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The value is already there, in that if they were switched about, you would be screwed. I assume you value not being screwed, no?

It is a different context, and therefore not appropriate in this context. I would also contend that metaphysical and epistemological axioms are more fundamental, in that without metaphysics and epistemology, there would be no math.

You miss the point. Take "existence exists" as an example. In order to refute that, you must accept that you exist to refute it. Therefore, "existence" is a premise to any refutation of "existence exists". There can be no more fundamental form in which "existence exists" can be broken down to. It is primary. Not so silly, eh?

Thank You, Mr. Sunshine!

Actually, I don't view it as a tragedy. It is a shame that you do.

@utabintarbo: Finally i get it, at least partly. Your definition of an axioms really is different, and seems like a good idea. IMO my definition is also a good idea, since i do not think there are enough axioms of the kind that cannot be refuted without denying your own existence to get all the way to statements we want to make. (at least not that i have seen, unless i do, i do not think you can really convince me that 'axioms of the assumption type' have no purpose)

@Mr. Jaggers: Your axiom first requires the existence of humans. Unless if you see it as an observation, rather then an axiom. Also i do not think it is true, for one 'human nature' is rather vague. Secondly, we might not exactly persist in the same pattern of being born and such. (there are in-vitro children already, you know how the the future will look?)

That depends on what you mean...
Do you not see that there are implicit assumptions in what you are saying? The underlying assumption that only one who exists can refute existence. Based on that, of course your "existence exists" holds.

Philosophy does make starting assumptions, but they prefer to keep them hidden.

Good point, I would say that alternatively underlying assumption is that you yourself exist. Of course, assuming one thing to exist makes existence exist. But that does not prove that other things exist, nor that all those things have a specific nature.(Descartes logic on that does not seem very clear to me) I think my accepting the other definition was a bit premature. (surely utabintarbo will disagree ) Descartes logic about consciousness seems to assume you need consciousness to refute it.
Many axioms are a bit vague in any case, because something like 'existence' or 'perceive' is not really defined. (or defined with other words that are not) This is unlike mathematics, maybe this is because in mathematics axioms often are explicitly defined with relations, while in this discussion, they (hopefully!) have some form of these implicitly, because we have some logic in our brains handling things like 'perceive', 'existence', 'good'. This is why it might be subjective. It would be nice, (but perhaps too hard) to surface this logic explicitly. I consider feel-good one example of an attempt. Assuming there is only one thing, and that is the universe could be another, since it makes some axioms into interpretation on that universe. I do not think neither gets near to really surfacing the logic.

btw read that quote bns said wel, it can easily be misread. (i am sure a lot can easily be misread round here) I think he means that he sees an underlying assumption that: non-existent 'people' can not refute existence. Hmm sticking that to valuers, non-existent 'people' can be valuers.
IMO This Descartes logic only justifies belief on those three axioms, it does not prove them. Maybe it does justify them in a greater extent the other axioms are justified

I am not saying they have no use. Just that they are not axiomatic in the philosophical sense. As thought experiments, they are very useful.

My context is philosophical. Yours, well, is elsewhere....

Think of the implications of the alternative: one who does not exist may be able to refute existence. That would be some trick.

one who cant exist cant do anything and therefore cant prove anything.

So you admit that there is an underlying assumption, a.k.a. an axiom, upon which your axiom rests. BTW, I agree that your underlying assumption is reasonable, that doesn't mean it isn't there.

@Jasper:
The problem with Descartes is that he tried to generate axioms logically; but logic must rely on axioms -- you see the problem here. The reason the axioms we have developed here are less precise than we would like, is that we haven't worked on them for thousands of years.
These philosophical "axioms" are very reasonable, and I am willing to assume that they are true. But it's a very different thing to say that they are "irrefutable." They're just assumptions. It's left to each individual to choose what consistent system he/she wants to believe.

@bns: I agree, i only dig that the "existence-exist-axiom" follows from the axiom one exists himself. The consciousness axiom is one of "my" kind too:
Does not need to be true, one person could think a brain is just a system, and the system denies the existence of consciousness. Thinking about it more, consciousness is not really necessary axiom, one could consider 'consciousnesses' just systems, and this discussion and discussions about ethics just part of the workings. Your motivation on wanting ethics would then be "dont be the cancer"/"dont be the broken link in the clockwork". I do not think i could do without the consciousness axiom though, because i perceive myself, and others seem similar in this, and it just would take the value out of it for me.
Have tried reading up on Epistemology, that will take up a while.. But, i do have the feeling that people do not really talk about Epistemology but only mention it. Sometimes some says some opinion is based on his Epistemology, it seems weird that the "theory about knowledge" itself is not discussed. If i had to choose a epistemology now, i would chose internal models of the outside world, and rationality for math, since those are not based on what you see, but on what you assume. Then again, the assumption do depend on what you see. In physics: postulates, but many math axioms may be so-inspired too, and math may also be depend on the manifestation of it being in the physical universe.

Yes, we want to pick the axioms that seem to reflect the real world. I choose realism because I think that reflects the world around me, but I can't prove it so I take it as axiom. You (apparently) choose non-realism because it seems right to you. Your choice is every bit as logically sound as mine, but we each make our own choices. Some people (like bnonn, e.g.) choose some religiously motivated axioms. That's also logically sound, but reflects the world around us less well. I wouldn't say they depend on what we see, but rather that a good axiom consistently reflects what we see around us. That's an important distinction because in some situations you may have more than one system (e.g. realism/non-realism) that equally reflect what we see.

A few possible errors here:

1. The axiom is circular. Correct me if I'm wrong, but "existence" means "that which exists." As such, it doesn't really say a whole lot.

2. Someone (Ann Rand?) is butchering Descartes' argument. Descartes really said "I think, therefore I am." Note this does not prove the existence of mind-independent objects like trees. To eventually reach this conclusion, he presented a few "proofs" of the existence of God, upon which his entire epistemology rested (similar to what bnonn was presenting). IOW there's a giant gap in reasoning between proving you exist, and a tree exists. The term 'existence' is being equivocated to mean both yourself, and a tree.

3. To argue that something is true, because it can't be refuted is of course an argument from ignorance.

4. There's no reason we can't assume the axiom to refute the axiom ... 'reductio ad absurdum' (reduction to absurdity) is a valid form of argument which does just this. Ann Rand seems to have no formal training in philosophy and, quite frankly, is not a source to quote.

You are free to view it that way (as an "assumption"), if you wish. It does not change anything but the words, however.

The circularity (in this case) is what makes it axiomatic. One cannot refute it without conceding it.

I suppose if you had read down the page a bit further, you would have stumbled upon the bit about the external world.

And "existence" includes both me and the tree. It is not an equivocation, but a "class" of which the tree and I are both instances of sub-classes of the parent.

Where did I do that? If anything, I have most vociferously not done that.

Perhaps, but the refutation of existence concedes existence. If you have a valid refutation, present it for review.

Well, you have stated that you do have formal training, yet I would certainly not quote you as any kind of authority on philosophy.

How is this relevant, anyway?

Note though ... proving the existence of one member of a class does not prove another member also exists. For example: consider the class of men and unicorns.

You seem to be going back to the claim that because the assumptions can't be refuted, they are somehow more special than other assumptions.

I would describe it differently... just because we must assume something for the sake of communication, this does not prove those assumptions true, but it only means that everything we communicate depends on possibly faulty assumptions.

On a formal level, a proof consists of three parts:

(1) a set of assumptions (premises)
(2) a chain of reasoning
(3) a set of conclusions

You are defining an 'axiom' as an assumptions who's negation is not demonstrable, except possibly by R.A.A.

But there's no reason to go this far ... Rather, in a debate between two people A and B, the pool of assumptions are usually just the shared assumptions between them.

Really, for persuasive (or dialectic) argument though, all that matters is that person A builds on the assumptions held by person B.

The most common mistake in debate (the opposite of a dialectic argument) is that one person argues from their own assumptions ... the result is not a persuasive argument for the other party.

This isn't how R.A.A works though. It's not a concession: assume p, derive an absurd conclusion, then reject p.

It's not valid to restrict the use of the premise, as someone else may always use it in a dialectic argument.

One could also take an alternative set of assumptions that would lead to a different set of conclusions. For example:

(1) At most, one object exists.
...

AFAICT you are using a definition of 'axiom' that isn't standard.

The sources you are drawing from are mostly using Ann Rand's definitions ... compare to wikipedia, or other non-objectivist sources and you'll find a different definition. I'm just letting you know she's redefined some of these terms.

I've never seen anyone else distinguish between a philosophical axiom and mathematical axiom, except in the degree of formality.

Note yourself: I am not trying to prove that any other existent exists. Merely that existence itself exists. Nice try, though.

They are more special because one has to concede them in order to mount a refutation of them.

I don't care. I am not using it. Therefore your argument is irrelevant. Have a nice day.

If anything, they have been clarified. Nice strawman, though.

You should get out more.

"Concede them" ? You mean "assume." This is actually valid. Pick up a book on formal logic and read it.

I've been around enough to know you are just regurgitating Ann Rand's ideas and passing them off as your own.

Quibble. Call it what you will. If you feel better calling it an assumption then do so.

But if you use the conclusion as an assumption, are you not conceding it?

You obviously have not been around long enough even to know how to spell her name right. Ayn Rand. This calls into question whether you have enough knowledge to determine if I am merely regurgitating or not. Good day, sir!