Deductive Arguments And Multiplying Probabilities

[phidiasv]

Bump.

I'd like to hear from some theists. It seems that if my approach is right, that undermines a big chunk of WLC's case for God.

Something must be missing.

What part of Craig's case for God's existence is undermined by the fact that an argument's being "good" (in the way Craig defines it) does not guarantee the conclusion is more probable than its negation (which I take to be your point)?

[RichardChad]

P1. If gratuitous evil exists, God does not exist
P2. gratuitous evil exists
C. Therefor, God does not exist

probability of P1 is 70%
probability of P2 is 70%

The probability of C is .7*.7 = 49%

Demonstrating that the high likelihood of gratuitous evil does not demonstrate the non-existence of God.

Would you agree with this moot?

[RichardChad]

For atheism to be true, no god can exist.
The probability of any single god existing is not zero.

The probability that atheism is true then becomes, the probability that God does not exist * the probability that Allah does not exist * the probability that Vishnu does not exist * etc. etc.

now, even if in each case the probability that any particular god in the list does not exist is .99 (meaning, we only assign a 1% chance that that that particular god is real) all I need to do is come up with at least 70 gods and the probability that atheism is true becomes less than 50%.

Do you agree with this moot?

[RichardChad]

P1. God made everything perfect.
P2. Imperfection cannot come from perfection.
P3. Perfectly created beings cannot be the origin of evil.
C. Therefore, God must be the origin.

I am very confident of my premises, so I assign a .75 probability to each.
.75*.75*.75 = .42

So, it is highly improbable that God is the origin of evil.

Do you agree with this moot?

[Moot]

RichardChad:

I'm actually interested in this topic so please don't derail the thread.

If you insist on posting the same things I've told you many, many times isn't relevant to what I'm arguing, could you at least do it in one post instead of three.

Edit: I'll respond to your three questions, but if you want to continue this, please start a new thread. I won't be responding to this again here.

Argument 1. I agree. If those are the probabilities the argument alone does not establish that God's existence is improbable.
Argument 2. Makes no sense and has nothing to do with what I'm arguing (as I've explained many times).
Argument 3. Is invalid.

[Moot]

Bump.

I'd like to hear from some theists. It seems that if my approach is right, that undermines a big chunk of WLC's case for God.

Something must be missing.

What part of Craig's case for God's existence is undermined by the fact that an argument's being "good" (in the way Craig defines it) does not guarantee the conclusion is more probable than its negation (which I take to be your point)?

If we take the KCA, I could grant that both premises are more likely true than not while still claiming that an eternal Universe is more likely than the Universe having a cause. Surely that undermines the KCA somewhat.

The same thing seems to be true for Craigs version of the MA and the FTA. It puts a heavier burden on Craig in that he needs to show that the premises are quite a lot more probable than not.

... if I'm right that is.

Edit: Now that I think about it, this objection might not apply to Craig's version of the MA. At least not identically.

[RichardChad]

Just to clarify argument 2 for you

P1. If atheism is true, no god is real
P2. The God of Israel is not real
P3. Allah is not real
...
P80. Vishnu is not real
C. Therefore, atheism is true

I am VERY confident of my premises, so I assign a .99 probability to each (granting only a 1% chance that each god is real.

The probability of the conclusion is then: .99^80 = 44%.

Therefore, even granting that each god has only a 1% chance of existing, atheism is still improbable.

[Johan Biemans (jbiemans)]

So you agree with the method then Richard ?

[RichardChad]

So you agree with the method then Richard ?

Of course not, multiplying probabilities only works for independent events.

I'm showing that using this "method" on any deductive argument I can achieve an improbable conclusion simply by adding premises.

[Moot]

RichardChad:

I asked you to start a new thread if you want to discuss this. Please stop derailing.

[phidiasv]

Bump.

I'd like to hear from some theists. It seems that if my approach is right, that undermines a big chunk of WLC's case for God.

Something must be missing.

What part of Craig's case for God's existence is undermined by the fact that an argument's being "good" (in the way Craig defines it) does not guarantee the conclusion is more probable than its negation (which I take to be your point)?

If we take the KCA, I could grant that both premises are more likely true than not while still claiming that an eternal Universe is more likely than the Universe having a cause. Surely that undermines the KCA somewhat.

The same thing seems to be true for Craigs version of the MA and the FTA. It puts a heavier burden on Craig in that he needs to show that the premises are quite a lot more probable than not.

... if I'm right that is.

Edit: Now that I think about it, this objection might not apply to Craig's version of the MA. At least not identically.

Well, no. I don't think the mere possibility that one could find the two premises of the kalam more likely true than not and the conclusion more likely false than not undermines the effectiveness of the kalam (or any deductive argument, for that matter) at all. Craig spends an awful lot of time (in his debates and written work) arguing for the truth of the premises of his arguments for God's existence. So it doesn't seem like he's counting on people shrugging and assigning 51% to each of the premises.

But, suppose you are one of those people who find themselves in a situation where you think the premises are each more likely true than not, but find the conclusion more likely false than not. The argument is still not ineffective. Suppose, as Craig actually does, multiple arguments are presented for a particular conclusion. For example: A/B//G and C/D//G. And suppose you think the probability of each of the premises is 0.60 (and, following the rest of the thread for simplicity, assume these probabilities are independent). Taken individually, these two arguments only set the minimum probability of the conclusion, G, at 0.36. But, taken together, the minimum probability of the conclusion is 0.59: P((A and B) or (C and D)) = 0.59.

So even if something like your probabilistic scenario is the case with the kalam, it still can play a valuable role in a cumulative case for the conclusion. And that's generally how Craig uses it.

[RichardChad]

RichardChad:

I asked you to start a new thread if you want to discuss this. Please stop derailing.

How exactly is it derailing pointing out that multiplying probabilities only works for independent events, and that  using this "method" on any deductive argument I can achieve an improbable conclusion simply by adding premises,  on a thread titled "Deductive Arguments And Multiplying Probabilities"

I'm precisely addressing your OP!

[bdsimon]

RichardChad:

I asked you to start a new thread if you want to discuss this. Please stop derailing.

How exactly is it derailing pointing out that multiplying probabilities only works for independent events, and that  using this "method" on any deductive argument I can achieve an improbable conclusion simply by adding premises,  on a thread titled "Deductive Arguments And Multiplying Probabilities"

I'm precisely addressing your OP!

Agree. I was actually going to post the same type of objection that you posted.

[Emuse]

Just some initial thoughts as I think about this ....

Let's take the newer version of the KCA (forgive me if I'm not formulating it exactly right):

1. If the Universe began to exist, it had a cause.
2. The Universe began to exist.
C. Therefore, the Universe had a cause.

Let's not forget that a person who doesn't limit what possibly exists to material reality would not limit P1 to the physical universe and would conclude that if there are immaterial things which began to exist then these would need a cause too.  I would say that this is why P1 of Kalam is not making a claim specifically about the universe ...

P1. If something begins to exist then it must have a cause of its existence.

This can be reworded to express a set relation.  So, there is a set B and every member of B began to exist.  P1 is saying that every member of B must also have a cause.  P2 is saying that that the universe is a member of B.  So ...

P1. If X is a member of B (the set things which begin to exist) then X has a cause.
P2. The universe is a member of B.
C. Therefore, the universe has a cause.

How do set relations of this type impact on these probabilities?  It seems intuitive that it cannot be ignored because we're now dealing with states of affairs that are conditionally embedded. 

1. If my neighbour's dog is in the park, it's wearing a dog-sweater.
2. My neighbour's dog is in the park.
C. Therefore, my neighbour's dog is wearing a dog-sweater.

Edit: My neighbours dog only wears a sweater if it's in the park (it's not really the same structure otherwise).

A nitpick here.  If the dog only wears a sweater at the park then this actually needs to be expressed as ...

P1. If my neighbour's dog is wearing a sweater then it is in the park.
P2. My neighbour's dog is wearing a sweater.
C. Therefore, my neighbour's dog is in the park.

Which also gives us ...

P1. If my neighbour's dog is wearing a sweater then it is in the park.
P2. My neighbour's dog is not in the park.
C. Therefore, my neighbour's dog is not wearing a sweater.

The above doesn't mean that the dog must be wearing a sweater if it is in the park.  That would be affirming the consequent.  Again, we can think in terms of a set relation.  A is the set of activities engaged in by your neighbours dog.  P is a subset of A, and is the activity of being at the park.  S is a subset of P and is the dog wearing a sweater.

So again, how would this type of embedded scenario affect overall probability, if at all?

[Emuse]

P1. If gratuitous evil exists, God does not exist
P2. gratuitous evil exists
C. Therefor, God does not exist

probability of P1 is 70%
probability of P2 is 70%

The probability of C is .7*.7 = 49%

Demonstrating that the high likelihood of gratuitous evil does not demonstrate the non-existence of God.

Would you agree with this moot?

Don't forget to factor in the consequences of the modal ontological argument.