'Something exists' is unscientific

axiom
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'Something exists' is unscientific

1. For something to be scientific it must be in principle falsifiable.
2. The claim that something exists, can only be falsified if there was nothing
3. If there were nothing ‘falsification’ could not occur.
c: Therefore: The claim that something exists is unscientific.

 

Something i thought of, i figure its bs but i'd like to hear some responses.

 


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I would agree with #1 in

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.


Yiab
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MrRage wrote: I would agree

MrRage wrote:
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.

 

How? How can we deduce that something exists without first assuming that something exists?

 

Personally, I agree that "something exists" is non-scientific in so much as it can be interpreted as a meaningful statement at all.

 

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. 


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axiom wrote: 1. For

axiom wrote:

1. For something to be scientific it must be in principle falsifiable.



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

axiom wrote:

2. The claim that something exists, can only be falsified if there was nothing


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.

axiom wrote:

3. If there were nothing ‘falsification’ could not occur.


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

axiom wrote:

c: Therefore: The claim that something exists is unscientific.


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!

axiom wrote:

Something i thought of, i figure its bs but i'd like to hear some responses.


Yep its bs Tongue out

 

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axiom wrote:1. For

axiom wrote:

1. For something to be scientific it must be in principle falsifiable.
2. The claim that something exists, can only be falsified if there was nothing
3. If there were nothing ‘falsification’ could not occur.
c: Therefore: The claim that something exists is unscientific.

 

Something i thought of, i figure its bs but i'd like to hear some responses.

Apparently you're implying that it is undesirable that the axiom of existence is 'unscientific'.

But there's a flaw here: science is inductive. Axioms are deductive and necessarily true. Ergo the fact that the axiom of existence is not ammenable to scientific examination is moot: we already have certain knowlede it is true! In this case, science would be a 'spare tire' for a car with indestructable wheels....

 

 

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Yiab wrote: MrRage

Yiab wrote:

MrRage wrote:
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.

 

How? How can we deduce that something exists without first assuming that something exists?

And thereby we verify the necessary truth of the claim. 

 

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 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.

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...

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todangst wrote:

todangst wrote:
Yiab wrote:
How? How can we deduce that something exists without first assuming that something exists?

And thereby we verify the necessary truth of the claim.

No, thereby we demonstrate that we cannot prove it. If everything that could only be proven through circular reasoning was necessarily true, the entirety of reality would be inconsistent.

What you've said here amounts to saying "A implies A" is true, therefore "A" is necessarily true.

todangst wrote:
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.

Ah, Descartes, my old friend. "I think therefore I am"... except the statement "I think" requires that "I" already has a referrent, hence assuming its conclusion.

todangst wrote:
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...

Allow me to attempt to refute the axiom "something exists" by reductio ad absurdum.

Suppose there isn't anything that exists.

Wait... that's all I can say. I don't see any contradictions here. Do you?

It appears to contradict observations of the real world, but in order to have observations at all we must assume that there is an observer, that there is that which is observed and that there is an interaction between them producing the observation, so observations of the real world cannot be used to contradict this.

Speaking from a purely logical standpoint, there is nothing inherently inconsistent about the idea of nothing existing, it only becomes inconsistent when paired with another axiom.

You can't justify anti-nihilism using logic alone and inductive reasoning relies on there already being data, so the statement cannot be proven, demonstrated, verified or falsified, leaving it outside the realms of science and logic.

On the other hand, if we seriously entertain the possibility that the statement "something exists" isn't true, we get bored very, very quickly. Really, there's very little that anyone can do without assuming at least their own existence. Therefore we assume the existence of ourselves as a matter of preference - it's psychologically satisfying.

 

Notice, please, that I am not claiming that there actually isn't anything that exists, I am merely presenting that there is no case against that claim from logic or evidence.


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Yiab wrote: todangst

Yiab wrote:
todangst wrote:
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.

Ah, Descartes, my old friend. "I think therefore I am"... except the statement "I think" requires that "I" already has a referrent, hence assuming its conclusion.

 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. 


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Vessel wrote: Descartes'

Vessel wrote:
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.

 

The same mistake is made here and in any wording I have concieved of: You first need to demonstrate that thought occurs and any occurrence is sufficient demonstration of "something existing" that this proposition is unnecessary. Essentially, this is more circular reasoning. 


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Yiab wrote: Vessel

Yiab wrote:

Vessel wrote:
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.

 

The same mistake is made here and in any wording I have concieved of: You first need to demonstrate that thought occurs and any occurrence is sufficient demonstration of "something existing" that this proposition is unnecessary. Essentially, this is more circular reasoning.

 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.

 

“Philosophers have argued for centuries about how many angels can dance on the head of a pin, but materialists have always known it depends on whether they are jitterbugging or dancing cheek to cheek" -- Tom Robbins


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Yiab wrote: Allow me to

Yiab wrote:

Allow me to attempt to refute the axiom "something exists" by reductio ad absurdum.

Suppose there isn't anything that exists.

Wait... that's all I can say. I don't see any contradictions here. Do you?

Yes. The contradiction is in supposing that there isn't anything that exists. Supposing (thought) would have to occur to suppose that there isn't anything that exists and this requires that something exists.

Yiab wrote:
Speaking from a purely logical standpoint, there is nothing inherently inconsistent about the idea of nothing existing, it only becomes inconsistent when paired with another axiom.

There certainly is something inherently inconsistent about nothing existing as nothing and existence are mutually exclusive. It becomes even more inconsistent when you mention that it is an "idea of nothing existing" as the idea would require existence. Being as that nothing can, by definition, have no ontology, to consider its existence is an absurdity.    



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Yiab
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Vessel wrote: Yes. The

Vessel wrote:
Yes. The contradiction is in supposing that there isn't anything that exists. Supposing (thought) would have to occur to suppose that there isn't anything that exists and this requires that something exists.

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&quotEye-wink, 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. 

 

Vessel wrote:
There certainly is something inherently inconsistent about nothing existing as nothing and existence are mutually exclusive.

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.

 

Vessel wrote:
Being as that nothing can, by definition, have no ontology, to consider its existence is an absurdity.

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. 


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Yiab wrote:todangst

Yiab wrote:
todangst wrote:
Yiab wrote:
How? How can we deduce that something exists without first assuming that something exists?

And thereby we verify the necessary truth of the claim.

No, thereby we demonstrate that we cannot prove it.

We can't 'prove' it because proofs require logic, and  the axiom of existence is more basic than logic itself.

We need logic to create a proof. Some logical systems rest upon axioms. Axioms are atomic statements, incapable of being broken down into smaller components, and necessarily assumed in all statements, such as the axiom of existence.

To prove an axiom is therefore impossible, because we'd need something even more basic than an axiom, and, as we just said, axioms are the most basic statements possible.

However, proving axioms is unnecessary, because axioms are already defended by retortion! To deny an axiom leads to self refutation.

So the complaint that we 'can't prove axioms' is like saying "Wade Boggs couldn't hit 250." He couldn't because he's too busy hitting 350.

Quote:

If everything that could only be proven through circular reasoning was necessarily true, the entirety of reality would be inconsistent.

Not sure why you're bring up circular logic, but what you say here is untrue. Circular arguments are necessarily valid, so there is no inconsistency. The actual problem with circularity isn't that it they aren't consistent, it's that nothing is demonstrated by a circular argument, and the entire point of an argument is to demonstrate something!

CIRCULAR LOGIC Any argument wherein the conclusion to an argument is held to support the premise just as the premises are held to support the conclusion. In short: using a conclusion as a premise.

Some people like to note that circular arguments are trivially valid. They are right: - circular arguments are valid - after all, since nothing new is generated in the concluson of a deductive arument, all deductive arguments are 'circular' - in that the conclusion is made up entirely from the premises. However, while it is true that nothing "new" is generated in the conclusion of a deductive argument, this would not make deductive arguments 'circular' in the sense of a circular logic fallacy. Here is why:

Deductive arguments work just like mathematical equations: a set of equivalencies - we can even reformulate such arguments as tautologies. Therefore, the point of such arguments is to demonstrate some equivalency (or lack thereof) between two categories. So, yes, plugging the same statement into both a premise and the conclusion gives us an equality, but the fact that that the same exact statement gives us an 'equivalency' is not exactly noteworthy! This is why we call this an informal fallacy - nothing is being proven here, we aren't demonstrating an equivalancy, the equivalency is already a given prior to the argument!

 

Quote:

What you've said here amounts to saying "A implies A" is true, therefore "A" is necessarily true.

No, I don't think you're able to follow what I've actually said yet... You're still confused and still holding that we need to 'deduce' the axiom of existence when this is 1) impossible and 2) utterly unnecessary and backwards! 

We don't need to deduce the axiom of existence, to do so, again, would require a logical system more basic than the axiom of existence (!) which, presumably, would rest upon more basic axioms!  Talk about an infinite regress problem! We have to work outside of existence itself... I can forsee a few problems already!

Fortunately, we don't have to deduce the axiom of existence because, fortunately, this would be utterly unnecessary. The axiom is the most properly basic axiom of all, it is presupposed in all statements, necessarsily so, and it is defended through retortion: any attempt to refute it requires that you acknowledge, in some way, directly or implicitly, that the axiom of existence.... EXISTS.

Basically, you're trying to work out a deductive proof of the axiom of existence when in fact you prove it's necessary truth just by taking a shit. 

 

todangst wrote:
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.

Quote:

Ah, Descartes, my old friend. "I think therefore I am"... except the statement "I think" requires that "I" already has a referrent, hence assuming its conclusion.

You're confused. He's not 'assuming his own conclusion" here. The fact that "I" already has a referrent is the very point he's making: he's pointing to the axiomatic nature of existence (and the axiomatic nature of consciousness. His entire point is to demonstrate that it is INescapable that something exists. What he's doing is recognizing that existence is axiomatic. The point Descartes is making here is that no matter how much he tries to deny all of existence, his very denial forces him to concede that something does exist.

 

todangst wrote:
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...

Quote:

Allow me to attempt to refute the axiom "something exists" by reductio ad absurdum.

 Suppose there isn't anything that exists.

 Holding that 'nothing exists at all' has NOTHING to do with the axiom of existence.  

Quote:

Wait... that's all I can say. I don't see any contradictions here. Do you?

  If you want to say "nothing exists" then there is no contradiction. Nothing exists. Fine.

But this has nothing at all to do with the axiom of existence. The axiom of existence is a concept held by sentient minds: humans. The axiom itself is predicated on the existence of sentient brains. Given that a sentient brain exists, and is able to glean the axiom, it is necessarily true. THAT'S what the axiom actually means.

So I think you're confused here, and are misreading the 'axiom of existence' to mean that "there must be something no matter what"... that's not what the axiom says. The axioms says "given a sentient brain, we know that something exists.

So Descartes actually got it backwards:

I am, therefore, I think.

Quote:

It appears to contradict observations of the real world, but in order to have observations at all we must assume that there is an observer,

YES. Axioms cannot exist without a sentient brain to generate them, a priori.

Quote:

Speaking from a purely logical standpoint, there is nothing inherently inconsistent about the idea of nothing existing,

 Again, you're confused as to what the axiom of existence actually is....

 

Quote:

You can't justify anti-nihilism using logic

Yes you can, given the existence of a sentient brain. The existence of a sentient brain, able to produce the axiom, a priori, refutes radical nihilism.

Quote:

alone and inductive reasoning relies on there already being data, so the statement cannot be proven, demonstrated, verified or falsified, leaving it outside the realms of science and logic.

Actually, axioms are part of classical logic. Defense through retortion is a cornerstone of logic.  The defense of the axiom is logical. 

 

Quote:

On the other hand, if we seriously entertain the possibility that the statement "something exists" isn't true, we get bored very, very quickly.

We don't need to fall to such an argument. It's axiomatically true that 'something exists' is necessarily true.

Let me make it more clear:

Denying the axiom of existence requires THAT SOMEONE EXIST TO DENY IT.

This means that the axiom is defended through retortion. One must STEAL the very concept one is attempting to refute.

This is what is meant by the axiomatic nature of existence. It does NOT mean that 'something must exist' it means that given a sentient brain who is able to generate the axoim, said brain CANNOT logically deny the axiom.

 

 

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Vessel wrote: Yiab

Vessel wrote:

Yiab wrote:
todangst wrote:
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.

Ah, Descartes, my old friend. "I think therefore I am"... except the statement "I think" requires that "I" already has a referrent, hence assuming its conclusion.

Descartes' mistake is using the referrent "I",

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. 

Quote:
 

 but wouldn't 'Thought occurs, therefore something is' show that pondering if something exists requires that something exists?

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.

Quote:
 

 If nothing existed then thought could not occur, therefor as soon as a thought occurs it becomes axiomatic that something exists.

BINGO!  

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Yiab wrote: Vessel

Yiab wrote:

Vessel wrote:
Yes. The contradiction is in supposing that there isn't anything that exists. Supposing (thought) would have to occur to suppose that there isn't anything that exists and this requires that something exists.

Except that the given statement does not contradict itself.

Except that it does. To deny the axiom of existence requires that you exist to deny it.

Quote:
 

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

It does so, necessarily, at least implicility, if not explicitly. You're not thinking any of this through:  In order for there to be a thought in the first place it must EXIST.

How can there be a thought, without any existence?

 

Quote:
 

(and perhaps in the existence of the self which observed it). There are two mistakes in that assumption.

No, there are no mistakes.

Quote:
 

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.

 

The axiom of existence is implicit, and a priori. It is assumed in any and all statements. 

 

Quote:
 

Secondly, placing the thought into evidence already presumes an entity to have observed the thought

You're funny. A thought has to exist.  By doing anything at all, the axiomatic nature of existence is necessarily affirmed.

That's the entire point of the axiomatic nature of existence: that it is necessarily presumed and implied in any sentient thought.

Quote:
 

(in this case one's self) and that there is a thing which has been observed.

No specific entity is identified by the axiom of existence... merely that there is existence. This is undeniable.. literally.  

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todangst wrote: Except that

todangst wrote:
Except that it does. To deny the axiom of existence requires that you exist to deny it.

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. 

 

todangst wrote:
The axiom of existence is implicit, and a priori. It is assumed in any and all statements.

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

First, your two sentences subtly contradict each other.

wikipedia's article on a priori wrote:
A proposition that is necessarily true is one whose negation is self-contradictory (thus, it is said to be true in every possible world).

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.


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todangst wrote: axiom

todangst wrote:
axiom wrote:

1. For something to be scientific it must be in principle falsifiable.
2. The claim that something exists, can only be falsified if there was nothing
3. If there were nothing ‘falsification’ could not occur.
c: Therefore: The claim that something exists is unscientific.

Apparently you're implying that it is undesirable that the axiom of existence is 'unscientific'.

But there's a flaw here: science is inductive. Axioms are deductive and necessarily true. Ergo the fact that the axiom of existence is not ammenable to scientific examination is moot: we already have certain knowlede it is true! In this case, science would be a 'spare tire' for a car with indestructable wheels....

Exactly. Logic is one of the things on which science is built. One does not examine logic scientifically. One examines evidence logically, and we call that science.


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Yiab wrote:todangst

Yiab wrote:

todangst wrote:
Except that it does. To deny the axiom of existence requires that you exist to deny it.

Which is why I'm speaking externally about a proposed universe of discourse which is empty.

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...

 

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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,

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. 

todangst wrote:
The axiom of existence is implicit, and a priori. It is assumed in any and all statements.

 

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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.

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.

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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.

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.

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

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.

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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

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.

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. Saying that something is axiomatic simply means that we assume it, not that it is actually true.

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.

 

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Axioms need not be atomic in any sense.

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.

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Your idea that the "axiom of existence" occupies a place somehow before the rest of math is quite easily refuted

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.

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Once again, when dealing with a priori claims, with necessary truth, in short with logic, our universe is irrelevant.

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.

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Yes existence is axiomatic. Existence being axiomatic is something I've been agreeing with from the start.

That's what all my posts are about.

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It is not axiomatic to any pure logic or to quantifier logic,

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.

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but it is axiomatic to set theory and thus to almost everything else in mathematics and human reasoning.

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.

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Descartes' argument is far from a logical one since it takes into account only the universe in which we exist.

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

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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".

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.

Those who know the good, do the good. - Socrates

Books on atheism.


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todangst wrote: Vessel

todangst wrote:
Vessel wrote:

Yiab wrote:
todangst wrote:
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.

Ah, Descartes, my old friend. "I think therefore I am"... except the statement "I think" requires that "I" already has a referrent, hence assuming its conclusion.

Descartes' mistake is using the referrent "I",

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.

 

My problem with the use of the word "I" is that I take it to imply a concept of self that I don't think is necessarily supported by the axiom. "I" is too specific a referrent. Even before that it also assumes that the thought that occurs requires a thinker. It does not allow for the thought to simply be the existence itself, which seems as if it is not ruled out as a possibility by the axiom. Yes? No? Maybe?


“Philosophers have argued for centuries about how many angels can dance on the head of a pin, but materialists have always known it depends on whether they are jitterbugging or dancing cheek to cheek" -- Tom Robbins


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Yiab wrote: Vessel

Yiab wrote:

Vessel wrote:
Yes. The contradiction is in supposing that there isn't anything that exists. Supposing (thought) would have to occur to suppose that there isn't anything that exists and this requires that something exists.

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&quotEye-wink, 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.

 Todangst replied to this better than I could have.

 

Yiab wrote:
Vessel wrote:
There certainly is something inherently inconsistent about nothing existing as nothing and existence are mutually exclusive.

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.

 

Vessel wrote:
Being as that nothing can, by definition, have no ontology, to consider its existence is an absurdity.

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.

 

 

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.  

“Philosophers have argued for centuries about how many angels can dance on the head of a pin, but materialists have always known it depends on whether they are jitterbugging or dancing cheek to cheek" -- Tom Robbins