Sunday, December 18, 2011

Glenn Peoples' moral argument for God

Glenn Peoples' blog has been interesting me lately. He has just out up his version of a moral argument for the existence of God.

Glenn argues, as does Craig:

If there's no God, there are no objective moral values.
There are objective moral values
Therefore there is a God.


Of course, Glenn realizes his premises, especially the first premise, will require considerable support, so he makes his case for it here.

Here's part of my comment on People's moral argument...

Glenn – I’m tempted to start investigating your argument more but it would be really helpful if you could set out the argument more formally, so that the most basic premises supporting your conclusion are clearly identified. Make it very clear why there is objective moral value only if there is an all-powerful, all-good, personal God. E.g. why moral Platonism won’t do, for example. Why non-natural objective moral facts won’t do either. Why it’s got to be a person. Exactly how the is-ought gap plays a role in delivering the conclusion. It would also be good to see what your assessment of the probability of each of the basic premises of the argument is.

Notice by the way that as more premises are introduced that you may consider to be much more probable than not – that have, say, an 80% probability of being true – the probability of your conclusion being true may nevertheless drop like a stone. With, say, just five required basic premises of 80% probability each, the probability that your conclusion is true drops to just 32%.

That’s to say, the probability that your conclusion is FALSE is nearly 70% (p.s. given just those premises).

(Wes Morriston also points this out, I believe)

However some theists (not you) are very good at disguising this problem of plummeting probabilities with amazing rhetorical flourishes!


Post Script.

In case it's not clear, I am pointing out that a deductively valid moral argument based on even say five basic premises with an 80% probability of truth each, produces a conclusion that has 68% probability of being false, given just those premises. It's much more likely to be false than true!

Now your moral argument, which you putting up against the problem of evil (which it apears you've entirely failed to deal with, and which itself renders the moral argument more or less useless, even if its first premise *could* be established), seems on the face of it to be based on a series of thoughts which you find fairly plausible which you think entail your God exists. But even if (i) your argument makes say just 5 basic assumptions with an 80% probability of truth each, and (ii) they do collectively deductively entail your god exists, your argument is still a dismal flop.

I asked that you clarify what your argument is so we can check if this obvious seeming flaw in your argument is really there. But you say you haven't got the time.

POSTSCRIPT 21 DECEMBER. I have just added this comment...

Glenn and others want to create a smokescreen of technicality to disguise the fact that his argument, looks, prima facie, like a dismal flop given its based on a series of "more probable than not" premises. The rule I am applying is: to get the highest probability you can assign to the conclusion in a valid deductive argument, you just multiply the probabilities of the basic premises.

Now yes, there are some exceptions to this general rule. So for example, when a premises is redundant, like so: A, B therefore A. Here, you don't factor in the probability of B, for obvious reasons. Also, when the conclusion is a tautology, its probability will be 1, irrespective of the probability of the premises (though the premises are then all redundant, of course). Also, simple multiplication is not appropriate where there's a logical or known causal connection between premises. The probability of the conclusion may then be either higher or lower than the figure you get by simple multiplying. E.g.

A is male
A is female
Therefore A is male and A is female.

Given our background knowledge that being male makes it highly unlikely you are female (unless a hermaphrodite), it's clear we should not give a value of 26% to the conclusion given a prob of 51% to each premise. The probability is LOWER than you get by simply multiplication. Given that further background knowledge. Ditto (and here the we’re dealing with logical exclusion – the conclusion has a mathematically guaranteed probability of 0):

A is 60 years old
A is 61 years old
A is 60 years old and A is 61 years old.

Other times the probability of the conclusion can indeed be higher.

So yes, there are exceptions to the rule. But the point is they are exceptions to a general rule that does otherwise generally apply and which we'll be entitled to suppose applies in the case of Glenn's moral argument too, unless Glenn can explain why it doesn’t. At this point, we cannot tell for sure, because Glenn won’t even clearly set out what the basic premises of his argument actually are. In which case, we should just shrug and walk away. Glenn’s given us nothing.

Incidentally the “upper bound” stuff, while it looks awfully impressive especially when articulated using long strings of formulae, appears to be based on some rather dubious ideas. I cannot find any reference to it outside of theistic circles (e.g. Tim McGrew). Can you point me to some?

Craig’s reference to it is opaque, btw, in the context of what he says. That looks like an attempt to baffle with bullshit.

But I note in any case that the “upper bound” point, even if it is correct, appears to give us no reason at all to suppose that we cannot, on the basis of saying that Glenn’s basic premises are five with a probability of 0.8 each, draw the conclusion that the probability of his conclusion cannot reasonably be estimated as higher than 0.32, given knowledge of just those premises. Indeed, that’s exactly the conclusion we’re usually entitled to draw in such cases (noting, of course, that there are indeed a few exceptions – perhaps Glenn will say “God exists” is a tautology? In which case the premises will have a lower probability than the conclusion but will be redundant!). So why not in this case? That’s what Glenn would need to explain, once he’s actually identified what his premises are (hint: Glenn might insist there’s some connection between the premises that means the probability of the conclusion should be higher – but the onus is surely then on him to identify this connection). Remember, I am not saying the probability of Glenn’s conclusion will be low. I am saying that if it’s based on a series of merely more-probable-than-not basic premises then (unless this is some sort of special case – see above) the probability of the conclusion cannot be considered, on that basis alone, very high.

POST SCRIPT 23 DEC. Well, I have been getting clearer about how all this upper bound of 1 stuff works, largely thanks to Tim (McGrew?) who is v knowledgeable about it and has been commenting on Glenn's website. It now seems to me that the logic concerning an upper bound of 1 is indeed impeccable. And, it turns out, once all the logical symbolism etc. has been unpacked and understood, completely irrelevant to the point I'm making.

I'll explain exactly why in another full post. It's important to get this stuff straight because, if I am correct, saying "Ah but that's just the lower bound of the probability; the upper bound of the probability of the conclusion is 1" in response to the objection that the probability of the conclusion (assuming independent, non-redundant premises) given just validity and the probabilities of the premises is just those probabilities multiplied, is a complete red herring (indeed, the person who says this is committing the straw man fallacy).

54 comments:

Paul Baird said...

The supplier of the Hitchslap may have left the building but ...

NormaJean said...

Or in other words, the reason Law wants Peoples to say more is because the argument as-is seems intuitively correct and Law is simply not comfortable with that :-1

Steven Carr said...

William Lane Craig neatly trashes the idea that good acts and moral obligatory acts are identical by claiming that evil acts are morally obligatory if commanded by a god.

CRAIG
Rather, since our moral duties are determined by God’s commands, it is commanding someone to do something which, in the absence of a divine command, would have been murder.

The act was morally obligatory for the Israeli soldiers in virtue of God’s command, even though, had they undertaken it on their on initiative, it would have been wrong.

On divine command theory, then, God has the right to command an act, which, in the absence of a divine command, would have been sin, but which is now morally obligatory in virtue of that command.

NormaJean said...

Carr, what you fail to point out is that Craig is not saying that God's divine commands make evil acts good.

Patrick said...

NormaJean- Actually, the quote from Craig supports Carr's interpretation as much as yours. The first clause supports the common Christian interpretation that morality is determined by God's commands. The latter half supports Carr's interpretation. See how it presumes that, in the absence of a divine command to the contrary, the killings under discussion would be murder?

I'm inclined to think that Craig is doctrinaire on this point, meaning that Carr has misread him. But its a misreading that Craig has invited by being a bad writer. Craig probably believes that God has issued a sort of default command against genocide, and that God's commands can craft exemptions to it. But he didn't write that very well at all, and I'm forced to rely on my general understanding of Craig as a very, very vanilla believer in order to supplement his words.

Thrasymachus said...

Re. Probability. Craig himself seems to be of the bizarre opinion that the following conditions are sufficient for an argument to be good:

a) Valid argument
b) Premises more plausible than their negations
c) premises actually true.

This seems to me a bit of a mess. We don't need externalist criterion like (c) for a good argument - there might be good arguments for wrong beliefs, in the same way we might be justifiably believe wrong things.

More importantly, as lots of folks have pointed out, (b) is necessary but not sufficient. We surely want good arguments to lead us to think their conclusions are more plausible than not, but it is easy to show how arguments, even ones with eminently plausible premises, fail to do this (another example: roll 2 fair die: 1) Die 1 came up 1-4, 2) Die 2 came up 1-4, C) both die came up 1-4. Conclusion has P=4/9, but it passes Craig's conditions.)

Lots of guys on youtube said similar things. Craig's reponse seems completely inapposite:

http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=8273

(I've written a bit here: http://www.thepolemicalmedic.com/2010/09/what-makes-a-good-argument/)

Mike D said...

I offered my own comment on his blog:

http://www.beretta-online.com/wordpress/2011/the-conditional-premise-of-the-moral-argument/#comment-13433

Something that seems painfully obvious to me is that even if his argument is valid, nobody has direct, objective access to God; we have only unverifiable claims of "revealed knowledge". An objective moral law that cannot be objectively known is objectively useless.

Steven Carr said...

NJ
Carr, what you fail to point out is that Craig is not saying that God's divine commands make evil acts good.

CARR
So I point out that Craig considers good acts and morally obligatory acts to be two different things, and you refute my by saying that Craig considers commands by his god to be different from good acts?

What sort of refutation is that? Normally, you refute somebody by saying they are wrong , not by saying that they are right.

PATRICK
Craig probably believes that God has issued a sort of default command against genocide...

CARR
No god has ever issued any command.

But Craig believes his god ordered 'Now go, attack the Amalekites and totally destroy all that belongs to them. Do not spare them; put to death men and women, children and infants, cattle and sheep, camels and donkeys'

Thomas Larsen said...

Steven:

"Craig neatly trashes the idea that good acts and moral obligatory acts are identical by claiming that evil acts are morally obligatory if commanded by a god."

Craig doesn't claim that evil acts are morally obligatory if commanded by God. Rather, he claims that certain acts are good if commanded by God and evil if not commanded by God. That's an important distinction to make.

Also, there is a difference between good acts and obligatory acts, as you were right to point out. (But obligatory acts, I suppose, might be a subset of good or neutral acts.)

Steven Carr said...

LARSEN
Craig doesn't claim that evil acts are morally obligatory if commanded by God. Rather, he claims that certain acts are good if commanded by God and evil if not commanded by God. That's an important distinction to make.

CARR
Osama bin Laden made the same distinction.

Murder is good if commanded by Allah and evil if not commanded by Allah.


CRAIG (channeling the late BIN LADEN)
Rather, since our moral duties are determined by God’s commands, it is commanding someone to do something which, in the absence of a divine command, would have been murder.

CARR
So how can good come from God, when a god can declare eating meat moral on a Thursday and immoral on a Friday?

So how can good come from God, when a god can declare working on a Saturday and immoral on a Sunday?

All theists can do is wait for today's orders and declare them to be objectively morally good, even if they are commanded to do what they yesterday called objectively morally wrong.

warrantedbelief said...

Dr. Law,

You have misspelled Glenn's last name in the title of your post. You might want to change that. His last name is Peoples, not People.

Regards,

Dima

Richard Baron said...

For me, the main problem with Glenn's argument (not the only problem) is equivocation on "objective". This could mean lots of different things. If, for example, it means "something on which all rational beings (or perhaps, all rational human beings) would, after careful reflection, agree", premise 1 looks false, but premise 2 has a reasonable chance of being supportable. If, on the other hand, it means "something that has a source outside our minds" premise 1 is in with a chance, but premise 2 looks wrong unless the conclusion is true.

Whatever "objective" means, I think it has to mean something ontological rather than epistemological, and my first suggested meaning should be read accordingly. An argument to the effect that we wouldn't know what to do unless a divinity told us would face a different set of challenges, including the point that correct belief would do just as well most of the time.

Curt Cameron said...

It's the second premise that loses me. What would "objective" morality even mean? Morality is someone's opinion on the idea of an action. How can an opinion be objective?

I have my opinion on morality, Peoples has his opinion, and even if there is a God, then God has his own opinion on morality. It's always subjective! Just because an opinion is God's doesn't mean that it's objective, because I can disagree with his opinion (and if the God of the Bible exists, I certainly do disagree on many subjects).

Now there are some things that every sane person shares the same opinion about. They're still opinions, and they're still not objective. Torturing babies is a bad thing. We can all agree on that. But it's still an opinion, and it's still subjective.

Michael Fugate said...

Curt,
I agree. Perhaps NormaJean can give us a list of "objective" moral values for us to discuss.

Thomas Larsen said...

It seems pretty intuitive to me that moral values exist apart from people's opinions: of course, people will have a subjective opinion of moral values, but that doesn't mean that moral values are not objectively binding—so that it is not right, and in fact deeply evil, for a member of the Taliban to pour battery acid into a girl's face even if his society views such actions as acceptable. Other examples could be given: to rape, torture, and murder a little child for one's own pleasure is horrifically evil; to show love, mercy, and compassion on a sick man is a good thing; and so on.

In fact, almost every human being has an intuition that certain things are right for everyone and that other things are wrong for everyone; we've got no good, non-question-begging reasons to deny the veridicality of this intuition; so we should assume that it's veridical.

I personally find arguments from conscience and guilt more interesting than Craig's version of the moral argument.

cadfan17 said...

Thomas Larsen- What do you mean we have no good reason to doubt this intuition? The intuition that morals exist objectively doesn't seem to come in a vacuum. It comes connected to claims that specific acts are moral or immoral. And we have LOADS of reasons to doubt claims of that nature. Why should we sever the two issues? If the same intuition is at work in both cases, and it does seem to be, then the fact that is unreliable on the one part we can easily check should be relevant to our evaluation of its reliability on other matters.

In other words, suppose I have 5 art critics, and each claims that a different work of art is just obviously objectively the best. I might reason from this that intuitions about the objective superiority of art are not reliable intuitions. Now an apologist for art criticism might claim that just because we cannot reliably intuit which art is best, that doesn't mean that there exists no objective standard of art. But surely if our evidence for an objective standard of art is our intuition that some art is better than others, and if we know from experience that this intuition is unreliable and contradictory, that bears on whether it points to some objective standard in the first place? After all, if these intuitions did point to some objective standard, we would expect them to be more consistent amongst individuals and amongst cultures.

And we don't see that, not in art criticism, and not in morality. My earliest introduction to the morality of other cultures came from reading the Bible. It depicts a culture that was quite satisfied that the proper way to live was as a horde of murdering, raping savages who slaughter their neighbors and savage their minimally pubescent daughters. So satisfied, in fact, that the authors of the old testament placed these moral views in the mouths of their prophets and in the mouth of their God, and enshrined it in their holy text. If we can't even obtain reliable agreement on the morality of the use of pedophilic rape as a weapon of war during campaigns of genocide, why should we presume that our moral intuitions are truth aimed in the slightest?

Curt Cameron said...

Thomas, I don't get it. *I* think it's evil to pour acid on a girl's face, and you do too, but you yourself mention that there are some people who don't. Isn't that an admission that the morality of it is a matter of opinion? If it's objectively immoral, then how could some people think it's OK?

Paul Wright said...

@Curt Cameron: Thomas thinks there are moral facts independent of anyone's opinions (except perhaps God's, I'm not sure). If he were right then the mere fact that people disagree doesn't mean that there are no such facts, because people disagree about other things which are facts (pick your favourite bullshit belief as an example).

I think cadfan17 has a better argument: if the strongest evidence we have for there being moral facts is our intuition about it, we do in fact have evidence that our moral intuitions aren't reliable, namely that we disagree about morality a lot. It might be possible to argue that our meta-ethical intuitions are reliable but our ethical ones are, or something.

This looks a bit like Jeffrey Amos's second rebuttal to the Moral Argument: either God's ideas about morality are so far from our own that we're terribly wrong about it and it's then no stretch to say our moral intuitions are broken about other things, such as the existence of absolutes, or God's ideas are similar to ours, but then, hey, problem of pain.

Paul Wright said...

It might be possible to argue that our meta-ethical intuitions are reliable but our ethical ones are, or something.

Gah! "our meta-ethical intuitions are reliable but our ethical ones aren't, or something."

Anonymous said...

I. if there's no God, there are no objective moral values.
II. there are objective moral values
III. therefore there is a God.

For a start, the grammer is dreadful {in I. does "there's" refer to a posessive on 'there', or does it mean "there is".

II. is missing a final stop after the final "s".

III. should read "therefore, ..."

Assuming someone manages to confront People's about his bad grammer, the next question is does what he meant to say make sense?

I. just means, if there is no God, practically anything else can happen. It does, so I have no problem with I. .

II. is nonsense squared. Here's why. I have objective values, meaning there are certain things which I will or won't do. You and I have objective values. If you invited me to your house, I would not dream of inslting you by flouting your 'house rules'. I would not piss on your fitted carpet, but you may find that other rules apply were you to visit me. You may piss in my front garden, for instance, particularily if it is raining, and you don't annoy my neighbours.

Finally, you and I may study the objective morals of any particular individual, from history or the objective morals of any other group, company, association, country or collective.

Objective morals are a fact; but only if you understand that the are exactly 3 perspectives on the world, no more no less.

Changing the subject slightly, the idea of God existing before man is of course utter nonsense. If there was such a God, He would have felt compelled to create other autonomous beings, in order to escape the tyranny of solipsism. To be a solipsist is to admit that you are utterly mad, and alone in the world,

Pogsurf

Thomas Larsen said...

Pogsurf:

"I. just means, if there is no God, practically anything else can happen. It does, so I have no problem with I."

You agree with premise (1)—without God, there can be no objective moral values. Excellent.

"II. is nonsense squared. Here's why. I have objective values, meaning there are certain things which I will or won't do. You and I have objective values. ... Objective morals are a fact; but only if you understand that the are exactly 3 perspectives on the world, no more no less."

You agree with premise (2)—objective moral values exist.

From (1) and (2), then, you're rationally obliged to believe that God exists. I suppose you will now proceed to change your mind about one of the premises to avoid the conclusion of the argument...

"Changing the subject slightly, the idea of God existing before man is of course utter nonsense. If there was such a God, He would have felt compelled to create other autonomous beings, in order to escape the tyranny of solipsism."

Orthodox Christian theists claim that God is triune—a being made up of three divine persons who relate perfectly to one another. And it's quite likely that God exists timelessly, and perhaps that He has made other worlds in addition to ours. So solipsism isn't a problem for the Christian theist.

By the way, it's a little bit ironic that you should point out someone else's "bad grammer". ;-)

Thomas Larsen said...

Paul, Curt, cadfan17:

This issue raises a whole pile of questions about the extent to which we should trust our intuitions in the absence of compelling defeaters. And, as a Christian, my intuitions about morality are also tied up with my experience of God, which makes matters a bit more complicated.

Part of the reason people disagree so much on the nature of moral values, I think, is because people have a vested interest in behaving in certain ways that may, and in many cases may not, align with the actual set of objective moral values. (Which, as far as I'm concerned, can't be treated merely as abstract principles, or even principles hurled down to us by a distant moralistic deity: they're deeply tied up in the nature of God, and His purposes for His creatures.) But that many people think that certain actions you and I perceive as deeply immoral are instead moral should not lead us to abandon our intuitions that there are objective moral values, but rather to be careful and discerning.

I should note, by the way, that the subjects of moral values may change over time; this is where cadfan17's illustration of a piece of art being perceived differently by different people fits well into a moral analogy. For instance, most societies (in fact, all societies of which I am aware) understand that there is a certain degree of physical modesty which should be maintained in public places. But what that degree is may vary from place to place and time to time, and that's fine (provided other values, like the non-degradation of human beings, are preserved across the board).

I hope that helps to explain where I'm coming from.

Thrasymachus said...

Hello Thomas,

One problem which strikes me is that the warrant you want to apply to moral realism is arising from our particular moral judgements. You earlier appealed to particular things like pouring acid on people strike us as clearly wrong. It is from our belief that is wrong for everyone to do these things that we go to moral realism/universalism stuff like "there are facts of the matter about what should and should not be done".

So if the probative weight of these experiences are undercut, we lose these grounds for believing moral realism. If our urge to think things "really are" good and bad is coming from our intutions from seeing certain evil things, the fact we see on reflection that our particular moral judgements are wildly intersubjective, fails to track etc. etc. then I find it hard about to take our intuition that moral realism as particularly powerful evidence.

(It is also an intuition I do not share. I do find ethical things important, and hold certain particular moral judgements dear. Yet I think we can explain (and justify) these things without recourse to moral realism.)

Steven Carr said...

Throwing acid on faces?

In some people eye's , that is wrong.

Of course, William Lane Craig claims that evil things are morally obligatory if commanded by a god.

And they even stop being evil and become good.

CRAIG
On divine command theory, then, God has the right to command an act, which, in the absence of a divine command, would have been sin, but which is now morally obligatory in virtue of that command.

David Span said...

Why does morality have to be objective?

But to say that an act is morally good if commanded by X but morally bad when commanded by Y is moral relativism. Which seems pretty much to be what Craig is endorsing.

Thrasymachus said...

@Stephen

Re. Probabilities and lower bounds

From what I remember of McGrew's work on this, it is solid. But it reinforces the point you are making.

In a valid, non redundant deductive argument, the product of the premises probability sets a *lower bound* on the probability of the conclusion.* To see why this must be so, consider this argument.

1) If the moon is made of cheese, Socrates is mortal.
2) The moon is made of Cheese
C) Socrates is mortal.

This argument is valid, and P(1) and P(2) are both ludicriously improbable. However, the conclusion isn't. So we might want to assign the probability of the conclusion higher.

However, none of this helps Glenn. Glenn is presumably presenting this argument to try and convince us of the existence of God. So for this argument to be sufficient to persuade us, this lower bound needs to be above 0.5. Otherwise we can still think God does not exist whilst keeping the credences we do in the relevant premises.

I actually can't see any relevance to the more probable than not criterion. Arguments which satisfy all premises about 0.5 doesn't persuade us of the conclusion (we want to know if it is likely that *the collection of* premises is more likely true than false). Conversely, arguments with P<0.5 can be useful. If I think god is less than 1% likely yet hold Glenn's premises at 20% each, I need to reconsider.

*All probabilities need to be epistemic, but that's the right tool for the job.

Curt Cameron said...

Paul Wright said:
"Thomas thinks there are moral facts independent of anyone's opinions (except perhaps God's, I'm not sure). If he were right then the mere fact that people disagree doesn't mean that there are no such facts, because people disagree about other things which are facts (pick your favourite bullshit belief as an example)"

But if we're talking about the physical world, there are the facts, and then separately there are people's opinions about those facts. The world is spherish, but some people have the opinion that it's flat. It's true that the shape of the world is an objective fact, even though people can have differing beliefs/opinions.

However, in the case of morality, all morals are, are the opinions themselves. When we talk about morality, there is no outside, physical fact that we're imperfectly trying to perceive. Morality is opinions. It's simply each person's view of how we humans should act.

If someone is trying to make a case that there is some moral external reality, well, I'd be surprised because it's patent nonsense. But if he did want to make that case, he has a steep burden of proof to climb, and it's crazy-talk to simply use that as the premise of some other argument.

Stephen Law said...

Thanks Thrasymachus. Ah, so this is a McGrew-ism, not some well-established and generally endorsed logical principle? I suspected as much.

Well it does seem wrong to me (which is not to say it is wrong).

I am not sure what probabilities we are talking about for a start. What probability it is reasonable to assign to the conclusion and premises given ones total background knowledge?

Then obviously the probability of the conclusion could be higher than that of the premises. But, obviously, it could also be lower. In fact, even setting aside background knowledge, the probability of the conclusion could be zero despite two premises of say 0.5 each, as in

Ted is 61
Ted is 62
Therefore Ted is 61 and Ted is 62

So why set an upper bound of 1 on the conclusion, but not a lower bound of zero?

In any case, surely the relevant probability is that which we should assign given knowledge of the probabilities of premises alone (rather than our entire background knowledge) i.e. it’s the degree of support provided by the premises that’s relevant – the degree to which they show the conclusion is probable. Who cares what the probability of the conclusion is given other facts? Why is that even relevant?

But now, again, the probability of the conclusion could always go as high as one or as low as zero if we allow the conclusion might be a tautology or contradiction. So again, why set an upper bound of 1, but not a lower bound of zero?

Probably I’m missing something.

cadfan17 said...

David Span- It isn't actually moral relativism. Its divine command theory.

Divine command theorists almost never come out and admit this, because they're bad people who deserve to feel bad.

But in divine command theory, there's only one actual moral claim: "One should obey God." Everything else is derivative.

They never admit this because they tend to also be people who believe very strongly in moral intuitionalism, OR, people who know that their audience believes very strongly in moral intuitionalism. And divine command theory spits on popular moral intuitions like no other theory does. So they spend a lot of time and effort covering that fact up.

Stephen Law said...

PS if the moon/socrates example is McGrew's, that suggests he is talking about the probability of premises and conclusion given total ones background knowledge.

In which case, my response is - (i) why is the lower bound for the probability of the conclusion not zero for any deductively valid argument form (as the conclusion could always be a contradiction), and more importantly (ii) why is this notion of probability even relevant re Glenn's moral argument?

Thrasymachus said...

@Stephen

I think we should be clear that we are dealing with epistemic probability. This is the right sort to use when evaluating arguments. (Besides, many of the premises are postulated necessary truths, so it is only in epistemic probability we can values other than 0 or 1).

If the argument is *valid* you can't assign a credence in the conclusion lower than the product of the premises. Cos the premises entail the conclusion, and so you need to think it is at least as probable as all the premises being true. So valid deductive arguments set up rules among your credences like "I believe X and Y, but X&Y ==> Z, so I cannot believe Z is less likely than X&Y".

For invalid arguments, this does not apply. There is no link between premises and conclusion, so your credences can range freely. This applies in the Ted example you gave.

I agree that, when talking about an argument to persuade people, you need to argue them to accept the lower bound is > 0.5 (otherwise, who cares?) You can appeal to background knowledge when setting the credences for the premises.

My turn to be missing something!

Thrasymachus said...

And, right on cue, I did!

I just assumed the Ted argument was invalid because the conclusion was absurd. Oops. Yet it seems to follow conjunction introduction. I'd want to say something like the language which we use to state our premises implies the contradiction, and when explicitly stated in a symbolic language this deriving contradiction counter-example to the lower bound rule is wrong. So "Ted is 61" is shorthand for "Ted is 61 and not any other age at time t" or similar. That might be counter-exampleable.

I think the underlying theory of lower bounds is robust. I think I've seen similar ideas bouncing around, although more with maths and inference than philosophy. I'm an amateur in those too!

Stephen Law said...

Yes, it is valid. Now I deliberately chose a maths example so it wasn't a formal logical contradiction (at least not obviously). Similarly,

x is red all over at t
x is green all over at t
Therefore x is red all over at t and x is green all over at t

These are famous cases in which the contradiction cannot be, it seems, reduced to a formal logical one (this I seem to remember was how Wittgenstein's logical atomism started to flounder - but I'm no expert on that).

However, if the conclusion of a valid argument form can be a contradiction (formal or not), then why isn't the lower bound of the probability of the conclusion for that argument form zero, irrespective of the probabilities of the premises?

If McGrew pushes the upper bound to 1 because the conclusion could be a tautology, why not push the lower bound to zero because it could be a contradiction? I'm flummoxed.

Thrasymachus said...

(Third time lucky)

I think I've got a much more satisfying answer to the Ted problem:

In the same way premises can be positively covary (they tend to be true or false together), they can also be negatively covary (the more likely one is, the less likely the other is). With positive covariance, the lower bound will be higher than the produce of premises, with negative covariance, the real lower bound would be lower.

I can't construct the mathematics offhand, but I'm pretty sure the limiting case of contradicting premises would have the lower bound at zero. Sound alright?

John Griffith said...

"It's the second premise that loses me. What would "objective" morality even mean? Morality is someone's opinion on the idea of an action. How can an opinion be objective?"

Curt,

You're right, it is mostly opinion. The "opinion" is not the facts of morality but the underlying moral rule of thumb you work from such as "Whatever God prohibits is impermissible" (DCT) and "Whatever harms without warrant is impermissible" (humanism of sorts).

From these rules of thumb objective moral facts do arise such as a divine prohibition on murder. Under this account, premise 1 is of course quite obviously false on its face.

Stephen Law said...

I've been working through the maths but still not sure why the lower bound isn't zero.

But I think it is now clear that the "upper bound" point is that the probability of the conclusion cannot necessarily be deemed 0.32 given 5 basic premise of 0.8 because we need to factor in how probable the conclusion is anyway, even if it's not the case that the argument is valid and has true premises.

Is that right Thrasymachus?

But how is this news?

I mean, we always knew that to say that probability of the conclusion given the premises is 0.32 is not to say that the probability of the conclusion might not be much higher, all things considered.

I have gene x
Those with gene x get cancer y
I will get cancer y

if the premises have a probability of 0.5 each, and this is all the information available, I should conclude my probability of getting cancer Y is 0.25.

But if I have the undeniable symptoms of cancer Y, then I should assign a much higher probability to the conclusion.

Is there any more to the "upper bounds" point than this? Presumably, there is but I am struggling to see what it is at this point...

Paul Baird said...

@ Stephen - talking of McGrewisms, have you seen the revised section on Miracles in the online Stanford Encyclopedia of Philosophy ?

http://plato.stanford.edu/entries/miracles/

Everytime I read it I cannot help but think that if he's serious then Santa Claus really must exist too.

Thrasymachus said...

Hello Stephen.

I think it is lower bound, not upper bound. This example might help:

1) Thrasymachus is stupid, and, Thrasymachus is a medical student.
C) Thrasymachus is a medical student.

This is just an example of conjunct elimination. Suppose you hold a credence in (1) to be 0.5, say. Your credence in the conclusion needs to be at least 0.5. You cannot go lower than this and maintain consistent beliefs - you should have lower credence in a conjunction of premises (so long as they aren't contra-dependent) than you do in a single conjunct.

I think the lower bound point extends to similar arguments. Off hand, it seems to parallel closure under known entailment.

I'm no expert on Wittgenstein, but I think we can get around the problems of valid forms (with plausible premises) deriving contradictions by talking about contra-dependence like I tried to above. Some premises will be independent (in which case you multiply them together to get the lower bound); some covary with each other (in which case the lower bound will be *higher* than their product as the weight given to the "one right and one wrong" term will be lower); and some will covary against one another - that they will likely *not* be true together (in which case the lower bound will be *lower* than the product).

I'm not sure how to do the maths here, although I'm pretty sure it must be done somewhere; that said, I think this can take care of the examples you cite. Just say the collection of premises negatively correlate with one another to such a degree the lower bound is zero.

I think the lower bounds point is important for weighing up how persuasive a deductive argument is. The take home is with arguments with lots of premises you find dubious and no clear demonstration of independence (or otherwise), you are well within your epistemic rights to be sceptical of the conclusion even if you find all of the premises more plausible than not. I don't think there are many more applications in 'the real world' of weighing up arguments than that.

Stephen Law said...

Thanks Thrasymachus. By "upper bounds point" I meant an upper bound of 1. Sorry that's not clear.

You are right about that specific example, but what about:

I have gene X
Those with gene X get cancer Y
I will get cancer Y

With a prob of 0.5 for each premises, the right probability to assign to the conclusion is 0.25. However, given background knowledge, it could be reasonable to give a higher or lower probability to the conclusion. e.g. if i have symptoms of cancer Y, higher. If I have the very rare z gene that stops cancer Y, lower. And that lower probability does not require I revise the probabilities of the premises downwards, so far as I can see.

Thrasymachus said...

Hello Stephen,

I think the fact your credence in getting cancer might go higher than 0.25 is fine, but going lower because of cancer-proofing genes is problematic. I'm no sure there's an easy solution.

I was tempted to say "Any such argument involving credences might turn out to be wrong *in fact*, what matters is making sure your credences are consistent". But that won't fly, because the cancer-proofing gene is epistemically problematic. I might have good evidence I have this gene Z, as well as gene X. Yet we can construct deductive arguments to get incompatible bounds for our credence in getting cancer. That's bad.

I want to hope that if we laid out the cancer example in a wholly formal bit of propositional (or predicate) logic, we'd reveal an implied premise which our knowledge of a cancer-proofing gene would drive down the credence of.

One stable would be this: "those with gene X" needs to specify some set of people, and this set must either be those without gene z, or a random sample unselected for the presence of gene z. Once we know we have gene z (or the higher our credence is of having gene Z), we should now lower our credence of being a member of this set, as it is likely we are in a subset who are at lower risk of cancer than the rest.

However, that's messy (although I think the messiness is the fault of 'formal logic' and not probability theory - these sort of concerns are dealt with neatly and intuitively in Bayes), and even if you don't think my account isn't a load of cobblers, I doubt it will be hard to come up with another counter-example to which it doesn't apply.

cadfan17 said...

McGrew is using "multiply the probability of the premises to get the probability of the conclusion" as a proxy for "multiply the probability of the premises to get the probability that the argument is sound."

Then he's assuming that a sound, valid argument has a guaranteed conclusion, which he figures gets him from the latter quote above to the former.

Am I getting this right?

Steven Carr said...

LARSEN
And, as a Christian, my intuitions about morality are also tied up with my experience of God, which makes matters a bit more complicated.

CARR
You hear voices from your god telling you not to kill people?

What experiences of your god have you had?

How do they tie up to morality?

What do you think is moral that non-believers think is immoral?

Stephen Law said...

Well, I have been getting clearer about how all this upper bound of 1 stuff works, largely thanks to Tim (McGrew?) who is v knowledgeable about it and has been commenting on Glenn's website. It now seems to me that the logic concerning an upper bound of 1 is indeed impeccable. And, it turns out, once all the logical symbolism etc. has been unpacked and understood, completely irrelevant to the point I'm making.

I'll explain exactly why in another full post. It's important to get this stuff straight because, if I am correct, saying "Ah but that's just the lower bound of the probability; the upper bound of the probability of the conclusion is 1" in response to the objection that the probability of the conclusion (assuming independent, non-redundant premises) given just validity and the probabilities of the premises is just those probabilities multiplied, is a complete red herring (indeed, the person who says this is committing the straw man fallacy).

sam said...

I just listened to Peoples' moral argument "solution" to Dr. Law's EGC on the Xian podcast "Unbelievable", and I've clearly missed entirely how it addresses the EGC at all. The EGC as I understand it demonstrates the ‘flipability’ of all relevant ad hoc theodicies. How exactly is the moral argument not susceptible to the same vulnerability? Our Evil God must allow some happiness & hope to exist for certain evils, like disappointment & despair, to be logically possible.

Certainly, some kinds of evil & suffering require that we have knowledge & awareness of good & evil. Our Evil God must impart knowledge of good & evil to humans in order to create the opportunity for greater suffering when they violate their conscience, like poor old Paul (Rom 7:15-24 – I do not understand my own actions. For I do not do what I want, but I do the very thing I hate…For I do not do the good I want, but the evil I do not want is what I do…Wretched man that I am!), or when Evil God forces people to engage in evil acts, like sacrificing their own children to YHWH (EZ 20:25-26) in order to fill them with horror.

Evil God intentionally ‘writes’ ethical principles on our ‘hearts’ (Rom 2:14-15, Heb 8:10; JE 31:33), including an intense instinctual revulsion to murdering & eating one’s own children. Evil God uses this reflexive, instinctual revulsion to cannibalism as the source for psychological punishment to those who engage in polytheism by forcing them to eat their own children (LE 26, DT 28, EZ 5, IS 49, LA 2, JE 19). These people, of course, would not have been able to suffer from their deeds if they did not have a moral intuition of the evil in which they were being forced to engage.

Even William Lane Craig seems to intuitively understand this. In his breathtakingly repugnant (even for Craig) defense of the genocides of the Canaanites, he attempts to divert attention away from the Canaanite victims of rape, enslavement & slaughter by audaciously implying that the true victims of these divinely commanded atrocities were the poor Hebrew soldiers ordered to engage in such depraved acts of bloodlust. He IS correct, at least, in implying that Evil God was intent on creating additional suffering for the Hebrews, as Evil God had presumably supplied them with knowledge of right & wrong, and as Evil God was perfectly able to commit the atrocities himself without exposing the Hebrews to more conflicts of conscience, as EX 32:27-35 demonstrates.

What am I not understanding?

Gaius Sempronius Gracchus said...

Some atheists are also moral skeptics in the sense that they think of morality as about nothing but taboo.

But that does not prevent us knowing the difference between kindness and cruelty, benevolence and malice, etc.

Not all evaluation is moral evaluation.

Thomas Larsen said...

Sam:

Craig does not defend a so-called "genocide of the Canaanites" or anything of the sort.

The trouble is that the "flippability" of a certain theodicy T does not show that T is a poor theodicy. Perhaps most theodicies used to neutralise arguments against the existence of a good God from evil in the world can be flipped to neutralise arguments against the existence of an evil god from good in the world; so what?

Stephen generally says something like, "Well, most of the arguments and theodicies used to support the existence of a good God and defend God's goodness despite the presence of evil in the world can be flipped and used to support the existence of an evil god, too; and, since theists don't accept that an evil god exists, they shouldn't accept that a good God exists, either."

But few theists arrive at the notion of God's goodness by hearing arguments for it; in most cases, some kind of personal experience or testimony is involved. Stephen's argument can be twisted around on a lower level and shown to be problematic: "Well, most of the arguments and theodicies used to support the existence of a kind Joe and defend Joe's goodness despite his occasional fits of anger and social behaviour can be flipped and used to support the existence of a Joe who is a serial killer, too; and, since nobody accepts the existence of a Joe who is a serial killer, they shouldn't accept that a good, kind Joe exists, either."

Thomas Larsen said...

*awkward social behaviour

(Feel free to edit.)

Thrasymachus said...

Larssen:

Flippability is problematic for a given theodicy as the dialectical context is something like this: Theist accepts that some nasty event (like the mutilation) appears at first glance to be a gratuitous evil. But, they urge, the theodicy in question can overcome this first impression, and show on reflection the likelihood of that evil being gratuitous ain't too high after all. In other words, the theodciy should adjust our initial credence of gratuity downwards.

If the theodicy in question is properly flippable (as in it seems to do just as well suggesting things really are gratuitous as them really no being gratuitous), then we shouldn't adjust it down. The theodicy and its flipped counterpart tug equally on our credence and cancel out, leaving our initial (problematic for Theism) assignment unchanged.

This doesn't apply to sceptical theists, who would say we should discard our initial assignment as we don't have epistemic access or whatever, but that is a different move to the one standard theodicy is trying to make. So, if you are willing to accept appearances of gratuity, then the fact a theodicy can be flipped means it does not make the evil less likely to be gratuitous.

Steven Carr said...

LARSEN
Craig does not defend a so-called "genocide of the Canaanites" or anything of the sort.

CARR
Yes he does. He claims murder is not murder if his god commands it.

CRAIG
Rather, since our moral duties are determined by God’s commands, it is commanding someone to do something which, in the absence of a divine command, would have been murder.


CARR
You still haven't answered the question of what your personal experiences are.

Do you hear voices from your god telling you what is right or wrong?

Or am I thinking of the Yorkshire Ripper?

Stephen Law said...

Hi Tom you say: "But few theists arrive at the notion of God's goodness by hearing arguments for it"

Well obviously not as I pointed out in my debate with Craig. This comment, it seems to me, is irrelevant to the EGC. The amount of evil is not supposed to be evidence for an evil god (it would hardly be very compelling evidence, given all the good), but evidence against an all-powerful, all-good good.

Suppose you work at a nursery with a collegue caled Tom. His wife thinks he is wonderfully kind. You see him be nice to some children, but regularly torture others with red hot pokers, etc. for no apparent reason.

You say to his wife - "I'm afraid Tom's not as wonderful as you think. Sometimes he is great, but very often is quite horrifically cruel. He's not all bad, I admit. But he's not all good."

Tom's wife says to you "But you are supposing I base by judgement of his character on what he does at the nursery."

What would be your response? Mine would be "Bafflement at the irrelevancy of that remark, I imagine."

Stephen Law said...

Sorry Thomas that didn't make much sense at the end. What I meant was that the wife saying "But I don't base my judgement about Tom's character on such and such" does nothing to neutralize the point that Tom's behavour at the nursery is indeed good evidence that he's not quite as wonderful as she thinks.

Regarding the thought that some might just know God is god directly, not via argument, you might consider this:

http://stephenlaw.blogspot.com/2011/09/but-i-just-know.html

sam said...

My central question was: How exactly is Peoples’ moral argument NOT susceptible to an Evil god theodicy, just as all the other flippable, good god theodicies? Evil god would have to provide us with a conscience and an awareness of good and evil in order for certain kinds of suffering to be possible, whether they are self-imposed (Rom 7:15-24) or forced upon us by Evil god (EZ 20:25-26). Even Professor Law seems to give a modicum of credence to Peoples’ moral argument if we grant that it’s sound. I don’t understand why.

Evil god gives us instinctive ethical intuitions (Rom 2:14-15, Heb 8:10; JE 31:33) purposely to increase suffering. Of course, this contradicts Gen 3:5, which presents a story that implies that humanity’s ability to have knowledge of good and evil was a direct consequence of disobedience to the will of yhwh. Did this god, good or evil, want us to know right from wrong, or not?

The supposition that Craig doesn’t defend the genocides of the Hebrew bible is so completely devoid of merit that it is not worth responding to.

Bogdan said...

Stephen Law,
From what you wrote in this post I understood that Wes Morriston raises the same objection to the Moral Argument as you do. Could you please point me to Morriston's paper?

Thank you and I'm looking forward to your next post on this issue.

wissam h said...

I have a similar probabilistic argument wrt to Islam.

Pr(Islam is true)= Pr(Qur'an is inerrant)= Pr(x1,x2,...,xn independent propositions in the Qur'an are true) which is always less than or equal to Pr(x1); where x1 is an independent proposition in the Qur'an.

So basically, all you need to do to discredit Islam is to find just ONE proposition in the Qur'an which is either improbable or inscrutable.

That shouldn't be very difficult :p