I would agree with #1 in that science uses inductive logic. The thing is, 'Something exists' doesn't need science because it can be deductively shown something exists.

For something to be a scientific theory it must be falsifiable....



That something exists is a fact (as far as I'm concerned, i don't want to get into a philosophical debate about this). The scientific theory would be an explanation of WHY something exists. It is the explanation not the fact that has to be falsifiable.



True... but facts themselves don't have to be falsifiable.



No, because it is a fact. Falsifiable means a fact could be produced that debunks the theory. Like fossil rabbits in the pre-Cambrian would falsify Evolution!



Yep its bs

 

And thereby we verify the necessary truth of the claim. 

 

It is reasonable to conclude it because it is axiomatic, and necessarily true.... to even ponder the point requires that you exist.  By pondering it, you affirm it's necessary truth.

And any attempt to 'refute it' relies on the axiom as step one in the refutation, leading to a self refutation. Ergo we can conclude that this axiom is necessarily true and defended through retortion...

 Descartes' mistake is using the referrent "I", but wouldn't 'Thought occurs, therefor something is' show that pondering if something exists requires that something exists? If nothing existed then thought could not occur, therefor as soon as a thought occurs it becomes axiomatic that something exists. 

 I disagree. You need not demonstrate that thought occurs. In order to demonstrate that thought occurs, thought would have to occur. It is self refuting to think that thought does not occur, as to do so, thought is required. The occurence of thought renders something's existence axiomatic. We can take nothing any further nor can we even begin to question the possibility that thought occurs and thus we must necessarilly conclude that something exists. Anything else leads us to an absurdity.

 

Except that the given statement does not contradict itself.

You are implicitly claiming that our self-observed thought in proposing the question in the first place gives evidence in favour of that thought's existence (and perhaps in the existence of the self which observed it). There are two mistakes in that assumption.

Firstly, there is an improper context implied here. In order to supply evidence in favour of a claim, you are admitting that the claim has not yet been proven logically necessary. You will likely say that you are simply providing a counterexample to a universal statement, but your counterexample is based on observations of reality rather than on pure deductive reasoning and hence belongs in the realm of science, not of logic.

Secondly, placing the thought into evidence already presumes an entity to have observed the thought (in this case one's self) and that there is a thing which has been observed. We truly can make no evidentiary deductions (that I'm aware of) without presuming existence.

 

That said, I should probably explain my methodology as I seem to have been misunderstood.

The claim has been made that "something exists" is logically provable (equivalently that it is necessarily true or that it can be arrived at deductively before evidence is considered). In the realm of logic, we propose a universe of discourse and examine it from the outside. Consistency of statements about our universe of discourse is determined by what statements are and are not provable within our deductive system. Similarly, statements concerning the universe of discourse are not considered a part of that universe of discourse, they are a part of the language (or meta-language) which we are using to conduct our discussion.

As such, given standard classical logic (or, honestly, intuitionistic logic or any of a variety of modal logics), standard quantifier logic (or even infinitely bounded quantifiers if you want) and a single axiom "there is no element in the universe of discourse" (more formally "for all x, x is not equal to x&quot, please demonstrate a contradiction.

I claim that there is no contradiction that can be derived from this situation and while I have not yet provided a deductive proof of that claim, the onus of discourse is on you to provide the contradiction demonstrating that our supposition is in fact decided within the realm of logic and not of science.

Once again, when speaking from the perspective of logic alone, we cannot use reality as a reference point. 

 

This is exactly why I used careful language in my previous post. I did not say that the statement we are dealing with is "nothing exists", rather it is "there isn't anything which exists". It is not the claim that the object "nothing" has the positive property "existence", rather it is the claim that given any thing "x", "x" does not possess the positive property "existence".

I may have actually misspoken previously, if I have please forgive me - I try to speak carefully but I still slip on occasion. Attention Deficit Disorder does have its downside.

 

An empty universe needs no ontology, true, but this does not demonstrate its absurdity, merely that our concept of "existence" is imprecise and this sits close to one of the grey areas. This is one of the reasons formal logic comes in handy - it allows us to examine possibilities using only an ontology external to the universe in question. This is also exactly the reason I am making statements externally to the empty universe under consideration.

In fact, in order for a structure to internally mimic itself (my impromptu model-theoretic interpretation of a universe having an internal ontology) it must already be highly complex and hence not be empty.

 

One comment on your previous post: You seem to be using "axiomatic" to mean "just plain true" or "self-evidently true". While this certainly was the way its ancient counterpart (postulates) was used in the time of Euclid, it does not reflect the modern term or its usage, at least in mathematics. In math, an axiom is effectively something assumed in order to develop a body of deductions which depend on it.

To give an example of what I'm talking about, you may be familiar with Euclid's "parallel postulate", his axiom that "given a line and a point not on that line there is exactly one line passing through that point which does not intersect with the first line." Euclid tried to prove this statement but could not, instead including it as an axiom since he found it too useful to do without. It wasn't until the late 1800s that the parallel postulate was proven independant of his other axioms.

This postulate being independant of his other axioms does not mean that it was proven wrong or that it was proven right or anything of the sort - it means that any inconsistencies that may exist with the parallel postulate included would also be present if its negation were included instead and vice versa. In other words, truth has nothing to do with whether or not the axiom is being used, merely interest and applicability.

 

In any case, it seems that you agree that "something exists" is not a scientific claim (as the original poster suggested), our current debate deals solely with whether or not it is a purely logical one. 

No, it is not. There's no mistake there. His goal was to demonstrate that existence was axiomatic. It was INESCAPABLE that he existed, in some form. 

Yes. But you're still importing "I" concepts here... "thought occurs'... well, what thought, and how do you know it occurs?

Answer: Because I thought it.

So we are right back where we started.

But where we started was fine to being with!.

ANY statement proves Descartes point. 

Saying "I just took a shit yesterday"  proves the axiom of existence. Saying  "faslfjasgoufoiasjfoiewafjaworfaofjasoifjd" proves it. Any sentient thought implies existence.

BINGO!  

Which is why I'm speaking externally about a proposed universe of discourse which is empty. Clearly I do not need to exist within a concieved universe in order to make claims about it. Requiring that I am in this universe would indeed demonstrate that said universe is non-empty, but showing that I am in a universe is a matter of evidence, not of logic. 

 

 I'd like to bring this statement into light for a little while.

First, your two sentences subtly contradict each other.

Your statement that the "axiom of existence" is a priori amounts to stating that it is necessarily true, that it is true in all possible worlds. In this case, we need not assume it.

On the other hand, you say that it is assumed in any and all statements, which is exactly what I've been saying through this entire argument.

When I said that Descartes' argument presumes its conclusion, this is saying that he is assuming the "axiom of existence" by making his statement.

 

I would also like to point you towards something I said in my previous post about the nature of axioms. Whether or not something is an axiom within a given context is irrelevant to whether or not it is true, we are assuming it is true because it is useful or interesting to do so. Saying that something is axiomatic simply means that we assume it, not that it is actually true.

Axioms need not be atomic in any sense. Firstly, I doubt that anybody would take the axiom of choice to be atomic and it certainly isn't in any mathematical sense. It is fairly obvious that if a system has finitely many axioms we may as well simply conjoin them into a single axiom in a formal sense for simplicity in certain calculations, after all "(A and B) implies A" is logically valid, so "A and B" can be a single axiom replacing axioms "A" and "B".

Your idea that the "axiom of existence" occupies a place somehow before the rest of math is quite easily refuted by noting its inclusion in the axioms of set theory (actually, it is quite often left out of the axioms of set theory but it can be deduced easily from the axiom of infinity which assumes the existence of an infinite set).

 

Once again, when dealing with a priori claims, with necessary truth, in short with logic, our universe is irrelevant. Thoughts we have do not need to be part of the universe under consideration. We examine claims through deductive reasoning alone where the deductive reasoning is external to the universe of discourse.

The second you demand that we are talking about our universe we are no longer in the domain of logic, we are likely within the domain of science. 

 

Yes existence is axiomatic. Existence being axiomatic is something I've been agreeing with from the start. It is not axiomatic to any pure logic or to quantifier logic, but it is axiomatic to set theory and thus to almost everything else in mathematics and human reasoning. There is nothing interesting we can get if we don't include the axiom of existence and this is exactly why we include it as an axiom - because it cannot be proven but we want to use it as true.

 

Descartes' argument is far from a logical one since it takes into account only the universe in which we exist. As such, we can argue for a long time about whether or not it is a scientific argument, but it is most definitely not a logical one.

 

By the way, in order to demonstrate the logical inconsistency of the negation of the axiom of existence, you need to show that both "A" and "not A" are deductive consequences of it for some well-formed sentence "A". If you have such a proof, I would request a polite mention in your forthcoming paper or journal article revising the axioms of finite set theory, and if you wish I can help you put it together.

This has nothing at all to do with the axiom of existence. The axiom of existence follows from a basic metaphysics: the existence of sentient brains. It automatically rules out an empty set by definition. Therefore, bringing up empty sets has no bearing, at all, on the matter.

Again, this is what started our discourse:

You: On the other hand, it is reasonable to assume that something exists since there is no harm in being wrong and plenty of good can come from the assumption.

Me: It is reasonable to conclude it because it is axiomatic, and necessarily true.... to even ponder the point requires that you exist. By pondering it, you affirm it's necessary truth.

And any attempt to 'refute it' relies on the axiom as step one in the refutation, leading to a self refutation. Ergo we can conclude that this axiom is necessarily true and defended through retortion...

 

And that is the very point of the axiom of existence.  That the existence of a basic metaphysic: the existence of sentient brains, leads to the axiomatic nature of existence.

That's all that is being said. 

 

By 'assume' I merely mean it is implicit in all statements. I used implicit in the last sentence, and used a synonym in the cause of good writing. There is no contradiction here.

Not exactly. That's what I have been saying through this entire argument. You, on the other hand, have been bringing up empty universes when they have NOTHING to do with the axiom of existence. You also have deny that existence is axiomatic in all declarations below! 

Once you recognize that empty sets have no bearing on the mattter, our discourse will come to an end.

Once again, he does not presume his own conclusion! In fact, he attempts to refute his own hypothesis, that's the entire point of his mediations! What he uncovers is that the axiomatic nature of existence is defended through retortion - attempts to deny everything lead to having to accept something exists.

We are talking about the axiom of existence. The axiom of existence isn't accepted because it's interesting, it's accepted because it's inescapable.

No, it does not mean that we simply assume it. If assuming were the sole element of an axiom, then anything we found 'intersting' that we choose to assume, would be an axiom.

It would then be axiomatic that my penis is 12 inches long.

 

You're no longer talking about the axioms of metaphysics. We are talking about the axiom of existence here, don't import other usages of the term 'axiom' into our conversation. I again refer you to our initial conversation above.

Nonsense. Any attempt to refute it requires that you first acknowledge THAT IT EXISTS. By beginning your refutation, you refute yourself necessarily.

Every existent that we can concieve necessarily carries with it  the axiom of existence. To exist is to exist as something, to have identity. TO denote anything, to concieve of anything, is to affirm the axiom of existence.

Again: Existence would not be axiomatic in a universe of zero dimensions, sans any intelligence. But this has nothing to do with the axiom of existence. If nothing existed, then yes, existence wouldn't be axiomatic!

What is actually being said, utterly in vain apparently, is that given a basic metaphysics, which requires sentience, the axiom of existence is necessarily true.

That's what all my posts are about.

No kidding! Its not necessary because it's already implied in any identification! It's not an axiom of logics, its a part of basic metaphysics itself!  The existence of any human thought (including logic) automatically implies the axiom of existence, even as the axiom is not included in the set of axioms for the logic.

Why is this so? Because it's utterly unnecessary! Any statement already IMPLIES the axiom of existence!

To say something like:

'This is a red ball, and it exists' would actually commit the error of using existence as a predicate. The word "exists" adds nothing concerning the identity of the ball, as existence is already implied in the terms "red ball"

To exist is to exist as something. Ergo anything at all (anything with identity, which means anything at all) already implies the axioms of existence and identity.

It's axiomatic to anything at all that exists that a human can concieve of, because it's an axiom of basic metaphysics which in turn all systems of thought rely upon. For this reason, it unnecessary to repeat basic metaphysical axioms in a logic, because the logic already implies it.

It would be like saying:

"the number '1' is defined as X, and by the way, the numer 1 exists, and has identity"

The definition already implies existence and identity.

It is logical. The entire point of his argument is that given a basic metaphysics of sentience, existenced is axiomatic.

All I need to do is demonstrate that you are stealing the concept by relying on the axiom in order to refute it.

To deny the axiom of existence requires that you first acknowledge that it exists. You therefore must rely upon the axiom itself in order to refute it. You steal the concept and thereby affirm its necessary truth.

This is why we say it is defended through retortion and is necessarily true.

Now, can you show me how to refute the axiom without referring to, or relying upon, any existent?

If not-you not-can, not-I will not-help you not-publish the non-paper. Just give me a non-mention.

 Todangst replied to this better than I could have.

 

 

I have been thinking on this subject quite a bit lately. There is something about nothing. Somewhere in the possibility of nothingness (as in a non-dimensional void) as a state there lies a contradiction. Give me a couple of years and I'll get back to you.