Axioms

[gumOnShoe]

Are simple truths that you believe in with out proof. They are the basis for things like math, and I believe are the basis for everything you do in life.

For instance, you believe that canabalism is wrong. You can't really prove that it is, but you believe it regardless. If someone were to tell you that you were wrong you would be horrified.

Morals are axioms. You can't prove that they are a correct line of thinking but you believe they are regardless. Your religous positions are mostly axioms, you can't prove that you are right but you believe anyway, you have faith (or a lack there of depending on your position).

The funny thing is, that you also hold some axioms which you believe are so correct and define your life, but at the same time they can be proved wrong. You just believe they are correct right now. If someone were to violate one of those axioms, you'd go crazy.

[Steel-Reserve]

One man's shame is another man's sanctimony.

[Orange]

Well I believe the axioms like cannibalism were developed to ensure a stable society. Then you get the religious ones, like discouraging people from cheating on their spouses, which doesn't have a very significant effect on the stability of a society.

[Dragon-Smaug]

Thinking about it, perhaps cannibalism itself isn't bad at all, just the disrespectfullness towards the dead (assuming the death of the entre of natural) that sometimes comes with it. In fact, there is a tribe of people in some forest somewhere that crushes up a person's bones when they die, to eat later as a community "when the time seems right."

[gumOnShoe]

At 11/14/06 08:39 PM, Orange wrote: Well I believe the axioms like cannibalism were developed to ensure a stable society. Then you get the religious ones, like discouraging people from cheating on their spouses, which doesn't have a very significant effect on the stability of a society.

In all honesty, given society, it could be proven that cheating on a spouse is bad for societies since it causes grief in the community. But that is a side note built on real axiums

You are thinking too big.

In religion, an axium might be that "when I die, something of me continues on" or even simpler the idea of good and evil is an axiom. In some ways one could argue that good and evil don't actually exist and they are terms invented by humans to help make the world a sensible place, but at the same time its hard to prove they don't exist, but if I did it would ruin some people's lives who have built their entire life on these ideas.

At 11/14/06 08:46 PM, Dragon-Smaug wrote: Thinking about it, perhaps cannibalism itself isn't bad at all, just the disrespectfullness towards the dead (assuming the death of the entre of natural) that sometimes comes with it. In fact, there is a tribe of people in some forest somewhere that crushes up a person's bones when they die, to eat later as a community "when the time seems right."

An axiom of yours might be that the dead deserve respect, when the reality might be (not that it is) the dead don't deserve anything because they no longer exist.

Axioms are statements that set order to the world for your mind, but can't be proven. In math an axiom might be that there is always a larger number than any number you could pick, or that if have a pattern, and can prove that the first few cases of something are happening then you can assume that the pattern will continue.

A common false axiom we all know of is "The world is flat"

But it could very well be that our axiom "Democracy is a good thing" is indeed false and in the future to be proven so.

[Dragon-Smaug]

Are you disagreeing with me?

At 11/14/06 09:48 PM, gumOnShoe wrote: An axiom of yours might be that the dead deserve respect, when the reality might be (not that it is) the dead don't deserve anything because they no longer exist.

It is part of my religion that the dead bodies deserve respect. I do not hold other cultures/religions (such as the aforementioned forest-dwellers) to the same customs and standards as mine, nor do I fault them for having different ones. That is why cannibalism is bad in my culture and I understand, agree, and uphold that, but cannibalism is not bad in terms of the human race. It's more natural than incest, which is an instinctual taboo for humans.

Axioms are statements that set order to the world for your mind, but can't be proven. In math an axiom might be that there is always a larger number than any number you could pick

I bet that could be proven. (I'm sorry, I don't mean to nitpick your generalizations. :) )

But it could very well be that our axiom "Democracy is a good thing" is indeed false and in the future to be proven so.

Yeah. In fact, democracy is decidedly a bad thing when the majority is wrong or operating under group psychology. If only the electoral system worked like it was supposed to....eh, I guess it's inevitable that it would get corrupted in some fashion.

[gumOnShoe]

At 11/14/06 10:03 PM, Dragon-Smaug wrote: Are you disagreeing with me?

A more pertinent question for yourself might be what your reaction would normally be if I were disagreeing with you. Whether you have some sort of pattern or axiom that you generally follow if I did disagree with your standpoint. It isn't necessarily whether or not I am disagreeing right now, but if I were would that cause you some sort of stress that you might feel the need to correct me. :)

In which case, whether or not you and I are in agreeance you still fall victim to your axioms.

[bakem0n0]

At 11/14/06 09:48 PM, gumOnShoe wrote: You are thinking too big.

In religion, an axium might be that "when I die, something of me continues on" or even simpler the idea of good and evil is an axiom. In some ways one could argue that good and evil don't actually exist and they are terms invented by humans to help make the world a sensible place, but at the same time its hard to prove they don't exist, but if I did it would ruin some people's lives who have built their entire life on these ideas.

Good and evil itself is not as simple as you can take it. Humanity seems to be drawn to the axium of opposition: Think of the number of opposing ideas you see everyday, be they order and chaos, good and evil, conservative and liberal, truth and falsehood, etc. None of the above are truely ends of a linear spectrum, yet common conception says they are. I think this is one of the most fundamental elements of human perception.

[ironzealot]

At 11/14/06 08:39 PM, Orange wrote: Well I believe the axioms like cannibalism were developed to ensure a stable society. Then you get the religious ones, like discouraging people from cheating on their spouses, which doesn't have a very significant effect on the stability of a society.

Logic cannot determine what is to be valued, it merely determines the most effective means of achieving/supporting those things of value. This is where axioms come in.

In the above quote you are demonstrating that there is reason behind axioms, but "cannibalism is wrong" is not an axiom, as you just proved cannibalism has a pernicious effect of the stability of society. The primary axioms we employ in our lives are of far greater scope.

Such axioms as "death should be avoided" and "We should endeavor to keep living and to be happy in our lives", those are the 2 biggies, nearly every other "axiom" is just a means of supporting those two true axioms. These axioms mentioned cannot be evaluated or supported logically, yet we accept them regardless.

Here is a tool for finding a true axiom: If a person gives their opinion on some issue, ask them why is it important. (for instance:' president bush's policies undermine our democracy.' why is democracy important?, 'because it protects us from tyranny and ensures our continued liberty.' why is liberty important? )

Continue asking the same question to every response they give, and when they finally reach a statement or value they cannot justify by simply stating that is supports some other value they hold, you have discovered a true axiom that this person holds.

[ironzealot]

At 11/14/06 09:48 PM, gumOnShoe wrote:
A common false axiom we all know of is "The world is flat"

But it could very well be that our axiom "Democracy is a good thing" is indeed false and in the future to be proven so.

a true axiom cannot be proven true of false, "democracy is a good thing" is not a true axiom. I'm sure you are speaking of whether or not a system of government is best conducive to a strong society.

Yet "strong society is a good thing" is not a true axiom either, as the logic says that a strong society is good because it best allows for healthy and happy people.

thus, "health and happiness are good things" is the true axiom being employed in the statement "democracy is a good thing"

we can even take it further, perhaps healthy and happy people aren't good because people have a negative impact on the evironment and thus people should be exterminated. Then your axiom would be "the environment should continue to exist and prosper" would be your true axiom.

it's difficult to articulate, but the point I'm making is that if a value is important only if it supports a higher value, then you have what is called an instrumental value. Instrumental values have no value of their own, but only valuable in the sense that they support a higher value.

An axiom is a value that is valueable independent of any other value, or it's valuable by it's own virtue, and not because it supports something else. This type of value is known as an intrinsic value and this is what is truely an axiom.

[A-Carrot-By-Dr-Riot]

Your "axioms" are far too complicated to be truly axiomatic.

A very obvious metaphysical axiom is that "something exists." It is unimaginable that that statement could be untrue.

A fundamental mathematical axiom might be " if X and Y have the same elements then X=Y"

I'll also put foward the following as undeniable, but only because the consequences of it being untrue make life meaningless. If life has no meaning then there's really no point in arguing. I might be a little off on a few of these, I'm open to a bit of debate but the fundamental idea is solid and undeniable.
"Knowledge (to some degree) is possible"
"Goodness exists"
"Moral actions are possible"
"Immoral actions are possible"

[gumOnShoe]

I'm happy in some ways that people are telling me I was too leniant. For one, I knew axioms in math, and thought that they probably applied outside of math, but was generally making up my own definition, which was stupid of me. Anyway, I like the idea some I'm going to look more into it.

I do believe though, and this is what I was getting at, that "false axioms" exist, in which case a person or persons believe its fundamentally true whether they have reason or not and in fact there might even be underlying reasoning to it that they ignore. When one person then breaks down this singular axiom of there's their brain can't handle that they were wrong, so they automatically begin to cope by either lashing back out, or if they are very lucky beginning to question the whole of their existance.

[EternalRabbit]

there is no way to prove something... you can only disprove it! that is the basis for theorums in math and laws in science

[Altarus]

In that case, all debate will ultimately boil down to a difference in axioms. Since axioms are unprovable, then there is no way to convince the other person in the debate that he or she is wrong and you are right. Therefore, all debate is pointless.

At 11/15/06 02:51 PM, EternalRabbit wrote: there is no way to prove something... you can only disprove it! that is the basis for theorums in math and laws in science

It is the basis for the laws in science, but I believe that theorems are supposed to be provable. Also, math does not really have any laws of its own, only theorems.

[A-Carrot-By-Dr-Riot]

At 11/15/06 02:51 PM, EternalRabbit wrote: there is no way to prove something... you can only disprove it! that is the basis for theorums in math and laws in science

You ever hear about mathematical induction? How about deductive reasoning? Look those up in an encyclopedia some time.

[WinTang]

It is not true that axioms are unprovable.

Axioms are statements that are considered true because they fit a certain observable pattern, and have not been proven false.

Yet.

[A-Carrot-By-Dr-Riot]

At 11/15/06 04:44 PM, WinTang wrote: Axioms are statements that are considered true because they fit a certain observable pattern, and have not been proven false.

Where did you come up with that definition.
An axiom is a statment that is fundamentaly true in of itself. It is not dependent on aything and stands on it's own not requiring any other statement to be true for it to be true.

[WinTang]

Where did you come up with THAT definition?

Here's dictionary.com:

ax‧i‧om  /ˈæksiəm/ [ak-see-uhm]
–noun
1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.
3. (Logic, Mathematics) a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
[Origin: 1475–85; < L axi&#333;ma < Gk: something worthy, equiv. to axi&#333;-, var. s. of axioûn to reckon worthy + -ma resultative n. suffix]

So basically, it's a statement not proven because it's either self-evident (1) or an assumption (3). An example of (1) is "1+1 always equals 2" (we do not have to infinitely make that calculation in order to be able to use the word 'always') and an example of (3) is "Let's assume the universe ends somewhere" enabling a discussion on what would lie beyond it.

Note that rules and principles (2) are not statements, they can not be proven wrong or right as they are not "claiming" something. Morals are principles.

My point is, the whole concept of proof is obsolete with the axioms OP is talking about.

[pt9-9]

At 11/14/06 09:48 PM, gumOnShoe wrote: A common false axiom we all know of is "The world is flat"

Axioms can be false? Please explain.

I've always thought axioms are the offsprings of other beliefs, and that there is no absolute truth, save for just the existance of justified true belief.

'The world is flat' is as false as 'the world is spherical'. However, when situated, perforce, humans classify these arguments as facts and realities to form societal structures. But they're really just perceptions.

That is, if you believe that one or more entities exist, you nihilist bastards.

[pt9-9]

At 11/15/06 04:11 AM, A-Carrot-By-Dr-Riot wrote:
I'll also put foward the following as undeniable, but only because the consequences of it being untrue make life meaningless. If life has no meaning then there's really no point in arguing. I might be a little off on a few of these, I'm open to a bit of debate but the fundamental idea is solid and undeniable.

I totally agree. Being an individual, it is much harder to understand, or posses 'hope' in life and it's meaning. That's why when you're in a depressing mood, you think thoughts of suicide and question purpose, because you loose faith in life.

This is why human nature to question is 'solved' by the implementation of humanity's social behavior, and why people have the need to communicate, so axioms can be made and enforced. Religion is one of the byproduct of this nature of humans.

Nowadays, I see more of my friends making their own assumptions and beliefs, rather than the old fashioned "like father like son" method. Which, may or may not be a good thing

[Elfer]

At 11/14/06 08:32 PM, gumOnShoe wrote: Are simple truths that you believe in with out proof. They are the basis for things like math,

Uh. What?

Aren't they more the basis for things like... not math?

[A-Carrot-By-Dr-Riot]

At 11/15/06 07:01 PM, WinTang wrote:

I think you're trying to cram more into a narrowly defined definition than is possible. There are a whole suite of words used to describe statements that are in different states of proof. There are postulates and lemmas and theorems and propositions.

Furthermore, it can be proven from axiomatic statements that 1+1 is always equal to 2. The proof is a bit hard to follow and it uses some mathematical thinking that might be a little weird to people. I'll post it later if you can't find it on your own.