are these statements logically equivalent?

[Jekyll]

The essential problem here is in the ambiguity of the term "believe". I think that if we rephrase to eliminate this term, the problem will go away.

P = "Gods Exist"

1): ~P
2): ~P

The whole "belief" thing muddies the waters to a massive extent.

No.

Consider:
There is proof no god exists.
Vs.
There is no proof god exists.

No ambiguity. They both say different things.

 

[arthwollipot]

No.

Consider:
There is proof no god exists.
Vs.
There is no proof god exists.

No ambiguity. They both say different things.

So your proposal is that:

P = "Proof Exists"
Q = "Gods Exist"

1): P(~Q)
2): ~P(Q)

That is indeed a significantly different logical construction.

 

[Bri]

I was trying to throw the negation on the left side of P instead of the right - to show the similarity of the statements.

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


1) I do NOT believe <P>
2) I believe NOT <P>

These are same. The problem is "believe". For some reason there appears to be a difference between NOT BELIEVE and BELIEVE NOT. Weird.

The problem is that there are three possibilities for belief of the truth of <P>: true, false, and unknown (whereas <P> itself must either be true or false).

A) I believe <P> is true.
B) I believe <P> is unknown.
C) I believe <P> is false.

Your statement 1 is equivalent to "I do NOT believe <P> is true" which can be either B or C.

Your statement 2 is equivalent to "I believe <P> is false" which is C.

So, your statement 1 is ambiguous, whereas statement 2 is not so ambiguous.

-Bri

 

[drkitten]

So your proposal is that:

P = "Proof Exists"
Q = "Gods Exist"

1): P(~Q)
2): ~P(Q)

That is indeed a significantly different logical construction.

Yup. And you get the same result with any other verb/proposition that takes a propositonal argument.

John said that Mary was unmarried.
John did not say that Mary was married. (He diedn't say anything at all.)

John saw Mary fail to win the high jump.
John did not see Mary win the high jump. (Since he was watching the discus throw.)

John told Mary not to eat the fish.
John did not tell Mary to eat the fish. (It was Bill who told her that).

John wrote that he wasn't in love with Mary.
John didn't write that he was in love with Mary (because he's illiterate).

and, of course, you get the same result with "believe that" as you do with "said that" or "told that."

John believed that Mary didn't love him.
John didn't believe that Mary loved him (because he didn't even know who Mary was).

 

[drkitten]

These are same. The problem is "believe". For some reason there appears to be a difference between NOT BELIEVE and BELIEVE NOT. Weird.

Not that wierd. You don't even need propositional verbs to get that effect.

The plane landed, but not at Springfield.
The plane did not land at Springfield.

In the second sentence, the plane may not have landed at all -- it may still be in the air, or it may have crashed somewhere instead of landing So there's equally a difference between LAND NOT (which implies LAND) or NOT LAND.

Similarly:

Susan baked a not-chocolate cake.
Susan did not bake a chocolate cake.

In the second case, Susan might have baked cookies, or pies, or bread -- or nothing at all. In the first, of course, we know she made a cake, but that the cake didn't contain chocolate. BAKE NOT vs NOT BAKE.

James submitted an unoriginal paper.
James did not submit an original paper.

SUBMIT NOT vs NOT SUBMIT.

Further examples are not presented; they are instead left to your not-inconsiderable imagination.

 

[bruto]

I was trying to throw the negation on the left side of P instead of the right - to show the similarity of the statements.

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


1) I do NOT believe <P>
2) I believe NOT <P>

These are same. The problem is "believe". For some reason there appears to be a difference between NOT BELIEVE and BELIEVE NOT. Weird.

The problem is the ambiguity of "believe," and the fact that there may or may not be a difference. Substitute "assert" for "believe," for example, and you'll have demonstrably different meanings. Not asserting far from asserting the negative.

 

[Kahalachan]

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?

Since the goal of the statement is to state a belief, we can examine the possibilities isolating just where P is true.

"I don't believe gods exist."



T T = I don't believe or gods exist.
T F = I don't believe or gods don't exist.


God can or cannot exist. This doesn't affect that statement of belief.

In an "or" statment both parts have to be false. So if they say "I believe or gods don't exist" then the statement if false.


"I believe that no gods exist."



T T = I believe and gods do not exist
T F = I believe and gods do exist



In both cases an assertion of P is what is important. What they believe. However, when they state they believe no gods exist, the negation of the second half will prove them wrong because this is an "and" statement where both have to be right.




Also to expand:

I might be assuming a gnostic atheist for the 2nd half so to furhter show the difference regardless of the statement of belief.....

Let P = I believe
Let Q = god exists

~P ^ Q
T T: F
T F: F
F T: T
F F: F

P ^ ~ Q
T T: F
T F: T
F T: F
F F: F

The tables for both of these statements differ to say "I believe and god exists"

 

[Mangafranga]

I am not sure what is going on in your post. It might help if you clarify this part.

"I believe that no gods exist."

T T = I believe and gods do not exist

Are you claiming that the first sentence in this quote is logically equivalent to the second sentence in this quote?

 

[Mozybyte]

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

The first statement is purely atheist in nature while the second implies a certain level of agnosticism by the affirmative "No" which is not present in the first.
This is better observed this way...

1) I Do Not Believe Gods Exist
1a) I Believe Gods Do Not Exist

These two are equivalent bar for mechanics of their elements.

2) I Believe That No Gods Exist

This statement differs from the first in its proposition, in that it includes the word No, not present in the first and is implicit of knowledge, while the first is irrational and non deterministic.

I expanded the first statement to its full complex to remove the ambiguity it purports. and swapped the verbal positioning for a (as requested) "polyglot" view.

 

[drkitten]

This is better observed this way...

1) I Do Not Believe Gods Exist
1a) I Believe Gods Do Not Exist

These two are equivalent bar for mechanics of their elements.

No, they're not. For example, if "I" am a coffee cup, I have no mind, and therefore am not capable of belief.

2) A coffee cup does not believe gods exist.
2a) A cofffee cup believes no gods exist.

Since for all propositions P, it is the case that "A coffee cup does not believe that P" and it is not the case that "A coffee cup believes that P" (since a coffee cup does not believe anything whatsover), we clearly see that 2 and 2a are different. But if this is the case, so are 1 and 1a.

 

[Mozybyte]

The Power of distinction rests with the word "No".
Coffee cups play no part in the exercise.
Statement two "Can Not" be reversed as statement one was without the use of different terminology (as you did), or it will make no grammatical sense, that in itself proves definition.
Semantics have rigours not born to philosophy.

 

[Dr Adequate]

Well, the first statement is compatible with the negation of the second, whereas the second obviously isn't.

 

[Dr Adequate]

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.

Well, Russell's teapot is an extreme example. However, suppose I was to make the following two statements (both of which are, in fact, true):

"I don't believe that there is extraterrestrial life in our solar system, and I don't believe that there isn't extraterrestrial life in our solar system."

However, it is true that normally we would parse the first statement as meaning "I believe that there is no extraterrestrial life in our solar system", unless it was accompanied by the second statement.

 

[Kahalachan]

I am not sure what is going on in your post. It might help if you clarify this part.Are you claiming that the first sentence in this quote is logically equivalent to the second sentence in this quote?

I might've made that part in haste and not explained clearly.

"I believe that no gods exist."

T T = I believe and gods do not exist

When both parts are true that is the result. When "I believe" is true and "no gods exist" is true then we have "I believe and gods do not exist."

So if the pragmatics involved in "I beleive that no gods exist" implies a contraction of those 2 statements we can derive that truth table I mentioned.

 

[Mangafranga]

I might've made that part in haste and not explained clearly.

"I believe that no gods exist."

T T = I believe and gods do not exist

When both parts are true that is the result. When "I believe" is true and "no gods exist" is true then we have "I believe and gods do not exist."

So if the pragmatics involved in "I beleive that no gods exist" implies a contraction of those 2 statements we can derive that truth table I mentioned.

And "I believe" means, or is true when?

 

[Mozybyte]

The exercise is in identifying the philosophical intent behind the semantics, if one is to change the semantics by introducing different propositions one runs the risk of corrupting the intent of the statement proposed.
In other words the argument is purely semantic in nature and must not be altered with the introduction of new elements, thus must be observed with its components intact.
Analogies of tea pots and planetary activity is but surreptitious deviation to prove the proposition of the observer not the statement.
In truth, if a statement is so ambiguous as to lack the fortitude of expressing its intent clearly to an interpreter, then the statement should not be made or given any credence.
If one has the misfortune of letting ones finger go through the paper, there is little point in arguing about whether the fault is in the paper for being too soft or on the misadventurous for pressing too hard, better go scrub ones nails, chuck the brush in the can, and hope it will never happen again.

 

[Mozybyte]

Hey! I just had a thought (fancy that)...
Maybe one of you should start a thread on the advantages/disadvantages, of folding versus scrunching, and on the likelihood of either returning the misfortune mentioned above.
Maybe even on whether the color of the paper has an influence on the affluence of the effluence.
(Isn't this dialect fun)

 

[Robin]

In your analogy you need to marry up EXIST with TRUE. Adding FALSE was trickery. Nice going, trickerer.

Nonsense. You only need to understand that P is the proposition "gods exist".

Thus:

I believe P is true
I don't believe P is true
I believe P is false

are three distinct positions.

They are the same. OK, if everyone is satisfied, let's go on to the next subject.

I see. So either you fully believe a proposition or you fully believe the negation of the proposition? No such thing as skepticism then?