Is it possible to be perfectly logical? Every logical statement

>>9043766
Sure if you are a machine, there are plenty of machines whose behavior would be described as perfectly logical.
Most computers, by virtue of being a logic machine would fit this bill

>>9043766

No, for the reason you suggest. Axioms are illogical, but you can't do logic at all if you reject axioms.

>>9043875
Then why are things the way they are? I mean, if it's impossible to be logical, then why does logic work despite its illogical origins?
In other words, what is the Universe's axiom?

bumping for truth

>>9043766
There does not exist a machine with absolute access to the underlying logic of the universe. All logical frameworks are composed of relative truths, and at its base, is always the computational "mind" and its senses. Which cannot be divided further without using themselves as proof. Self referential truths are faith based, not logical. This ultimately cannot be bypassed.

The closest you can get to truth is the highest precision, from the largest scale.

>>9043862
There is nothing that cannot be called a machine.
There is no machine that cannot be reduced to logic.
There is nothing that cannot be reduced to logic.
Logic arises via the base nature of the universe, and the potential presence of fixed underlying natural laws.

>>9043766
>>9043987

Logic has absolutely nothing to say about axioms so long as they are not mutually contradictory

you misunderstand what logic is or what it is meant to do.

the fact that logic happens after axioms are chosen does not make logic illogical, it means that your logical conclusions are contingent on those axioms.

which was always the case. that's what axioms are. They're statements prefaced with "supposing that ".

>>9046119
How can axioms be logical? How can we trust axioms? What hides behind axioms? How can they exist? That is what I'm trying to ask I guess.

>>9046134
Watch a lecture on formalizing proofs
https://scs.hosted.panopto.com/Panopto/Podcast/Syndication/c196dadb-385f-4f68-8c8a-ff11ed017839.mp4?mediaTargetType=videoPodcast

>>9046134
>How can axioms be logical?
I repeat:
Logic has absolutely nothing to say about axioms so long as they are not mutually contradictory

meaning, there is absolutely nothing more logical about choosing the axioms of euclidian geometry over the axioms of non-euclidian geometry for example. In fact it is impossible to say that either set of axioms is "more logical" . it does not make sense as a statement.. "logical" is not a quality that axioms can posses, except when comparing a set of axioms which are mutually contradictory with a set of axioms which are not mutually contradictory. Then we would say that the former were invalid as a set of axioms or we could call them illogical.

How can we trust axioms?
You don't. Who said to trust axioms? another word for an axiom is a postulate. By definition an axiom is a starting assumption. You aren't assuming that the assumption itself is true. You are making the postulate because you are unable to evaluate the truthfulness of the statement. like I said before, every axiom you decide to include in your logical system is prefaced with "supposing that" .
> What hides behind axioms?
elaborate, this question is unclear
>How can they exist?
how can any idea or statement exist?

>>9046075
Lel kek M8. We don't understand these "underlying natural laws" yet. Don't get ahead of yourself.

>>9043766
You must infer information and therefore must act on heuristics rather than pure logic.

But overall you can create a logical decision system that relies on high probability assumptions.

File: Badv5eFCIAADV_B.jpg (18KB, 309x265px) Image search: [Google]

18KB, 309x265px

>>9046629
>elaborate, this question is unclear
I am sorry anon, I think my thoughts as a whole are unclear. I have an idea, but I don't quite know how to explain it, get it into words. I will try saying some things that are tangent to the core concept. See, anything that is said ultimately derives from one or more axioms, so where did the first axioms come from? What is the axiom of the Universe and where did it come from? What is the first axiom of all of Mathematics and why does it exist? We use logic in our own favor. The scientific method is largely based on logic. From that, we have things like antibiotics and computers. But if axioms do not reflect a higher truth, then doesn't that mean Science is not necessarily reflecting reality or "truth" as a whole? Suppose you have two sets of axioms that are ultimately contradictory. Each of the sets allows several logical statements to be done as a result. What does that say about the nature of logic? I don't know. What is the axiom of everything? And how can it be made? I have been trying to get the idea which these questions orbit translated in words for literal months, I guess I'm just a brainlet. Please forgive me for being dumb.

>>9046744
>where did the first axioms come from?
If I understand it right and axioms mean things that we universally take as true without doubt, then the original axioms come from our natural instinct as a lifeform. Take a statement "fire burns our hand, therefore we shouldn't put our hand in fire". We accept this because our natural instinct tells us that pain is bad >>> hand in fire means pain >>> hand in fire shouldn't happen. However, this theory is tested in the world 24/7 and the only reason that the axiom stands is the fact that everytime it is tested, the result is the same.

Overall logic is the same, except it's mostly guessing. You want to get something from something, you have to guess how it works, using logic. Logic is just guessing with experience. The more axioms you have, the easier/faster it is to find another axiom. Now that I think about it, natural things like burning your hand in a fire doesn't have much to do with math-like logic, it's just a way of acquiring experience and training your brain to search for scenarios in the past or in your knowledge that might help you find a solution. The original axioms of sciences came out of simple experiments.

Take 1+1=2. That's obvious, right? Why?
Because every time you look at it, every time you think about it, test it in real life, it makes sense. It's logical, because we set meanings for those symbols and when put together they just make sense. From this you built onwards. Try more things and create more axioms, learn already known axioms in school, so you can go on and create even more complicated axioms to get things like antibiotics and computers.

Everything works fine while it is in theory. The problem is real world application. Antibiotics and computers work on principles that were tested several times over and have been proved working.

cont.

>>9046744
>Suppose you have two sets of axioms that are ultimately contradictory
Then you have a big ass problem on your hands and you must either change the base of your understanding of whatever you're dealing with, or ignore it and deal with it otherwise. In my opinion this is very likely to happen in the future, if it's not happening now, but only while applying things to the real world. As you may know, doing stuff in 100% theory is pretty fun, because everything can be logical, since you know all the factors. It's when you get to the real world and have to deal with the fact that there are things you cannot affect, things that you cannot have information about, that you must use the logic you have a problem with. You have to guess, approximate and do things that limit you, even though you can still get the outcome you seek. This is where axioms start to be questionable and this is where the problem of two axioms contradicting may rise up.

In the end, we will most likely never have an axiom of everything and the only thing left is guess until we can and use it to get as far as we can. Truth be told, what the fuck does it matter as long as it works?

bampu