is real. We observe it to be real and assume that the observation will consistently apply across all time and space.

Another thing that I should mention that is an axiom of our universe is probability. WE have no way of knowing why rolling dice or random variables follow the rules of probability. These are just arbitrary rules and we assume that they're consistently true about our universe. Logic along with probability are two things that we have zero methodology of verifying the veracity of but we just assume these two things are fundamental properties of the universe.

A more elegant way to look at it is to just assume probability is the foundational axiom of our universe. Logic is just a special case of probability where all causal connections are 100%. Of course given inherit unreliability and limited knowledge of all things we never actually see or can verify 100% causality on anything. This effectively limits logic to mathematical and axiomatic games while science is the only available tool for the real world.

Science is a whole different beast. Given the assumptions that probability is real and that logic is real, science is an attempted methodology to verify theorems or statements about the universe using the axioms of probability and logic.

For example Newton guesses that a ball should travel a certain distance according to his made up laws of motion. Using science we perform several experimental observations of moving a ball and statistically correlate to a certain degree that yes the ball does indeed move according to newtons laws of motion. This is what science is. It is making a hypothesis and using statistics to sort of verify it. The term "sort of" is key here because science is limited to the fact that it can never prove anything.

One thing to note here is that EVEN when we assume logic and probability is true, science is unable to prove anything is true. You can make 10,000 observations about newtons law, it proves nothing because at any point in time a new observation can render the entire hypothesis as false. Thus falsification is possible with science [1] but proof is impossible. Proof is the domain of mathematics and logic games and cannot exist in the real world due to limited knowledge.

This is not some pedantic philosophy I'm making up. This is foundational to a true understanding of what science and logic is. To quote Einstein:

"No amount of experimentation can ever prove me right; a single experiment can prove me wrong."

There are a lot of intelligent people who don't understand the true depth of the above quote. But if you get it, then you truly understand what science is, and the differences between science and logic. Obviously both the OP and the parent poster don't fully get it... by combining logic and science into one thing and calling it the "science of the possible" it shows that they don't have a clear delineation of the two terms. Most people think of science as some kind of fuzzy "technical study" of a topic. No. This is wrong. There is a clearer definition of science that separates it from logic and mathematics.

[1] Note that technically total falsification is also impossible. Inherit unreliability of observation tools and limited knowledge makes it so that no observation can be 100% reliable. Thus even falsification is technically limited to the domain of logic and mathematical games.

[ivalm]

> Logic is one of the fundamental axioms of the universe

This definitely a very opinionated view on what is logic. There is no reason to embed anything in universe/anything else. If you remove expressability, I’m not sure what properties remain. At the same time you can have rules outside of anything physical (in a sense of denoting something that subsists). Consistency of re-writing rules (in a sense that one can always write a propositional string that cannot be reduced to true or false), is an entirely separate beast.

> Logic is just a special case of probability

This is factually false. Probability is embeddable into predicate logic, but predicate logic is not embeddable into (Bayesian) probability. This is actually an open problem (how to define a probability theory that is equivalent to predicate logic).

> Science is a whole different beast

On this I do agree, I wouldn’t call logic a “science.”

[systemvoltage]

> This definitely a very opinionated view on what is logic.

It is by definition, not opinion.

[ivalm]

It is neither the accepted modern nor historic definition of the word “logic.” Your definition is also unrelated to the word’s etymology. In a sense that people can have personal definitions of words I generously called it “opinionated.” I guess I should have said “wrong.”

[deltasixeight]

>This is factually false. Probability is embeddable into predicate logic, but predicate logic is not embeddable into (Bayesian) probability. This is actually an open problem (how to define a probability theory that is equivalent to predicate logic).

Completely wrong. How can someone say I'm factually false when your own statement is completely and utterly incorrect. I don't think you're really aware of what's going on here:

https://en.wikipedia.org/wiki/Subjective_logic

It's not an "open problem" or aka "unsolved problem" in the sense you implied. Far from it. Rather it is just not a popular field of study.

>This definitely a very opinionated view on what is logic. There is no reason to embed anything in universe/anything else. If you remove expressability, I’m not sure what properties remain.

I don't think you get it. The nature of an axiom IS by definition an opinion. An axiom is an Assumption. Assumptions are just things that are assumed to be true, they are NOT things that are proven to be true. Thus the only thing an assumption can be if it is an unproven statement is that it is an OPINION. When anyone makes a statement about logic such as my statement "Logic is a fundamental axiom of the universe." Or "Logic is NOT a fundamental axiom of the universe" is by DEFINITION a statement of OPINION.

When I say it's a fundamental axiom it means that it is something all of humanity consistently assumes to be true. Our culture, our science, our mathematics, our interpretation of reality and the universe as we know it is founded on the assumption that logic is true. It is a general statement about the broad "opinion" of all of humanity.

Look at your own statement. You said and I quote: "There is no reason to embed anything in universe/anything else." What does this statement even mean? What is reason? Reason IS Logic. Look it up. You are literally saying there is no logical reason to embed logic into our universe. Yet here you are making a logical statement in a universe where you say we cannot assume logic is true.

We assume logic is true. You can't make a single argument otherwise. Literally all arguments you've ever made in your life hinge on logic being true. That is unless all your arguments are illogical. Are you saying your own argument is illogical?

There's really nothing left to argue about here. Our entire technical framework of reality is founded on the "Opinion" that logic real.

>On this I do agree, I wouldn’t call logic a “science.”

If you truly understood what's going on, you would agree with me on all points. Not just this.

[ivalm]

Not going to address your weird attempt at wordplay but again just so you know, subjective logic, which you linked, is equivalent to propositional (in a sense you can express any statement in subjective logic via a set of propositions, eg Ap distributions make this connection), and does not embed predicate logic (eg any statement of this system can be expressed in predicate logic, but not vice versa)…

Also, axiom can be just a rule in a rewriting system. Doesn’t have to be an assumption/opinion as it is just a proposition (or higher order predicate) that is true within some system (not necessarily related to anything that exists).

Things can be outside universe yet discussed by people in-universe (subsisting vs existing without multiple worlds).

What I am saying isn’t controversial in analytic philosophy/ epistemology…

Edit: on a more reconciliatory note, a classic essay that I enjoy that touches upon the idea of denotion/subsistence/existence/difficulty with predicates is Bernard Russel’s “On Denoting”. I suspect you may enjoy it: https://www.uvm.edu/~lderosse/courses/lang/Russell(1905).pdf

[deltasixeight]

>Not going to address your weird attempt at wordplay

There's absolutely zero need to be rude. There is no "wierd" word play here just misunderstandings and impoliteness by you.

>Also, axiom can be just a rule in a rewriting system. Doesn’t have to be an assumption/opinion as it is just a proposition (or higher order predicate) that is true within some system (not necessarily related to anything that exists).

This is obvious. You're just restating what I said and coming up with a circular argument. A rewriting system is a universe you create, not dissimilar to our own universe that we live in. An axiom in this system is an statement made by you stating something is true without any proof. A statement made without proof IS an assumption. Now this explanation may seem like word play to you but it is not. The exact identical words "assumption" and "axiom" serve to confuse your reasoning and blind you from the actuality of the concept at hand. What I am doing is unraveling your misunderstanding in attempt to explain your confusion but you are unable to see it and you view the argument as "word play." Axiom and Assumptions are two words that mean the exact same thing. There is one concept at hand and two words for that same concept that are confusing you.

>subjective logic, which you linked, is equivalent to propositional (in a sense you can express any statement in subjective logic via a set of propositions, eg Ap distributions make this connection), and does not embed predicate logic (eg any statement of this system can be expressed in predicate logic, but not vice versa)…

This system has axioms and theorems that use predicate logic. It is built off of predicate logic.

I recommend reading this: https://projecteuclid.org/journals/statistical-science/volum...

When you set the subjectivity to 100% the result is something equivalent to predicate logic. So logic is both a special case of probability as well as foundational building blocks for subjective probability itself. You can arbitrarily pick and choose which came first and which one is axiomatic. Probability or Logic.

You are indeed wrong here. Please politely admit it without calling my statements weird. If you disagree there is no need to resort to derogatory statements.

[Koshkin]

> Logic is one of the fundamental axioms of the universe.

Is it the classical logic of the quantum logic you are talking about?

[deltasixeight]

Hard to say which came first. Probability can be defined in terms of axioms and classical logic just read any probability book. Classical logic can also be defined in terms of probability by setting all causal relations to be 100% (See bayes theorem).

I'm making a vague sweeping statement here that eventually gets a bit more cleared up later in my writeup.

[boris_m]

Read the whole paragraph of the book.

[deltasixeight]

I read it. Science is not logic in the same way that a brick building is not a brick. Your description is inconsistent. You differentiate logical theories and scientific theories as different yet you call logic the science of what's possible.

Maybe you were trying to promote understanding over correctness but I would recommend that you do both as such fuzzy wording leads to people inconsistently and incorrectly using the word "science."