Deductive Arguments And Multiplying Probabilities

[Johan Biemans (jbiemans)]

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.

I think that the problem is coming in because you are trying to apply the probability to:

If my neighbour's dog is in the park, it's wearing a dog-sweater.

Can you apply a probability to an if-then statement ?  Aren't they true or false necessarily ?  I think for these is it an either on or off switch that you must take.  You either accept or reject it.  I don't think you can accept a probability on a conditional statement.

[Moot]

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.

I think that the problem is coming in because you are trying to apply the probability to:

If my neighbour's dog is in the park, it's wearing a dog-sweater.

Can you apply a probability to an if-then statement ?  Aren't they true or false necessarily ?  I think for these is it an either on or off switch that you must take.  You either accept or reject it.  I don't think you can accept a probability on a conditional statement.

Why? I can't see any problem with assigning a probability to a if-then statement. Say my neighbour's dog wears his sweater two times out of three when he's in the park. It seems pretty obvious that this would justify a .66 probability to the statement "If my neighbour's dog is in the park, it's wearing a dog-sweater", don't you think?

[kurros]

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.

I think that the problem is coming in because you are trying to apply the probability to:

If my neighbour's dog is in the park, it's wearing a dog-sweater.

Can you apply a probability to an if-then statement ?  Aren't they true or false necessarily ?  I think for these is it an either on or off switch that you must take.  You either accept or reject it.  I don't think you can accept a probability on a conditional statement.

Why? I can't see any problem with assigning a probability to a if-then statement. Say my neighbour's dog wears his sweater two times out of three when he's in the park. It seems pretty obvious that this would justify a .66 probability to the statement "If my neighbour's dog is in the park, it's wearing a dog-sweater", don't you think?

Seems fine to me, and your numbers check out I think, so everything looks good to me. I see no problem with your scenario. It is just demonstrably false that conclusions must have P>0.5 if all the premises have P>0.5.

[Moot]

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.

I think that the problem is coming in because you are trying to apply the probability to:

If my neighbour's dog is in the park, it's wearing a dog-sweater.

Can you apply a probability to an if-then statement ?  Aren't they true or false necessarily ?  I think for these is it an either on or off switch that you must take.  You either accept or reject it.  I don't think you can accept a probability on a conditional statement.

Why? I can't see any problem with assigning a probability to a if-then statement. Say my neighbour's dog wears his sweater two times out of three when he's in the park. It seems pretty obvious that this would justify a .66 probability to the statement "If my neighbour's dog is in the park, it's wearing a dog-sweater", don't you think?

Seems fine to me, and your numbers check out I think, so everything looks good to me. I see no problem with your scenario. It is just demonstrably false that conclusions must have P>0.5 if all the premises have P>0.5.

Ok, thanks.

I take it from the responses so far that this is (at the very least) a reasonable objection to Craig's standard of a good argument. But how would someone like Craig defend it? What would the counter objections be?

[Johan Biemans (jbiemans)]

I think though, if 2 times out of 3 your neightbors dog is in the park it is wearing a sweater, the correct premise would be:

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

In a deductive argument, the premise must be true, or the argument breaks.  The premise cannot be .6 likely true, or you cannot do deduction.  Deduction only works on true premises, which is why Dr. Craig says that you ought to accept a premise as true if it is more plausible than its negation.  This means that if it is .6, you need to accept at as 1 in order to proceed with deduction.  This to me is a major problem.

He likely shies away from inductive arguments because of the problem you bring up with probabilities.

[kurros]

I think though, if 2 times out of 3 your neightbors dog is in the park it is wearing a sweater, the correct premise would be:

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

In a deductive argument, the premise must be true, or the argument breaks.  The premise cannot be .6 likely true, or you cannot do deduction.  Deduction only works on true premises, which is why Dr. Craig says that you ought to accept a premise as true if it is more plausible than its negation.  This means that if it is .6, you need to accept at as 1 in order to proceed with deduction.  This to me is a major problem.

He likely shies away from inductive arguments because of the problem you bring up with probabilities.

You don't have to do that. Probability can refer to the probability that a proposition is true. So putting the word "probably" into the proposition itself makes something like Pr(”my dog is probably in the park") hard to interpret. Better to just have Pr("my dog is in the park").

[Johan Biemans (jbiemans)]

I am fine with that.  It would make the conclusion:

C. Therefore, probably, my neighbor's dog is wearing a dog-sweater.

Right ? 

Which again is a reasonable conclusion based on the premises.

Now, if it was:

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

I don't think that you could even conclude:

C. Probably, my neighbor's dog is wearing a sweater.

I don't think it follows any more....I just can't point to exactly why.

[Moot]

I am fine with that.  It would make the conclusion:

C. Therefore, probably, my neighbor's dog is wearing a dog-sweater.

Right ? 

Which again is a reasonable conclusion based on the premises.

Now, if it was:

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

I don't think that you could even conclude:

C. Probably, my neighbor's dog is wearing a sweater.

I don't think it follows any more....I just can't point to exactly why.

I agree with Kurros. We don't add "probably" to every premise in deductive arguments if we're not sure. We explain our confidence level after presenting arguments.

If we did accept this reasoning, we would add "probably" to the premises of the KCA as well. Even Craig isn't claiming to be certain of the premises.

[kurros]

And if you do add it to the propositions directly, you are probably going to screw up the logic, because you will not be able to rigourously keep track of the proper relationships between probabilities. The probability calculus is a superset of the propositional logic calculus, so you will lose information if you don't explicitly work in the superset.

[Johan Biemans (jbiemans)]

I think I agree, which is why I think that, in order to do deduction, you have to assume that the premise is actually true, otherwise the probabilities mess everything up.  My problem, as with yours, is where you draw the line for when you assume the premise is true.  Does it need to be really well supported ?  Just a little supported?   More probable than it's negation ? Etc.

[Moot]

My problem, as with yours, is where you draw the line for when you assume the premise is true.  Does it need to be really well supported ?  Just a little supported?   More probable than it's negation ? Etc.

But that's not a problem as long as you multiply the probabilities as far as I can see.

[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.

[Moot]

Come on. Can't you people see that I'm totally pwning Craig here. Object to the OP dammit!

[Bertuzzi]

You should email him.

[Moot]

You should email him.

Yeah, maybe. Do you think he'd respond? It shouldn't be necessary though. I'm sure there are people here who can defend the standard. Do you have an objection to the OP?

Edit: Craig responded to the Miller objection on his podcast, but he never really explained what was wrong with it. He pretty much just said that it was a common standard.