Deductive Arguments And Multiplying Probabilities

[kurros]

If the latter says that the dog always wears a sweater in the park, then doesn't the former say that if the dog is in the park then it is always wearing a sweater while it is in the park ?  I don't see why one implies always and the other implies sometimes.

This is why I'm querying too.  However ..

P1. If the dog is wearing a sweater then it is in the park.
P2. The dog is in the park.
C. Therefore, the dog is wearing a sweater.

... affirms the consequent.  So do we have to apply logic to a conditional before assessing its probability?  Isn't that what logic is for?

I don't see why this example would be different. We take the probability that P1 is true, namely the probability that it's true that the dog is in the park if it's wearing a sweater, and we multiply it with the probability of P2.

Maybe I'm missing something?

Well when you are translating to probabilities, the conditional is not part of the proposition, it is a separate proposition on which the first proposition is conditional.

E.g.

If the dog is in the park, it is wearing a sweater

Should be thought of as

Pr("the dog is wearing a sweater" | "the dog is in the park")

Which reduces to probability one if P1 is true.

The inverse case, if the dog is wearing a sweater then it is in the park, likewise generalises to

Pr("the dog is in the park" | "the dog is wearing a sweater")

With the two cases being related by Bayes theorem.

[LADZDAZL]

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.

This is fine in principle but I would strongly disagree that Craig does make a cumulative case. He makes a sequential case to try to arrive at the Christian God of the bible. The KCA is an argument for the Universe having a cause. It doesn't argue that this cause is God. It only argues that the cause is personal in the second part which requires more premises and more multiplication of probabilities and therefore a less probable conclusion. He doesn't present any other arguments for the the Universe having a cause.  Nothing cumulative here. He gives an argument for the Universe being designed but doesn't say anything about the identity of any designer and whether this designer might also be responsible for the initial creation.

His moral argument is interesting in that it's conclusion is that God exists, but as far as I'm aware the argument really argues for a non-human objective standard of morality. Does he discuss other supernatural possibilities or does he just assume God is the only possibility?  Again more premises seem to be needed.

Craig acknowledges that the resurrection argument only works if you are already convinced that miracles are plausible explanations. i.e. you need to accept multiple other arguments before running the resurrection argument.

The best one can say is that if you accept the KCA at 0.36 (to keep with the theme of the thread) and you accept the FTA and MA at whatever value, then, by Occam's razor, God is an excellent all encompassing solution to all of these conclusions. But the probability of all these separate and (I think) largely independent arguments is the conjunction of all these probabilities. i.e. 0.36 X P(FTA) X P(MA). So if this low probability scenario were true then God is a great explanation. But this scenario is very probably not true.

[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.

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.

This is fine in principle but I would strongly disagree that Craig does make a cumulative case. He makes a sequential case to try to arrive at the Christian God of the bible. The KCA is an argument for the Universe having a cause. It doesn't argue that this cause is God. It only argues that the cause is personal in the second part which requires more premises and more multiplication of probabilities and therefore a less probable conclusion. He doesn't present any other arguments for the the Universe having a cause.  Nothing cumulative here. He gives an argument for the Universe being designed but doesn't say anything about the identity of any designer and whether this designer might also be responsible for the initial creation.

His moral argument is interesting in that it's conclusion is that God exists, but as far as I'm aware the argument really argues for a non-human objective standard of morality. Does he discuss other supernatural possibilities or does he just assume God is the only possibility?  Again more premises seem to be needed.

Craig acknowledges that the resurrection argument only works if you are already convinced that miracles are plausible explanations. i.e. you need to accept multiple other arguments before running the resurrection argument.

The best one can say is that if you accept the KCA at 0.36 (to keep with the theme of the thread) and you accept the FTA and MA at whatever value, then, by Occam's razor, God is an excellent all encompassing solution to all of these conclusions. But the probability of all these separate and (I think) largely independent arguments is the conjunction of all these probabilities. i.e. 0.36 X P(FTA) X P(MA). So if this low probability scenario were true then God is a great explanation. But this scenario is very probably not true.

Right, I forgot about this. If we take Craig's five most common arguments, they don't actually make a cumulative case. You could argue that the KCA and FTA both work towards a creator of the Universe, but they do nothing for God being good for example (as also Law has pointed).

We'd need to devide the arguments in to sections based on what they're actually arguing for and calculate the force the different sections have. Then we'd need to multiply the probability of the different sections being true.

[LADZDAZL]

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.

This is fine in principle but I would strongly disagree that Craig does make a cumulative case. He makes a sequential case to try to arrive at the Christian God of the bible. The KCA is an argument for the Universe having a cause. It doesn't argue that this cause is God. It only argues that the cause is personal in the second part which requires more premises and more multiplication of probabilities and therefore a less probable conclusion. He doesn't present any other arguments for the the Universe having a cause.  Nothing cumulative here. He gives an argument for the Universe being designed but doesn't say anything about the identity of any designer and whether this designer might also be responsible for the initial creation.

His moral argument is interesting in that it's conclusion is that God exists, but as far as I'm aware the argument really argues for a non-human objective standard of morality. Does he discuss other supernatural possibilities or does he just assume God is the only possibility?  Again more premises seem to be needed.

Craig acknowledges that the resurrection argument only works if you are already convinced that miracles are plausible explanations. i.e. you need to accept multiple other arguments before running the resurrection argument.

The best one can say is that if you accept the KCA at 0.36 (to keep with the theme of the thread) and you accept the FTA and MA at whatever value, then, by Occam's razor, God is an excellent all encompassing solution to all of these conclusions. But the probability of all these separate and (I think) largely independent arguments is the conjunction of all these probabilities. i.e. 0.36 X P(FTA) X P(MA). So if this low probability scenario were true then God is a great explanation. But this scenario is very probably not true.

Right, I forgot about this. If we take Craig's five most common arguments, they don't actually make a cumulative case. You could argue that the KCA and FTA both work towards a creator of the Universe, but they do nothing for God being good for example (as also Law has pointed).

We'd need to devide the arguments in to sections based on what they're actually arguing for and calculate the force the different sections have. Then we'd need to multiply the probability of the different sections being true.

Yep. And this to me explains the difference between apologists that make "respectable" claims and those who are guilty of hyperbole. Many thoughtful Christians like Keith Ward make an argument that theism is a rationally permissible world view. There is a YouTube discussion between Keith Ward and Arif Azi when he very clearly states that this is his aim. Such Christians tend to "lose debates" and sometimes it seems as though they aren't really arguing "for" Christianity. But truth be told I think they just realise the limits of apologetics, i.e. a defence of the possibility, not a case for the probability.