Is This Statement Logical

[JoeyKnothead]

If god does not exist, then objective moral values do not exist.
Objective moral values do exist therefore god does exist.

Please help me understand how this statement is logical. As a matter of debate I say it ain't, put I could be wrong. I guess my question is why must one exist in order for the other, even if one exists at all?

[Py]

Evales, I think you might be mixing up the contrapositive and the converse. Given the statement "If P, then Q," its converse is "If Q, then P," which is not logically equivalent. Its contrapositive is "If not Q, then not P," which is logically equivalent; "possibility" doesn't factor into it at all. Also, the statement "P when Q" is equivalent to "If Q, then P," not the other way around.

Here's the logical argument being made here, represented more formally:

Let statement A be "God exists" and let statement B be "objective moral values exist."
Assumption 1: "If not A, then not B" is true.
Assumption 2: B is true.
By the definition of contrapositive, assumption 1 is the contrapositive of "If B, then A."
Since a statement is logically equivalent to its contrapositive, "If B, then A" is true.
The statement "If B, then A" is logically equivalent to "B is false or A is true."
By assumption 2, B is not false.
Therefore, A is true.
By the definition of statement A, God exists.

Unless there is something logically invalid in the above argument, the conclusion is correct given the assumptions. If you think something in there is logically invalid, please point out which step and explain what's wrong with it.

[Wellington]

It is invalid. All you have to do is remove the clauses "does not" and "do not" in order to see why.

If God ... exist[s] then objective moral values ... exist
Objective moral values exist
therefore God exists.

If A then B
B
Therefore A

^Invalid. It does not follow.

Actually, removing the clauses "does not" and "do not" changes it from "if not A then not B," equivalent to "if B then A," to "if A then B." Since it's not a biconditional statement, this changes the meaning and possibly the truth value of the statement. The arguments are basically:

If not A then not B
B
Therefore A

This is logically valid.

Actually it doesn't. B and A are not interchangeable. So:

"if B then A" Doesn't imply "if A then B" They are not "equivalents" as you described.

you cannot make that leap. It is invalid.

Think of them as a group. B is a small group within group A. If you are in group B you are in group A. If B then A.

However. If you are in group A you are NOT neccesarily in group B. You cannot switch the argument. Therefore, if you make an argument that says A therefore B, you are making an invalid argument. It doesn't follow.

It's pretty simple. I showed where I removed the clauses. they are represented by the "..." and I bracketed the letter "s" that I added.

[Wellington]

Evales, I think you might be mixing up the contrapositive and the converse. Given the statement "If P, then Q," its converse is "If Q, then P," which is not logically equivalent. Its contrapositive is "If not Q, then not P," which is logically equivalent; "possibility" doesn't factor into it at all. Also, the statement "P when Q" is equivalent to "If Q, then P," not the other way around.

Here's the logical argument being made here, represented more formally:

Let statement A be "God exists" and let statement B be "objective moral values exist."
Assumption 1: "If not A, then not B" is true.
Assumption 2: B is true.
By the definition of contrapositive, assumption 1 is the contrapositive of "If B, then A."
Since a statement is logically equivalent to its contrapositive, "If B, then A" is true.
The statement "If B, then A" is logically equivalent to "B is false or A is true."
By assumption 2, B is not false.
Therefore, A is true.
By the definition of statement A, God exists.

Unless there is something logically invalid in the above argument, the conclusion is correct given the assumptions. If you think something in there is logically invalid, please point out which step and explain what's wrong with it.

I think I get it now. You are absolutely right. I can't just drop the negative clause. I have to reverse it in order to drop it.

If not A then not B = no B without A
So the argument becomes: If B then A

If B then A
B
therefore A

I stand corrected. Thanks for the explanation. I should probably read ahead before I respond.

If not A then not B
B
Therefore A

^Valid.

[Evales]

Wow that is some fancy footwork there Py. It would appear you are right!

[ShadowRishi]

If god does not exist, then objective moral values do not exist.
Objective moral values do exist therefore god does exist.

Please help me understand how this statement is logical. As a matter of debate I say it ain't, put I could be wrong. I guess my question is why must one exist in order for the other, even if one exists at all?

In the strictest logical framework, let's define somethings.

Statement A can be any general statement or claim. So can B be a general statement or claim. There's a logical concept called implication, which is generally defined as " => ". A way to think about implication is that "The fact that Mary had bloody hands after Jenny was killed implies that she killed Jenny."

But in our more compact logical notation:

A = Mary has bloody hands right after Jenny's murder.
B = Mary killed Jenny.

A => B

Which we'll call statement C. (Statement C is the claim that A implies B)

If we switch A and B, we get something known as the converse of claim C:

B => A (Or, A <= B)

The converse statement reads, "Mary killed Jenny, therefore Mary has blood on her hands."

Generally speaking, if you prove a converse statement, it does not imply that the original statement is true. In this example, unless we know that Jenny was explicitly stabbed, we don't know that she could have had blood on her hands. There are all sorts of other logical possibilities; she may have strangled or poisoned her, for example. (Forgive the morbidness of this example)


So, from the previous logic, you have two statements:

A. "If god does not exist, then objective moral values do not exist."
B. "Objective moral values do exist therefore god does exist."


B is the converse of A. Therefore, if you prove B, you have not proven A.

[ShadowRishi]

[strike]*whoops, posting error*

Please delete.[/strike]

I'll just use this post then:

Evales, I think you might be mixing up the contrapositive and the converse. Given the statement "If P, then Q," its converse is "If Q, then P," which is not logically equivalent. Its contrapositive is "If not Q, then not P," which is logically equivalent; "possibility" doesn't factor into it at all. Also, the statement "P when Q" is equivalent to "If Q, then P," not the other way around.

Here's the logical argument being made here, represented more formally:

Let statement A be "God exists" and let statement B be "objective moral values exist."
Assumption 1: "If not A, then not B" is true.
Assumption 2: B is true.
By the definition of contrapositive, assumption 1 is the contrapositive of "If B, then A."
Since a statement is logically equivalent to its contrapositive, "If B, then A" is true.
The statement "If B, then A" is logically equivalent to "B is false or A is true."
By assumption 2, B is not false.
Therefore, A is true.
By the definition of statement A, God exists.

Unless there is something logically invalid in the above argument, the conclusion is correct given the assumptions. If you think something in there is logically invalid, please point out which step and explain what's wrong with it.

I think I get it now. You are absolutely right. I can't just drop the negative clause. I have to reverse it in order to drop it.

If not A then not B = no B without A
So the argument becomes: If B then A

If B then A
B
therefore A

I stand corrected. Thanks for the explanation. I should probably read ahead before I respond.

If not A then not B
B
Therefore A

^Valid.

Actually, sorry, but no, this is also fallacious logic.


You, and possibly your opponent (I didn't read his full argument), are lacking a necessary caveat:

"If and only if not B then not A
B
therefore A"


The logic splits this way:

"If not A then not B" means the same thing as "If A then B"

But, "If B then A" can only be concluded when "A <=> B" (or, if and only if A, then B. This means that if you know one is true, you know the other must also be true. If you don't know if this relationship exists, then you cannot conclude the converse statement is true. Or in logical terms, "If "A <=> B" then "A is true" => "B is true" and "B is true" => "A is true")

So, what you need to prove in order to make the proof valid is that B => A. Otherwise, your argument is fallacious.

[FinalEnigma]

this is getting a little silly with two pages of A's and B's. wanna try it this way?

If god does not exist, then objective moral values do not exist(=A)
objective morals do exist(=B), therefore God must exist(=C)

A) for objective moral values to exist, god must exist.
A(rephrase) the existence of objective moral values is dependent upon the existence of God
B) objective morals exist.
Conclusion
C) God must exist.

If you can prove both A and B, then you've got a valid logical argument.

for the record, while this is logically valid, I don't believe it is sound. Meaning I disagree with A, and think B is uncertain.

[Wellington]

this is getting a little silly with two pages of A's and B's. wanna try it this way?

If god does not exist, then objective moral values do not exist(=A)
objective morals do exist(=B), therefore God must exist(=C)

A) for objective moral values to exist, god must exist.
A(rephrase) the existence of objective moral values is dependent upon the existence of God
B) objective morals exist.
Conclusion
C) God must exist.

If you can prove both A and B, then you've got a valid logical argument.

for the record, while this is logically valid, I don't believe it is sound. Meaning I disagree with A, and think B is uncertain.

Right. We are just trying to determine whether it is logical or not. I think A should have been rephrased (as you have done) by the original poster to avoid all the confusion.

[David E]

If god does not exist, then objective moral values do not exist.
Objective moral values do exist therefore god does exist.

Please help me understand how this statement is logical. As a matter of debate I say it ain't, put I could be wrong. I guess my question is why must one exist in order for the other, even if one exists at all?

An argument is logically valid if, when its premises are true its conclusion must be true as well.

But to be a sound (as well as merely logically valid) argument its premises have to be true as well.

And, of course, both premises have been argued against by atheists.

[David E]

I stand corrected. Thanks for the explanation. I should probably read ahead before I respond.

Quote:

If not A then not B
B
Therefore A

^Valid.

Actually, sorry, but no, this is also fallacious logic.


You, and possibly your opponent (I didn't read his full argument), are lacking a necessary caveat:

"If and only if not B then not A
B
therefore A"

I think they WERE right.

It would have been better if the argument had been stated as modus ponens:

if P then Q
Q
Therefore P

Rather than

If not P then not Q
Q
Therefore P

But the second, if clumsy, is valid as well.

At first I thought as you do but on further examination I think we were mistaken.

For the argument to be invalid it would have to be possible for all 3 of the following propositions to be true at the same time:

1. If not P then not Q
2. Q
3. Not P

In this specific case:


1. If God doesn't exist then objective morality doesn't exist.

2. Objective morality exists.

3. God doesn't exist.

But 2 and 3 are logically incompatible with 1, therefore the argument is of a logically valid type.

Which is not, as I noted before, to say that its premises are actually true.