are these statements logically equivalent?

[bpesta22]

Can't figure this out:

1) I don't believe gods exist.
2) I believe that no gods exist.

Trying to figure out if these two are equivalent, or differ logically. For example, would it be wrong to characterize (1) as a form of agnosticism (or weak atheism) and (2) as a form of atheism / strong atheism.

Or, do the two statements say exactly the same thing, logically.

I'm struggling with the difference between belief (which classifies one as atheist or theist) and knowledge (which classifies one as gnostic or agnostic). I have problems with using K to label people, as I think K (justified true belief) is impossible, and I think it's redundant / not independent of B -- we couldn't possibly know something we don't believe in.

So, the standard 2 x 2 table that labels people:

believe that god exists but dont know it (agnostic theist)
believe that god exists and know it (gnostic theist)
Believe that no gods exist but dont know it (agnostic atheist)
believe that no gods exist and know it (gnostic atheist)

seems to be either a straw-man, or a mislabeling, or a confounding of 3 variables (belief, knowledge, belief in god versus believing gods don't exist) when only 2 are needed to label.

it seems like you don't need the K distinction, and that the proper labels should be:

..............Gods exist............No gods exist
yes........theist...................strong atheist
no.........weak atheist.........deist / watchmaker type

can't call it yes or no; agnostic.


The standard table:

http://wiki.ironchariots.org/index.php?title=Atheist_vs._Agnostic

(see bottom)

Just seems wrong to me.

It seems underspecified in that it should allow / draw out cells where belief, knowledge, and "god exists" / no gods exist are all crossed. When you do that, you get to some absurd cells, which suggests to me that the standard table is not specified correctly.

Of course, I could be wrong.

help?

 

[andyandy]

1) I don't believe gods exist.
2) I believe that no gods exist.

1) can either be a negative rejection or a positive assertion dependent on context.

2) is a positive assertion

Therefore the two sentences can be viewed as functionally identical in some contexts, but functionally distinct in others.

 

[Mangafranga]

I don't really follow the rest of your post, but to just address this part (and to flesh out andyandys response)-

1) I don't believe gods exist.

To me 1 reads as "I don't have the belief that "p"" (this is the negative rejection interpretation). This leaves open whether or not that person has the belief that "~p". The person could just lack a belief either way. For example if you were to ask me if I had the belief that you have a car, I would probably say I neither believe that you have a car, nor do I believe that you don't have a car. And it is also possible that they do have the belief that "~p".

On the other hand it is possible to interpret 1 as "I believe that "~p""(the positive interpretation), although that intrepretation isn't natural to me. In this case it would be logically equivalent to 2.

 

[quixotecoyote]

I struggled with that for a while too. What I ended up with is that they are equivalent. They mean the same thing in any context you will actually see used, that you don't think a god exists. The reason the odd formulation has so much popularity is that it's really easy to get some wiggle room if you aren't making a positive claim. For that reason many atheists will phrase it as 1 in order to maintain the semantic high ground.

Unless you've never given the matter any thought at all, you're likely to have a belief on whether or not god exists, even if you aren't sure. The only way 1 is different than 2 is if it's meant to express a lack of any belief, not merely a negative one. Unless you truly think that god's a 50/50 toss up, no data to suggest a likelihood, or the thought's never crossed your mind, I think it's a weaselly way to phrase it.

 

[arthwollipot]

Think about it this way:

1. I don't believe that there is a teapot orbiting Pluto.
2. I believe that there are no teapots orbiting Pluto.

When you divorce the question from its emotional content, everything seems much clearer. The first allows for the possibility that there is a teapot orbiting Pluto, the second one does not.

Hence, they are not logically equivalent statements. What's more, one is a negative statement and one is a positive statement.

 

[baron]

The statements are identical in meaning. The end result of a belief in nothing is the same as no belief in something, i.e. a lack of recognition of the subject in question.

 

[arthwollipot]

I disagree. The lack of belief in the presence of a teapot is not the same thing as a belief in the nonpresence of a teapot. Sure - both imply that there is no teapot, but the method of coming to that conclusion is completely different.

But I'm not going to get all excited about it.

 

[quixotecoyote]

I disagree. The lack of belief in the presence of a teapot is not the same thing as a belief in the nonpresence of a teapot. Sure - both imply that there is no teapot, but the method of coming to that conclusion is completely different.

But I'm not going to get all excited about it.

Going with the teapot, would you really believe someone who said that he refused to think that there were no teapots around Pluto, but would not think that there were teapots. I'd think he was playing semantic games.

 

[blobru]

On knowledge vs. belief, I think:
belief is knowledge that such & such is more probable than not;
knowledge is belief in such & such for which one can conceive no meaningful alternative.
e.g., I know tomorrow will be Tuesday vs. I believe it will rain tomorrow.

So, "I believe God [doesn't] exist" vs. "I know God [doesn't] exist", seems the proper way to frame the combinations of [a]theists and [a]gnostics.

As for the two sentences:
1) I don't believe gods exist.
2) I believe that no gods exist.
... the only difference I can see is superficial -- 1) has asserted "gods exist" which I deny; 2) has asserted "no gods exist" which I accept. As a whole, the two statements appear logically equivalent (my belief in no gods, or non-belief in gods, makes either true). In parts, 2) is either doubly true (both assertion and belief) or doubly false; 1) is conflicted: either true and false, or false and true; however, the fact of gods existing or not still makes the beliefs identically true or false (which is the gist of either statement), so again they're logically equivalent.
There may be some peculiar sense of "belief" I'm overlooking... for now I'll say, logically at least, 1) = 2).

 

[volatile]

Going with the teapot, would you really believe someone who said that he refused to think that there were no teapots around Pluto, but would not think that there were teapots. I'd think he was playing semantic games.

I think these kind of "semantic games" are actually quite important if precision is to be achieved in thought and in communication. You can see what a tangle BillieJoe got himself in over in the "Proof of God" thread for evidence of that.

It comes down to falsifiability again, which is important if we are to be able to justify atheism as a rigorously achieved opinion and not just something taken on faith. It's too easy to allow theists to view atheism as "just another religion" if we're not very clear about the logical thought process that led us there.

Arthwollipot is absolutely correct - "The lack of belief in the presence of a teapot is not the same thing as a belief in the nonpresence of a teapot. Sure - both imply that there is no teapot, but the method of coming to that conclusion is completely different."

 

[JoeEllison]

I disagree. The lack of belief in the presence of a teapot is not the same thing as a belief in the nonpresence of a teapot. Sure - both imply that there is no teapot, but the method of coming to that conclusion is completely different.

But I'm not going to get all excited about it.

I'd expand on this, by saying that #2 is a position of faith, while #1 is really a lack of faith. You can infer this from the fact that people use the word "belief" in very specific ways, especially when it comes to these subjects.

 

[Jekyll]

Can't figure this out:

1) I don't believe gods exist.
2) I believe that no gods exist.
Or, do the two statements say exactly the same thing, logically.

Well if you wanted to express this in a logical predicate, the differences are between: ~B(G) and B(~G), where ~ means not, and B(...S...) expresses your belief in a statement S. Symbolically they're different, although you could still argue that they are equivalent in meaning.

However, I think there is a meaningful difference between the two as well. If you view the strength of a belief as some kind of probability, then `I have no belief(in X)' asserts a lack of bias while `I believe that not X is true' is a bias towards other explanations.

I'm not sure how meaningful this distinction is when talking about belief in God though. Many of the more sophisticated believers seem to only believe in God as some kind of philosophical prime mover and are as sure as atheists that god is not responsible for what other people would call divine intervention.

 

[drkitten]

I'm struggling with the difference between belief (which classifies one as atheist or theist) and knowledge (which classifies one as gnostic or agnostic). I have problems with using K to label people, as I think K (justified true belief) is impossible, and I think it's redundant / not independent of B -- we couldn't possibly know something we don't believe in.

Simple. Justified true belief is not impossible, by any means.

For example, Mr Randi holds up his left hand, displays a sponge ball, closes his hand, then asks me which hand it's in. I believe -- justificably so -- that it's in his left hand.

My slightly more sophisticated friend has more knowledge of magic than I and believes -- also justifiably so -- that it's in his right hand because he recognizes the possibility of a trick.

Mr Randi, who is doing the trick, believes (justifiably so) that neither hand holds a sponge ball, because he put the sponge ball in his trouser pocket.

We all have justified beliefs, but only one of them (probably Randi's) is actually true.

You're making the standard confusion between having knowledge of P and having knowledge that you have knowledge of P. Just because I have a justified belief doesn't make it true. But just because I can't prove my justified belief true doesn't make it false.

 

[drkitten]

Going with the teapot, would you really believe someone who said that he refused to think that there were no teapots around Pluto, but would not think that there were teapots. I'd think he was playing semantic games.

Teapots on Pluto are of course an extreme example; no rational person even thinks that they might be there.

But there are lots of examples where people don't hold opinions. Do you believe that La Estrellita is the best Mexican restaurant in Boulder Colorado? Never been to Boulder?
Well, is there a difference between not believing that that some restaurant you've never heard of is the best (because, fundamentally, you neither know nor care), and actively believing that some restaurant you've heard of isn't the best?

 

[dvide]

A newly born baby lacks a belief in God, but it does not positively believe God does not exist. The baby is too young to have even considered it. In the case of most athiests they lack a belief in God simply because they see no logical reason to do so, but they haven't decided to believe God does not exist.

I have found that there are some agnostics, however, who think atheism is defined as the positive belief that God does not exist. They are uncomfortable with this, which is why they call prefer to call themselves agnostics. I think a lot of athiests and agnostics would actually completely agree with one another - they're just using two terms for the same thing.

 

[Bri]

I think the two statement are usually intended to show the difference between a weak atheist (agnostic atheist, sometimes just called an "agnostic") and a strong atheist ("gnostic" atheist, sometimes just called an "atheist").

The first doesn't make a positive claim, but is an admission that the person doesn't know whether or not there is a god (agnosticism is a statement about a lack of knowledge of gods, whereas atheism is a statement about a lack of belief of gods). The second sentence is a positive claim that no gods exist (it implies a certain amount of knowledge about a lack of gods, usually stated in the form "I think it is more likely that no gods exist").

That said, the two points of view probably represent a continuum because agnosticism and atheism both represent a continuum (how strong you think your knowledge against the existence of gods is and how strong your belief against the existence of gods is). So most atheists would lie somewhere between the two extremes of "I have no idea whatsoever whether or not there is a god" and "I know for a fact that there is no god."

Most weak atheists will say that it is more likely that there are no gods but admit that they don't know for sure whether there are gods or not. Most strong atheists say that they believe that there are no gods, but admit that it is possible that there is a god. Therefore, if you are somewhere in the middle of the continuum, it is possible to make either statement and mean the exactly same thing.

Some question whether any valid belief exists at either extreme. Few people have no opinion whatsoever about whether or not there is a god, which would imply that they're probably not at the far "weak atheist" end of the continuum (i.e. they believe that some evidence exists that would tip the probability one way or the other). At the same time, few believe that it's possible to know for certain that there are no gods (although I have heard a few strong atheists claim to believe that it is impossible that a god exists because they think that the existence of a god is logically impossible.)

The real question is how much and of what quality you think the evidence for or against the existence of gods is (i.e. how likely you think it is that a god exists or doesn't exist).

-Bri

 

[Bri]

Teapots on Pluto are of course an extreme example; no rational person even thinks that they might be there.

I believe they might be there. It is highly unlikely that they are there, but it is certainly possible.

-Bri

 

[Roboramma]

But there are lots of examples where people don't hold opinions. Do you believe that La Estrellita is the best Mexican restaurant in Boulder Colorado? Never been to Boulder?
Well, is there a difference between not believing that that some restaurant you've never heard of is the best (because, fundamentally, you neither know nor care), and actively believing that some restaurant you've heard of isn't the best?

Exactly. I don't believe that bpesta ate eggs for breakfast today, but I also don't believe that he didn't eat eggs for breakfast. I simply don't know.

Of course, saying that i don't know doesn't mean I know nothing about it - I can say that it's more likely than that he ate spiders, for instance. And if I had access to some decent statistics for his part of the world, and knew what part of the world he lives in, I might be able to narrow down that likelihood even further. If I knew the person that cooked his breakfast and could ask him/her, I might narrow it down even further. And if I found enough evidence, I might go from saying "I don't believe you had eggs for breakfast" to saying "I believe you didn't have eggs for breakfast".

None of that last paragraph (or this one) was in response to you drkitten. I just think there's a parallel here with atheism. It's possible to say "I don't know if there's a god, but I don't believe that there is" without saying that you have no information one way or the other. But at the same time it is different from saying "I believe there is no god."

 

[IMST]

I would say that statement one applies to me, where statement two does not. I feel the concept of gods as usually stated is unfalsifiable, therefore it is equally meaningless to believe and believe not. There's just no way to have any evidence either way, so it's pointless.

 

[bpesta22]

Thanks for the replies so far-- !

Knowledge is justified true belief. I guess I'm hinging on TRUE. True with certainty, or to some degree of probability? I think it makes a difference, as in my experience, it seems like many agnostics feel that unless they can know for sure, they can't call it, and hence are agnostic versus atheist.

Plus, is knowing a feeling or does knowing imply that what is known is true (not just to the person, but true given the evidence)? Can you know something which in reality is false. I'd say yes, but the definition of K seems to say no. Also, if K is justified true belief, than both the atheist and the theist cannot K that there belief is true.

So, I still think there's a problem with that 2 x 2 box, but I haven't figured it out to my satisfaction.

Thanks again!