Friday, February 22, 2013

Craig on Intentionality and Mathematics

Here.

140 comments:

Doctor Logic said...

Really?

What is mathematics? Mathematics is an enumeration of consistent systems. We choose some axioms (the rules of the system) and see what structures and theorems result. We can pick any axioms we want, even ones that seem completely counter-intuitive (like non-commutative algebras for quantum mechanics, or paraconsistent logics). Of course, we prefer mathematical systems that have interesting properties or math systems that map onto physical processes.

Why can we map physics with mathematics? The fact that the universe can be modeled mathematically is just a consequence of the fact that the universe is a consistent system! That's all.

Even if there was more to mathematics, Craig's argument goes nowhere. The mere existence of a god does not predict that the world can be understood by mathematics. A god could make it impossible for us to understand the world with mathematics. If the world had resisted our ability to use mathematical modeling, I'm confident that Christians would be the first to say their god is the kind of god who would make a math-resistant reality! Christians are perfectly happy to declare parts of reality to be mysterious and beyond mathematics when it suits their needs.

Doctor Logic said...

Another annoyance: theists always assume that their god is the kind of god that would make a world just like the one we see. They conveniently pretend that what we see is just what we would expect from a theistic world with no peculiar assumptions. But they're not so generous to physicalism. They'll ask, Why should physics look like it does when it could have been different?

This is completely unfair, and naturalists need to start playing this game, but in reverse. There are far more imaginable theistic worlds than reductionist physical worlds. Given the far larger space of alternative theistic worlds, it is irrational for us to believe we just happen to be in one of the theistic worlds that looks just like one of the more limited reductionist physical worlds. Given a deity, why should the world look this way instead of like some other physical world, or like some non-physical world (the space of non-physical worlds being vastly greater than the space of physical worlds)?

A simple question: Is reductionist physics more or less limited than god?

From what I see on apologetic arguments, you all think that god can do much more than reductionist physics can do. If the space of theistic worlds is much larger than the space of reductionist physical worlds, then, upon finding ourselves in an apparently reductionist physical world, it is rational for us to conclude we probably live in an actual reductionist physical world. It does not matter that a god could create something that looks like a reductionist physical world. What matters is that all reductionist physical worlds have certain features, but only a small subset of conceivable theistic worlds would have those features.

Another example of this double-standard is the fine-tuning argument. God can make a world full of creatures without any fine-tuning because ghosts don't need fine-tuning at all. Can angels dance in the cores of stars and supernovae? Sure they can, because they have no physical restrictions on their existence. Angels are not conditioned to stars and stars are not conditioned to angels.

On the other hand, under reductive physicalism, we're going to find life (and ourselves) finely adapted to physical conditions in our universe (and our part of it) in every possible world (not just a fraction of the time as we would expect under theism). Fine-tuning, if it were even a problem for physicalism, is a hallmark of... you guessed it: physicalism. Under theism, we don't expect fine-tuning.

WMF said...

"Mathematics is an enumeration of consistent systems."

Yeah, like ZFC which is provably consistent except not.

William said...

DL:

I believe that a consistent system has at least one solution. Please tell me what that is, for the universe? 42 I guess?


Or, what do you actually mean by consistent system?

WMF said...

"Or, what do you actually mean by consistent system?"

A set of propositions from which one cannot logically derive a contradiction.

ozero91 said...

Why should we assume that god wouldn't want to minimize the number and frequency of miracles in the universe?

cautiouslycurious said...

Ing,
“Why should we assume that god wouldn't want to minimize the number and frequency of miracles in the universe?”

That’s fine to assume, but you have to do it before the discovery of the phenomenon. You can’t just find something and then be like “God wants the universe to be like X” and then use X as evidence for God. By adding that assumption, the theist is making the hypothesis ad hoc and hence X is not valid evidence for the hypothesis.

William,
“I believe that a consistent system has at least one solution. Please tell me what that is, for the universe? 42 I guess?”

Asking “what the solution to the universe is?” is like asking what the solution to arithmetic is; it just doesn’t make sense.

Doctor Logic said...

WMF,

Godel's incompleteness theorem doesn't affect my argument at all. The theorem says that in systems large enough to include Peano arithmetic, not every theorem in that system has a finite proof. Any such system wherein every truth is finitely provable is inconsistent.

There are systems (like ZFC) which are believed to be consistent, even if some of its theorems don't have finite proofs. In fact, ZFC was invented to avoid paradoxes (like the librarian problem) in naive set theory.

If you don't like my definition of mathematics, then change it to this: "An enumeration of axiomatic systems." Do we use inconsistent axiomatic systems to describe reality? Nope. If a description of reality is rule-based and consistent, it's going to map onto an axiomatic mathematical system.

grodrigues said...

@Doctor Logic:

"There are systems (like ZFC) which are believed to be consistent, even if some of its theorems don't have finite proofs."

Wrong for trivial reasons: *every* proof is finite.

grodrigues said...

@Doctor Logic:

"Why can we map physics with mathematics? The fact that the universe can be modeled mathematically is just a consequence of the fact that the universe is a consistent system! That's all."

The universe is a "consistent system"? Really?

1. What is the language for the formal system known as "the universe".

2. What are the specific wffs of the language that are the axioms (or axiom schemas) of the formal system "known as the universe". Are they recursively enumerable?

3. What are the deductive rules for the formal system known as "the universe"?

Inquiring minds wish to know.

ozero91 said...

"That’s fine to assume, but you have to do it before the discovery of the phenomenon. You can’t just find something and then be like “God wants the universe to be like X” and then use X as evidence for God. By adding that assumption, the theist is making the hypothesis ad hoc and hence X is not valid evidence for the hypothesis."

What? Im not asking if it is fine to assume, Im asking what justification there is for assuming that.

ozero91 said...

If Hume's description of causality is true, is the universe really rule based and consistent?

Doctor Logic said...

grodrigues,

Maybe you should address what you know I mean instead of criticizing my terminology and showing off.

And please don't mistake the map for the territory. Physics is a map. There are many formulations of physical description, and these descriptions are mathematical. Look for your "languages" there. Physical theories are mathematical because they are consistent, rule-based descriptions. If the physics were inconsistent (or not rule-based), the theory would predict everything (and nothing).

If the world has regularities, they're inevitably going to have a mathematical description. Agree or disagree?

The purpose of physics is to identify the axioms of the physical description of the universe. But since we only have the theorems to go on (physical experimental data), our theories are always under-determined.

Doctor Logic said...

ozero91,

Hume said that there's no deductive proof of the principle of induction. I agree. But that's what you would expect if induction is a principle of rationality.

The principle of non-contradiction also has no proof because that would be circular. But this doesn't mean a rational person should reject non-contradiction. Non-contradiction is a rational principle, so it won't have a rational proof. At best, we can say that if the principle of non-contradiction isn't true, it wouldn't be false either because there would be no true or false without it.

Not knowing the axioms of the ultimate description of the world means we lack deductive reason to be certain the past was a guide to our future. I don't think we should interpret the problem of induction to be saying something deep about the universe. In any case, the patterns we have found to date, to the extent they have structure, are going to have a mathematical description. They only way they could fail to do this is for physics to be radically inconsistent.

ingx24 said...

Ing,
“Why should we assume that god wouldn't want to minimize the number and frequency of miracles in the universe?”


I never said this D: that was ozero91

Doctor Logic said...

ozero91,

“Why should we assume that god wouldn't want to minimize the number and frequency of miracles in the universe?”

Why should we assume that physicalism wouldn't just take the form of our physics with the observed peculiar physical constants?

It seems like theists want to ask why they shouldn't assume things about God, but turn around and ask why they should assume analogous things about physicalism.

Making an inference from physics to god or to reductive physicalism requires that we account for the whole space of possibilities in each theory. God has a much larger space of possibilities than reductive physicalism. So, finding ourselves in a reductive, physicalist universe implies theism (certain kinds of it) are probably false.

grodrigues said...

@Doctor Logic:

"Maybe you should address what you know I mean instead of criticizing my terminology and showing off."

Translation: "I will talk out of my ass to fool the unwary and the gullible, but when my tripe is called out I will say that they are showing off! I am really smart!"

ozero91 said...

Im not a math guy and this is off topic, but is there any symbol or operation in math that cant be described by the english language?

Like "2+2=4" can be translated into "two and two are the same as four."

BenYachov said...

>Yes, rodrigues can be a pedantic ass,

Zack in my experience is a primary example of "unwary and the gullible".

Just saying....

I love what a hypocrite you are Zack. Having the Chutzpah to call a professional mathmatician like grodrigues an "ass" while acting like a dick yourself.

Don't you see how self-defeating that is?

Doctor Logic said...

Thanks, Zach.

I've seen Godel's proof, and I know it is technical. The details and finer points certainly escape me. However, is Godel's incompleteness theorem relevant to this discussion?

My intuitive understanding is that Godel's theorem says any formal system that is large enough to contain the axioms of arithmetic will either (a) contain some truths that cannot be proven, or (b) be inconsistent. For example, the Goldbach Conjecture might be true, but not provable.

This is oversimplified to be sure, but is it so far off that I'm wrong about its relevance to our discussion about Craig's claim?

If mathematicians find a particular mathematical system inconsistent (e.g., naive set theory), what do mathematicians do in response? They fine-tune their choice of axioms to avoid the inconsistency. (History of ZFC is a great example.)

If we find a regularity in nature, is it even conceivable that it wouldn't have a consistent mathematical description?

This is the real question.

I can't imagine saying "I know exactly how gravity will move objects, but I can't come up with a consistent mathematical model of it."

cautiouslycurious said...

Ing,
Sorry for the name switch.

Ozero,
DL beat me to the punch. We’re not assuming a particular notion of theism. I don’t know what justification a theist would give for making the assumption you gave.

DL,
“If the world has regularities, they're inevitably going to have a mathematical description. Agree or disagree?”

Don’t forget, we even have a system made for things that don’t exhibit regularities, it’s called probability. So, regardless of how the universe actually is, we have a system that we can fit to our observations. Asking why mathematics fits the universe so nicely is almost like asking why my shirt fits so nicely, it was fitted after the fact by humans.

William said...

MMF:

"A set of propositions from which one cannot logically derive a contradiction."

Since DL has claimed that the universe is such a thing as you are defining, are you then saying you believe (or think DL believes) that the universe is a set of propositions?

William said...

Seriously, I believe there is a circularity in claiming that the universe fits mathematical structures because it is a system and has regularities, or fits certain probabilities.

Why should the universe be a system? Why should tend to fit certain probabilities? If I admit that I can't imagine it being otherwise, I merely admit my own limitations.

WMF said...

If you don't like my definition of mathematics, then change it to this: "An enumeration of axiomatic systems."

There is no reason for why this would have any interesting results whatsoever.
As an exercise, write down the group axioms and then try to find at least 5 interesting results using first order logic. If I recall correctly, there is at least one that can be found this way. If you can find a second one, I'd be genuinely interested in hearing one.

Do we use inconsistent axiomatic systems to describe reality? Nope.

How do you know this? In particular, how do you know that ZFC is consistent?

ozero91 said...

Personally, I would characterize our universe as a collection of concrete objects which behave in certain ways.

William said...

ozero91: " universe as a collection of concrete objects which behave in certain ways"

What is this "behavior" and these "ways"? Is it a concrete object?

Zach said...
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ozero91 said...

By concrete object, I mean an object which can cause something. Unlike abstract objects which cannot cause anything, like f=ma. Matter has certain properties and certain thing that they "tend towards." Like how virtual particles, which come from vacuum fluctuations, "tend towards" dissipation. Long lived particles, such as electrons, do not display that tendency. We can describe these tendencies and behaviors through language and math. Okay, I guess the universe includes abstractions as well.

Doctor Logic said...

William,

"Seriously, I believe there is a circularity in claiming that the universe fits mathematical structures because it is a system and has regularities, or fits certain probabilities."

Then we agree. Intelligibility and the ability to model something mathematically are the same thing.

"Why should the universe be a system? Why should tend to fit certain probabilities? If I admit that I can't imagine it being otherwise, I merely admit my own limitations."

If the universe were unintelligible, then there are two possibilities that I can think of.

1) The universe has no structure, in which case, it's not even clear that it exists because our concept of existence is going to be bound up with consistency. There would be no properties because any proposition about a property of the universe would be simultaneously true and false.

2) The universe is so complex that our brains cannot model the world, not even statistically. But if that were the case, there would be no cognitive function at all. Evolving a brain would provide no benefit because the neurons in our brains couldn't possibly model the complexity of our environment. The fact that brains can evolve and learn to deal with our physical environment means it is possible to find patterns in it using the kind of hardware (wetware) we have.

Thus, under physicalism, we're always going to find ourselves in a universe in which things are intelligible because we cannot find ourselves otherwise. ("Finding" is a cognitive function.)

On the other hand, God could do something else. If cognition is non-physical and not conditioned by evolution, then we could find ourselves (that cognitive process again) without being able to comprehend anything physically regular. Just imagine being an angel or ghost in an ethereal realm, being able to understand speech and morality perhaps, but being utterly confused by all physics.

BenYachov said...

>Yeah Ben because a professional mathemetician would never be a pedantic ass on a blog.

Rather as a profession mathematician he has forgotten more about the issues at hand than you have actually pretended to learn.

Never the less this still doesn't explain your hypocrisy in unjustly calling him a "pandantic ass" while being a dick yourself.

>Go back to hiding this blog is better w/o u.

Speaking of blogs I took a look at your blog.

Yikes!!! I'd call it amateurish and plebeian but that would be an insult to amateur plebes everywhere.

OTOH I can't decide if anything you wrote is lamer than DL last blog post on Theistic Evolution.

William said...

DL:

It seems there is a workable transcendental argument for the formal (patterning) causality of nonmaterial things in the world, and that you agree with that argument.

That such is far from any argument for God or for a physics beyond the 4 dimensions of our mudane existence, I agree.

BenYachov said...

>lol Ben if you had said anything specific in critique about my blog, instead of just spouting like a 12 year old boy who is in over his head with a real intellect, then I would actually care what you think. Go back under the table to keep sucking off Feser, you no-thinking parrot. He will never know who you are, and nobody will ever care.

That just speaks for itself.

Wow Zack you have got some serious mental problems my friend.

Serious problems.

Zach said...
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Zach said...
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BenYachov said...

>Ben you can dish it but can't take it, eh? You started by calling me a 'dick' don't forget.

Or did you start this by calling grodriges a "pandantic ass" then I asked if it wasn't a little hypocritical and
self-defeating to act like a dick? Then out of left-field you dragged poor Feser into this with the creepy vulgar
gay remarks. Yeh what's that about? Where does this irrational hatred of Feser stem from? What did he do to you?
That was a move worthy of PhysicsDave (who like you seems to sharet the same psychotic hatred).

What can I say? Wow!

>You are the weak boy who hits someone but then goes bawling to the teacher when the response is that you got flat-out leveled. lol

Bawling to the teacher? This is a schoolyard to you?

>Now just step off, the adults are having a conversation.

You count as an adult here?

K'ay....

grodrigues said...

@ozero91:

"Im not a math guy and this is off topic, but is there any symbol or operation in math that cant be described by the english language?"

1. The subset answer: any mathematical language is a formalized, very restricted, subset of natural language; therefore, everything you can describe in some formalized language can be described in a natural language like English.

2. The translation answer: you yourself have provided a translation for a mathematical statement; with a little bit of care, every statement in a formalized language can be translated in a natural language: the quantifiers have translations, the logical connectives have translations, etc. Since each wff has a strict syntactical structure, you can build up your translation from the translations of the proper sub-sentences, etc. More often than not, such a translation will be unwieldy and unreadable.

3. The in-principle answer, translation round II: suppose that there was a sentence with a problematic translation. So there is a subsentence (possibly proper) of the whole sentence that is problematic. But this sentence has meaning; it means something to the mathematicians that can understand it, otherwise they could not even communicate. But if it means something, it is in principle translateable. You can then either offer a natural language verbal paraphrase of the meaning, and thus obtain a translation, or introduce a new name as a short-hand for whatever the (possibly proper) problematic subsentence means or denotes, and then again obtain a translation of the sentence into natural language.

@BenYachov:

Thanks, but there is really no need to fret about such a minor issue. I am indeed a pedant. English not being my primary language, I am not quite certain of the entire range of connotations of "ass", but as far as I can tell, I am also *something* of an ass. I also have very little patience and tolerance for know-nothings, fakes, frauds, phonies, sharpies and poseurs. But all of this, what I am or what I am not, is quite irrelevant and immaterial to the truthfulness, relevance and cogency of what I said.

Doctor Logic said...

Zach,

Yes, this argument is essentially the same as the one I gave before, except this is more general.

The other thread was useful for me. I had initially used my argument to try to pick out physicalist worlds. The best challenge was when Crude pointed out that the set of physicalist worlds could include bizarre worlds in which arbitrarily complex structures are brute facts, e.g., spontaneous generation of humans or cylons. Crude's claim was that any physical world God could make was indistinguishable from bizarro physicalism, as the bizarre physical features could just be brute facts.

My revised argument specifically argues for reductive physicalism, wherein the universe starts off in a relatively simple state (e.g., in the Big Bang) with no complex structures, just lifeless elementary particles. In that case, the only known way to get complex life is evolutionary biology. It's also the kind of physicalism I had in mind when I formulated the argument.

BenYachov said...

@DL
>Crude's claim was that any physical world God could make was indistinguishable from bizarro physicalism, as the bizarre physical features could just be brute facts.

Wow your learning? I'm somewhat impressed.

>My revised argument specifically argues for reductive physicalism, wherein the universe starts off in a relatively simple state (e.g., in the Big Bang) with no complex structures, just lifeless elementary particles. In that case, the only known way to get complex life is evolutionary biology. It's also the kind of physicalism I had in mind when I formulated the argument.

I reply: Yeh you are equivocating here between Abiogenesis vs Evolution. They are not the same.

http://edwardfeser.blogspot.com/2013/02/noe-on-origin-of-life-etc.html

Indeed apparently some Atheist philosophers of Science like Alva Noƫ believe QUOTE"that while we have a good idea of how species originate, there is no plausible existing scientific explanation of how life arose in the first place:"END QUOTE.

Now a Thomist in principle has no problem with Abiogensis since on a metaphysical level it is no different than Spontaneous Generation and before Pascal disproved SG scientifically all Thomist believed in Spontaneous Generation and of course believed it was a phenomena of nature not the supernatural.

Anyway I think another revision is in order. Lose the fallacy of equivocation. Abiogenesis is not the same as evolution. They many be related but they are not the same.

Papalinton said...

" .. and before Pascal disproved SG scientifically all Thomist believed in Spontaneous Generation and of course believed it was a phenomena of nature not the supernatural."

Yes. Pascal, an ardent follower of the Jansenist heresy as the Catholic Church proclaimed it to be. So once again it seems Thomists are prepared to base their evidence on illusions, no matter how it might advance their cause, this time relying on a heretic for 'scientific' disproofs to underwrite their dogma.

I'm not sure you're aware of, let alone appreciate the real humour and irony of where you pull your information from, Ben. But it is deliciously amusing.

Doctor Logic said...

BenYachov,

I know the difference between abiogenesis and evolution. It's already integrated into my argument.

Theists argue that we don't know how life first started on Earth. And they're right. We know that complex biochemicals can be created from inorganic compounds, but we've only got as far as creating simple proto-cells and proteins in the lab.

The question is, if reductive physicalism is true, is it expected that we would know how abiogenesis occurred by now?

This is where theists usually make their mistake. They think it's likely we would have solved this by now, when it's not obviously likely at all. In fact, assuming reductive physicalism, it would be most surprising if we knew how abiogenesis worked given our investment.

What is the experimental volume we've tested in abiogenesis experiments? Let's suppose it is 100 cubic meters of raw materials, and we've been running experiments for 50 years (a huge overestimate, I would say).

In contrast, what is the range of parameters, material volumes and time periods that were available to the early Earth?

The current volume of the oceans is about 1.3 billion cubic kilometers, and the window in which life might have formed is on the order of 50 million years. The fact that we haven't replicated abiogenesis might have something to do with the fact that we've (a) not invested much time and effort on the problem, and (b) the effective experimental volume we've worked with is at least 24 orders of magnitude smaller than the early Earth had to work with.

If we're really generous, we might conclude that there's a 50/50 chance we would have solved abiogenesis by now if reductive physicalism is true.

What is the probability of us failing to find abiogenesis mechanisms under the design theory? Well, it's not obviously 100%, but even if it were 100%, it wouldn't matter.

The lack of a successful theory of abiogenesis doesn't affect the Bayesian calculation by more than about a factor two. Whether design is 1 in a trillion or 1 in 500 billion doesn't make much difference.

(This situation would be different if we had totally explored all possible early Earth environment parameters, nutrient concentrations, chemistry, etc., and found abiogenesis to be impossible under reductive physicalism. As I've explained, we're far more than 24 orders of magnitude away from doing that.)

BenYachov said...

As per usual we are on two different pages DL.

>Theists argue that we don't know how life first started on Earth. And they're right. We know that complex biochemicals can be created from inorganic compounds, but we've only got as far as creating simple proto-cells and proteins in the lab.

You are equivocating between Intelligent Design Theorists & other devotees of Paley vs Theists in general. As I pointed out as a Thomist I have no objection to primitive life having a natural cause. Thought granted some Aristotilian Thomists like Oderberg believe philosophically in principle it is not possible for life to have a natural origin it's by no means the mandated view.

Certainly God can & does act threw Secondary causes which is why neither Evolution nor abiogenesis are outside the scope of Theism.

http://edwardfeser.blogspot.com/2013/01/metaphysical-middle-man.html

>This is where theists usually make their mistake. They think it's likely we would have solved this by now, when it's not obviously likely at all. In fact, assuming reductive physicalism, it would be most surprising if we knew how abiogenesis worked given our investment.

It doesn't really matter if you solve it or not. The issues are philosophical in nature not scientific. You can't prove physicalism via Science without begging a host of questions. You can try to make a philosophical case but there are massive incoherencies involved.

http://edwardfeser.blogspot.com/2013/02/the-limits-of-eliminativism.html

As a philosophy Materialisms is in retreat & physicalism is not better than YEC IMHO. There are better ways to be an Atheist & if I where ever to become one like Nagel would be forced to adopt some type of modified Aristotelian view.

But do what you like it's a free country.

Cheers.

Doctor Logic said...

BenYachov,

"Certainly God can & does act threw Secondary causes which is why neither Evolution nor abiogenesis are outside the scope of Theism. "

I agree with this, but I don't believe you appreciate the argument I'm making.

Suppose I have a 6-sided die and a 6000-sided die. I pick one at random, roll that die, and tell you that I rolled a 3. Which die did I probably roll?

Of course, it's much more likely that I rolled the 3 on the 6-sided than on the 6000-sided. In 6000 of these games, I would expect one 3 on the 6000-sided die and 1000 3's on the 6-sided die. Thus, the probability that I had rolled the 6000-sided die is extremely small (about 1 in 1000), but not zero.

Yes, it's POSSIBLE I rolled the 6000-sided die, but I would be irrational to believe that I had, because there are far more things I could roll on a 6000-sided die than on a 6-sided one.

While God could limit himself to efficient causes that look like physicalism, I'm sure you'll agree that he doesn't have to. There are theistic worlds we can imagine that look very different.

For example, if we entered an age of miracles, you wouldn't throw out your God theory on the grounds that "God would limit himself to apparently unguided physical causation!" No, you would be unfazed because God can easily violate the laws of efficient physical causation if he thought it was best.

On the other hand, unguided reductive physicalism HAS to have the kinds of natural history seen on Earth (including abiogenesis). Reductive physicalism is the 6-sided die. Design theism is a trillion-sided die.

ozero91 said...

Well, I think Ben would argue that God isn't just limiting himself to efficient causes. According to history, materialism recognizes just material and efficient causes as fundamental to nature, and design theorists adopted that metaphysical view as well. Ben, following A-T metaphysics recognizes formal and final in addition to the other two.

ozero91 said...

Off-topic, but if it can be argued that a multiverse is to be expected under theism, then there might be a "solution" to the PoE. Anyways, that's the feeling I've been getting from reading the prosblogion recently.

Doctor Logic said...

ozero91,

"Well, I think Ben would argue that God isn't just limiting himself to efficient causes. According to history, materialism recognizes just material and efficient causes as fundamental to nature, and design theorists adopted that metaphysical view as well. Ben, following A-T metaphysics recognizes formal and final in addition to the other two."

I'm sorry if my phrasing has been confusing, but I think this misses the point. Yes, there are other kinds of causation in Ben's metaphysics, but there are also vastly more patterns of life and patterns of abiogenesis possible in his worldview. God can create vastly many more worlds than can reductionist physics. Whether or not there are other forms of causation makes no difference to this point.

Indeed, stipulating alternative forms of causation won't reduce the number of sides on the theistic die. If anything, it will increase the number of sides, making it even less competitive with materialism.

Over and over, I see this struggle on the part of theists to find ways that it is possible for god to have made a world like ours. This is totally misses the point. It's like devising just-so stories in which it is possible to roll a 3 on a 6000-sided die. Of course it's possible for God to make a world like ours! The point is that it is extraordinarily improbable, and granting God more powers only makes the situation worse for the theist.

William said...

DL: I'm glad that you have such a good grasp of what your god is like as a creative agent, to be able to use your knowledge of the range of her preferences as part of your argument :).

I might speculate that such a creator might like the challenge of working within the constraints of physical structures...but then, I'd rather leave the theology to others.

Dustin Crummett said...
This comment has been removed by the author.
Dustin Crummett said...

My revised argument specifically argues for reductive physicalism, wherein the universe starts off in a relatively simple state (e.g., in the Big Bang) with no complex structures, just lifeless elementary particles. In that case, the only known way to get complex life is evolutionary biology. It's also the kind of physicalism I had in mind when I formulated the argument.

Compare:

"My revised argument specifically argues for theism+, wherein God creates the universe in a relatively simple state (e.g., in the Big Bang) with no complex structures, just lifeless elementary particles. In that case, the only known way to get complex life is evolutionary biology. It's also the kind of theism I had in mind when I formulated the argument."

Doctor Logic said...

Dustin,

Unfortunately, that won't work unless you're talking about a non-designer god. The kind of god who isn't intent on designing life might be expected to create physical universes, and let them run their course, whether they create life or not. If life forms in such universes, it had to evolve with no help. But a God who intends to design life has far more options, and that's why the argument demolishes design specifically, not all forms of theism.

Consider three other kinds of worlds from Christian mythology: Heaven, Hell, and Eden. All three of these worlds would be obviously designed and non-physicalist. So, even a survey of Christian mythology reveals obviously designed worlds to be 3 times more common than worlds like our own. The number of life-bearing worlds God can create is vastly greater than the number of life-bearing worlds reductive physicalism can create.

BenYachov said...

@DL

>Suppose I have a 6-sided die and a 6000-sided die. I pick one at random, roll that die, and tell you that I rolled a 3. Which die did I probably roll?

God is not "a being" who exists alongside other beings. God is more analogous to Existence Itself/Being Itself. Thus how can you coherently apply probability to the Divine in the Classic sense? You can't.

Gee DL what part of "not a Theistic Personalist Paley deity" do you not understand?

>While God could limit himself to efficient causes that look like physicalism, I'm sure you'll agree that he doesn't have to. There are theistic worlds we can imagine that look very different.

Sorry but as you conceded before Crude showed how you could have a 6,000 dice reality with Atheism. Second God in the Classic Sense is "limited" in that He cannot make a logically impossible world. But given God's Infinite Nature in the Thomistic Sense it is incoherent to conceive God is ruled by "efficiency" so there is no type of world he is obligated to create nor that He may refrain from creating as long as it partakes of His Goodness.

>For example, if we entered an age of miracles, you wouldn't throw out your God theory on the grounds that "God would limit himself to apparently unguided physical causation!" No, you would be unfazed because God can easily violate the laws of efficient physical causation if he thought it was best.

There are no such things as "laws" of nature that is a Paley Theistic Personalist concept not a classical one. In nature there are observed regularities we call "Laws". Supernatural Acts in the Classic Sense are nothing more than God who is Pure Act actualizing potencies directly instead of threw Secondary Causes & Miracles are nothing more than God actualizing a potency beyond a substances' natural capacity to do so. The "suspending Laws of Nature" nonsense doesn't enter into it.

Also as Crude might point out if we entered into an "Age if Miracles" there is no reason why we might not think using your language some other unknown "physical law" naturally/randomly kicked in to overide the normal regularities or maybe the apparent "violation" of the "laws of efficient physical causation" may be some non-local natural extra dimensional causal phenomena causing physical object to behave in a-typical ways.

BenYachov said...

PART TWO

>On the other hand, unguided reductive physicalism HAS to have the kinds of natural history seen on Earth (including abiogenesis). Reductive physicalism is the 6-sided die. Design theism is a trillion-sided die.

No there is no reason to believe this. A "Ghost world" is just an exotic physical world. If you can believe under physicalism mere matter can be conscious (ignoring the incoherence here for the sake of argument) then why not "energy" or "dark matter" or "exotic matter"? Ghosts in a Ghost world would be physicalism for that world.

Of course in classic Theism Spirits or Angels are not some lame arse Cartesian "immaterial substances" or similar wrong headed notions. They are substansive forms.

Arguments via probability are not philosophical arguments but scientific ones.

If what you call "god" could be proven scientifically sans philosophy then the "god" you would come up with could NOT be God in the Classic Sense. Which in my view actually means Atheism if you succeed vs failing since I will not on rational grounds except anything less then the Classic View as God.

Like I said not even on the same page. You argument is based on a post enlightenment metaphysics that I soundly reject. Try it on the ID people it means nothing to me.

Let me save you some time DL. Your argument is "scientific" in nature not philosophical. Thus any "god" you seek to disprove I can assure you I am a strong Atheist toward believing in in the first place.

So no I don't appreciate your argument but I thank you for your time.

Cheers.

grodrigues said...

@Doctor Logic:

"The number of life-bearing worlds God can create is vastly greater than the number of life-bearing worlds reductive physicalism can create."

Maybe you believe that your pet argument is the best thing that happened to humanity since the invention of sliced bread ("and that's why the argument demolishes design specifically, not all forms of theism"?), but it is not. Here are a few reasons off the top of my head.

1. The set of possible worlds under reductive physicalism is infinite; arguably, the former is a proper subset of the set of possible worlds under broad theism, but this is hardly any consolation since the latter may still have the same cardinality as the former.

2. You are pulling numbers out of thin air. Given that there is no non-trivial uniform probability measure on an infinite set, what exactly is the probability distribution you are using? How on earth can you even answer the question? Does the question even make sense?

3. You are implicitly using a uniform probability distribution over an infinite set. Let us throw you a bone and assume that some sense can be made out of this. But why assume the probability is uniform in the first place? Why assume that God, upon surveying in His omniscience the landscape of all possible worlds, picks one at random? This is just plain stupid. It is like saying that since in the set of all possible decisions you can make, the subset of irrational decisions is overwhelmingly larger than the rational ones, there is an overwhelming probability that you will make an irrational decision. I think no extra comment is needed on the asinine i-logic of this.

4. It utterly and completely *misses* the point of all the traditional, classical arguments for the existence of God, which do not argue from a specific feature of the universe such as the existence of life, but rather from such general metaphysical data as the fact that change exists, or order exists, facts that undergird the very possibility of science in the first place.

Zach said...
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grodrigues said...

@Zach:

"grod are you capable of responding respectfully to someone you disagree with?"

So it seems your problem with me is that I do not respond "respectfully", is that it? This from the guy whose first address to me was to mispell my name (a tradition you continue) and then crack some witless jokes about tortillas? Sorry, but you can take your suggestions and shove them where the sun does not shine.

WMF said...

"His argument is about combinatorics, which you can work out independently of probability distributions."

This is true, nothing about combinatorics requires us to consider probability distrubitions.
However, probability distributions are absolutelycentral to Doctor Logic's argument, so everything grodrigues has pointed out applies here.
I can asure you that this isn't simply being pedantic, these are issues that inevitably arise when dealing with distributions on infinite sets.
The set of possible worlds given physicalism/theism is infinite, because in one world my name is "1", in one my name is "2", and so on, so assuming each of these instances has a probability, no uniform distribution can exist.

In fact, there are very few probability distributions that are even possible to imagine in such a scenario (we don't have a Haar measure for this scenario, so any finite convex combination of point measures of an arbitrary finite number of points is all I can think off here).

And unless this issue gets resolved, considerations of whether or not physicalism or theism allows more worlds of a certain variety aren't going to get us anywhere.

BenYachov said...
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BenYachov said...
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grodrigues said...

@WMF:

"In fact, there are very few probability distributions that are even possible to imagine in such a scenario (we don't have a Haar measure for this scenario, so any finite convex combination of point measures of an arbitrary finite number of points is all I can think off here)."

There are ways to construct non-trivial measures in "bare", "structureless" sets (e.g. by appealing to the ultrafilter principle, possibly in addition with the Hahn-Banach theorem as in the construction of Banach limits). Needless to say, these are all mathematical "intangibles" only of interest to mathematicians.

Doctor Logic said...

grodrigues, WMF,

Though I am not convinced, I think that is is a good idea to criticize the fact that I'm comparing sets of worlds in which there are infinite numbers of elements. However, I think you need to expand on this or else face the risk that you invalidate all inference from experience.

Suppose you are on a jury on a murder trial. You see witness testimony and physical evidence that makes it seem highly probable that the defendant is guilty. However, there are an infinite number of possible histories in which the defendant murdered the victim, and an infinite number of possible histories in which the defendant did not murder the victim, all consistent with testimony. For example, there's the history in which the defendant is a vacationing visitor from an alternate universe 37652353, and happened to be in the wrong place at the wrong time.

Even if we assume no extraordinary physics was involved, the number of possible histories is still infinite in each case because the physical phase space each person could move in is infinite. Did the defendant swung the axe 1mm to the left, 2mm to the left, 3.00000023mm to the left, etc.

I think your best shot here is to argue that statistical comparisons of infinite spaces are okay when you have made empirical measurements of them.

Nevertheless, I don't such an approach will ever be enough to stop the juggernaut. No matter how you narrow the parameters for life (e.g., by specifying that there are 10 million species or less), the number of ways God could create that spectrum of life is vastly greater, and quite possibly infinitely greater than unguided reductive chemistry. God can do more than chemistry alone, and I think you should acknowledge this has consequences in how we should reason from experience.

As for me speaking for God, that's where you have it backwards. By assuming a uniform distribution, I'm refusing to speak for God. I'm doing what ID folk do, and assuming nothing about the designer (assuming nothing means taking a uniform distribution).

You know exactly how this works, as you have seen fine-tuning arguments on this blog. Who gave you the right to speak for nature and assume a uniform distribution of physical constants for universes? Maybe 99.9999% of universes have parameters like ours, and you're just ignorant of the mechanisms. So, if you're going to outlaw the application of uniform distributions where there are unknowns, I look forward to seeing your critical posts on Christian blogs whenever fine-tuning arguments are presented. And to Las Vegas in general.

Likewise, I shall assume you also forsake any argument that speaks to the relative improbability of reductive physical states to god-designed states.

BenYachov said...

@grodrigues

Dr. Oerter attempted an argument similar to DL's. Only he deals with the Fine-Tuning argument not the Argument from Mathematics.

http://somewhatabnormal.blogspot.com/2012/12/rp-fine-tuning-supports-naturalism.html

Oerter was open to the idea his argument might not apply to a Classic View of God.

I'll give him props for that.

Dustin Crummett said...

"The kind of god who isn't intent on designing life might be expected to create physical universes, and let them run their course, whether they create life or not. If life forms in such universes, it had to evolve with no help. But a God who intends to design life has far more options, and that's why the argument demolishes design specifically, not all forms of theism."

Oh, no, you misunderstand. On theism+, God chooses the initial conditions of the universe to ensure that life like us will arise someday. In fact, this makes the existence of an evolutionary process greater than on reductive physicalism as stated; on reductive physicalism as stated, it's quite possible (maybe very likely) that no life arises at all, whereas on theism+ the probability of life arising through an evolutionary process is (as I just told you) 1.

Doctor Logic said...

Dustin,

Your claim is exactly like the following:

"A theory called 6000-sided+, in which the forces and parameters of the dice throw guarantee (in the Newtonian sense) that the roll of the 6000-sided die was going to come up as a 3."

It's true, if you assume a very specific kind of throw of the dice (i.e., that 6000-sided+ theory is true), then the 6000-sided die would roll a 3 with probability 1.

But you have no more reason to assume the 6000-sided+ theory than the 6000-sided- theory which states:

"A theory called 6000-sided-, in which the forces and parameters of the dice throw guarantee in the Newtonian sense that the roll of the 6000-sided die was going to come up as a 5999."

Or any of the other 5993 numbers greater than 6.

That's why the dice game as I posited it causes us to rationally believe that the rolled die is much more likely to be the 6-sided die.

Yes, you can always fine-tune your theory to keep it alive by artificial means, i.e., by assuming some peculiar, rare variant of the original theory that satisfies the observations. But it's just a conspiracy theory of the worst kind, and fails to be a rational inference because the alternative (and failing) assumptions outnumber the good assumption you just made by a higher ratio than in the competing theory.

BenYachov said...

>As for me speaking for God, that's where you have it backwards. By assuming a uniform distribution, I'm refusing to speak for God. I'm doing what ID folk do, and assuming nothing about the designer (assuming nothing means taking a uniform distribution).

So I was right this is an anti-ID argument.

I'm out of here guy.

Of course a parting question "Is Craig's argument an ID argument or not?"

grodrigues said...

@Doctor Logic:

"However, I think you need to expand on this or else face the risk that you invalidate all inference from experience."

You have the burden of proof backwards.

"I think your best shot here is to argue that statistical comparisons of infinite spaces are okay when you have made empirical measurements of them."

"our best shot"? Once again you have the burden backwards. As far as your question, maybe read up on Bayesian justifications of knowledge? And as far as the putative actions of an omniscient God go, how exactly are your analogies relevant? They all presuppose a background where certain laws of nature operate, and certain assumptions about human action are reasonable. But how is this even remotely relevant to the actions of God?

"God can do more than chemistry alone, and I think you should acknowledge this has consequences in how we should reason from experience."

So let me see if I got this straight: you, and only you, is here mounting an argument from the set of *possible worlds*, what could have happened, and yet you are counseling me with a straight face on how we "should reason from experience"? Really?

"You know exactly how this works, as you have seen fine-tuning arguments on this blog."

There is a misunderstanding here; my fault in this case. The only reason I responded was to defuse your categorical pronouncement of victory that your argument "demolishes design". It does no such thing. But otherwise, I simply do not care about design arguments as understood in the modern sense. They are either simply wrong, or if intended as a reductio (say, against naturalism), and even if successful, they prove too little. But why settle for minor arguments, when there are much better ones at hand?

So when you say such things as quoted above, I simply shrug my shoulders. I do have some sympathy for cosmological design and fine-tuning arguments; but ultimately, the reason why I have sympathy for such arguments lies on the fact that they point, even if barely perceptibly, to the things to which *only* God can ground; not this or that feature of the universe such as the existence of life, as if God were just another cause among causes, elbowing its way to have a share in the causal cake so as not be reduced to an irrelevant item in the universe, but rather as the very cause -- in the appropriate sense -- of *any* causality going on in the universe.

Not that your objection to fine-tuning arguments is cogent; it is not. My point is rather, that even if it was, it would be irrelevant to me.

Doctor Logic said...

grodrigues,

"They all presuppose a background where certain laws of nature operate, and certain assumptions about human action are reasonable. But how is this even remotely relevant to the actions of God?"

This is the same prejudice I see from theists whenever these arguments arise. The prejudice says that God has so many more options open to him then we cannot even fathom the depths of possibility, so how dare I suggest that the odds of god doing any particular thing is lower?

Which, of course, is exactly the point. It's like you're okay with the 6-sided versus 6000-sided die argument, but you want to say the argument breaks down in the case of God because God has so many possible sides, we can't begin to count them. Even if we say that potential reductive chemistries also have uncountably many sides, for each side on the reductive chemical dice, there are countless variations of the theistic dice.

"So let me see if I got this straight: you, and only you, is here mounting an argument from the set of *possible worlds*, what could have happened, and yet you are counseling me with a straight face on how we "should reason from experience"? Really?"

You talk a good game (albeit an abusive one), but then you say things like this. All inductive reasoning springs from this principle. The thing that makes the 6-sided die the likely culprit are the alternative possibilities (even if they never actually occurred).

Zach said...
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grodrigues said...

@Doctor Logic:

"This is the same prejudice I see from theists whenever these arguments arise. The prejudice says that God has so many more options open to him then we cannot even fathom the depths of possibility, so how dare I suggest that the odds of god doing any particular thing is lower?

Which, of course, is exactly the point."

So I ask you how exactly is the 6-sided analogy is relevant, and your answer is to repeat the analogy? Shrug shoulders.

And my point is that "odds" does not mean the same thing when it refers to rational agents as it does for natural processes, and much less for an "agent" like God. It is possible to justify the probabilities attached to throwing a 6-sided dice, either on empirical grounds, or presumably (do not know if anybody has done it) by appealing to the equations of motion of a rigid body in a fluid or some such, in an analogous way as the properties of thermodynamical systems can be justified, up to an extent at least, by a consideration of statistical properties of large ensembles. But absolutely nothing follows from the fact that the set of *logically possible* actions of God is humongous. Literally nothing. I am *not* saying that because the set is humongous that "the argument breaks down", although that too is true of the way you formulate it, I am saying that the whole approach is muddleheaded, because, to repeat myself, without more information absolutely nothing follows from the fact that the set of logically possible courses of action is humongous, just as nothing follows from the fact that as of this writing, the set of logically possible course of actions that I can take is potentially infinite (speaking informally).

If you want to rehearse a reverse fine-tuning argument, then I suggest you take a closer look at it, as the serious proponents do *not* say, "Oh the set of free parameters in physical theories is humongous, therefore the set of possible universes is humongous; but the range of life-permitting universes is very narrow. Thus, the probability of hitting one such is vanishingly small". If they did, or do, say such a thing, then they would be, or are, making an incorrect argument.

"All inductive reasoning springs from this principle. The thing that makes the 6-sided die the likely culprit are the alternative possibilities (even if they never actually occurred)."

Actually no, it does not. This is a misunderstanding of how scientific knowledge proceeds. I repeat what I said; if you want to know the answer read up on epistemic justifications of induction. I will say however that this is a can of worms that you do *not* want to open up, as metaphysical naturalists do not look good in the picture -- but this is not related to the question of the existence of God, or at least not directly so.

William said...

grod:
"
It is like saying that since in the set of all possible decisions you can make, the subset of irrational decisions is overwhelmingly larger than the rational ones, there is an overwhelming probability that you will make an irrational decision. I think no extra comment is needed on the asinine i-logic of this.
"

Perfect grod!

This is why DL's argument fails. He is treating his god as a random variable.

WMF said...

There are ways to construct non-trivial measures in "bare", "structureless" sets (e.g. by appealing to the ultrafilter principle, possibly in addition with the Hahn-Banach theorem as in the construction of Banach limits). Needless to say, these are all mathematical "intangibles" only of interest to mathematicians.

For clarification, I'm aware of these, which is why I said they were hard to imagine.
I believe it's even worse than that because as far as I recall, the existence of these objects is undecidable without Zorn's lemma.

Suppose you are on a jury on a murder trial. You see witness testimony and physical evidence that makes it seem highly probable that the defendant is guilty. However, there are an infinite number of possible histories in which the defendant murdered the victim, and an infinite number of possible histories in which the defendant did not murder the victim, all consistent with testimony. For example, there's the history in which the defendant is a vacationing visitor from an alternate universe 37652353, and happened to be in the wrong place at the wrong time.

My (I'm guessing most people's) approach to such scenarios is to completely disregard all scenarios except finitely many (which is admittedly fairly arbitrary). In this case however, it seems like this isn't an option.

No matter how you narrow the parameters for life (e.g., by specifying that there are 10 million species or less), the number of ways God could create that spectrum of life is vastly greater, and quite possibly infinitely greater than unguided reductive chemistry.

There seems to be a fairly simple fallacy at work. As I understand it, the argument is
1) If life were to originate via chemistry in a world where God doesn't exist, then God could create life the exact same way in any world where God would exist
2) In any world where God would exist, there are ways God could create life, that could exist in no world where God would not exist
3) There exists an injective map from the set of ways life could originate via chemistry alone into the set of ways life could originate via God (from 1)
4) This map is not surjective (from 2)
5) No bijection between these sets exists (from 3 and 4)
6) The set of ways life could originate via God is greater than the set of ways life could originate via chemistry (from 3 and 5)

Irrelevant nitpick: we don't know if these are sets.
Serious problem: 5) does not follow from 3) and 4) if both sets are infinite.

However, even if we grant 6, why should this mean anything about the probabilities involved?

P.S. My opinion on design arguments are similar to the ones held by Ben and grodrigues.

William said...

DL:

If your argument is actually only one which you are making to weaken a fine tuning argument for theism, it does succeed in underlining the point that we don't actually know that any given god would have wanted a world like ours.

So maybe that's where the emphasis should lie for you? Not that theism makes the world less likely, but that there is no reason to think it makes our exact world more likely?

grodrigues said...

@WMF:

"I believe it's even worse than that because as far as I recall, the existence of these objects is undecidable without Zorn's lemma."

The ultrafilter principle is strictly weaker than Zorn's lemma by a deep result of Halpern and Levy. On the other hand, by a result of Pincus and Solovay, also from the 1970's it cannot be proved in the "constructive" fragment ZF + DC of ZFC where DC is (countable) dependent choice. If I have not botched things horribly, it is equivalent to the axiom of choice for families of finite sets, but the monograph of Rubin and Rubin is the go-to place to settle such questions.

Doctor Logic said...

grodrigues,

"And my point is that "odds" does not mean the same thing when it refers to rational agents as it does for natural processes, and much less for an "agent" like God. It is possible to justify the probabilities attached to throwing a 6-sided dice, either on empirical grounds, or presumably (do not know if anybody has done it) by appealing to the equations of motion of a rigid body in a fluid or some such, in an analogous way as the properties of thermodynamical systems can be justified, up to an extent at least, by a consideration of statistical properties of large ensembles."

I'm afraid this is another canard I keep running into. There is no difference between dice and rational agents for the purposes of this argument. In the absence of information, we don't have to justify uniform distributions. If I told you that the 6-sided die was loaded, but not in what way, then the odds still come down to 1 in 6 for any roll because you have no information to make you prefer one side to another.

Thus, to the extent that you assume nothing about God, that you don't speak for what God would do, you make God EXACTLY like a die. You can't use mystery to improve your side of the argument. Mystery only makes it worse.

If you had a predictive model of what a god would do, then you would be in a position to beat naturalism. If, in spite of violating conservation of energy, you could pray coal into existence, then you would have evidence that mental concepts (like desire) dominate over physical processes. If you had a theory of god that predicted specific physical constants, then you would be way ahead. Of course, you actually have nothing predictive. You only have mystery.

And, um, your version of the ID arguments on fine-tuning are exactly what they give.

Dustin Crummett said...

"Yes, you can always fine-tune your theory to keep it alive by artificial means, i.e., by assuming some peculiar, rare variant of the original theory that satisfies the observations."

Yes. Good. That was my point.

Now what you need is some reason why restricting yourself to worlds "wherein the universe starts off in a relatively simple state (e.g., in the Big Bang) with no complex structures, just lifeless elementary particles" (NB: and the laws of nature continue to hold, and--unless you really want to try to abuse the anthropic principle--the fundamental laws and constants are such as to make life a possibility, and...) is less arbitrary than theism+.

Doctor Logic said...

Dustin,

It's not an abuse of the anthropic principle. If physics is all there is, then we can only find ourselves in a world where we evolved and in a world that doesn't give a damn about us (as observed).

On the other hand, if design theism is true, we can find ourselves in far more kinds of worlds (e.g., where evolution is plainly not true, or in which we are not dependent on physics for life as per ghosts, angels, etc.).

Your argument fails for the same reason that we can infer anything at all from evidence. In any murder trial, no matter how much incriminating evidence is found, we can always devise some sort of elaborate conspiracy theory in which the defendant is innocent, but has been framed by invisible powers. By your reasoning, trials would be useless. Yet they are not useless because the number of ways of framing a suspect for a crime far exceeds that number of ways the suspect can actually commit the crime.

Your logic would leave you impervious to evidence - there is nothing you could ever see that would alter your opinion. You're effectively saying that you'll stick with theism as the explanation no matter how much evidence accumulates on the other side of the ledger - that it's all an elaborate divine conspiracy theory.

In contrast, I'm being clear to define what alternatives would look like on both sides of the coin. All the reductive naturalist coins look basically like the one we're observing. The vast majority of design scenarios look nothing like the features of our universe or biosphere.

grodrigues said...

@Doctor Logic:

"If I told you that the 6-sided die was loaded, but not in what way, then the odds still come down to 1 in 6 for any roll because you have no information to make you prefer one side to another."

So even if it was wrong to assume that the dice was fair you would still assume the dice was fair "because you have no information to make you prefer one side to another"? Wow, just wow.

"You can't use mystery to improve your side of the argument. Mystery only makes it worse."

Where did I invoke mystery to explain anything whatsoever? Where?

And you do realize that there is a difference between pointing out a flaw in an argument purporting to prove not-P and giving arguments for P, don't you? I did the former, not the latter.

"If you had a theory of god that predicted specific physical constants, then you would be way ahead. Of course, you actually have nothing predictive. You only have mystery."

So now the argument is no longer about the relative sizes of the set of possible worlds under the two hypothesis, but that theists have no predictive theory of what the physical, fundamental constants can be. Not that you have any predictive theory either, but by any chance did you actually read what I have written?

WMF said...

The ultrafilter principle is strictly weaker than Zorn's lemma by a deep result of Halpern and Levy. On the other hand, by a result of Pincus and Solovay, also from the 1970's it cannot be proved in the "constructive" fragment ZF + DC of ZFC where DC is (countable) dependent choice. If I have not botched things horribly, it is equivalent to the axiom of choice for families of finite sets, but the monograph of Rubin and Rubin is the go-to place to settle such questions.

I'll have a look at that, thanks.

Doctor Logic said...

grodrigues,

This is full of awesome:

"So even if it was wrong to assume that the dice was fair you would still assume the dice was fair "because you have no information to make you prefer one side to another"? Wow, just wow."

I have a 6-sided die. It's loaded so that the expected number of rolls on each side in 6N rolls is not N. Not a fair die, you'll agree.

I roll my loaded die. Based on the information I have given you, what is the probability distribution for rolling each number?

REMEMBER! It's a fair die! Which number is most likely to come up and why?

Doctor Logic said...

grodrigues,

"So now the argument is no longer about the relative sizes of the set of possible worlds under the two hypothesis, but that theists have no predictive theory of what the physical, fundamental constants can be."

What makes you think that the argument has changed? If theism predicted a smaller set of compatible universes than reductive physicalism, then my argument would rule theism more probable, would it not?

I realize that you don't accept my argument, but I'm not being inconsistent here.

grodrigues said...

@Doctor Logic:

Just stop; you are embarrassing yourself. Read aloud and ponder over the sentences:

"I roll my loaded die. Based on the information I have given you, what is the probability distribution for rolling each number?

REMEMBER! It's a fair die! Which number is most likely to come up and why?"

If you still do not get what is wrong with them, read them again. And again. And again...

grodrigues said...
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BenYachov said...

I see a contradiction.

WMF said...

"If theism predicted a smaller set of compatible universes than reductive physicalism, then my argument would rule theism more probable, would it not?"

No, for the reasons laid out earlier?

William said...

wiki on the principle of indifference:

====
Applying the principle of indifference incorrectly can easily lead to nonsensical results, especially in the case of multivariate, continuous variables. A typical case of misuse is the following example.
Suppose there is a cube hidden in a box. A label on the box says the cube has a side length between 3 and 5 cm.
We don't know the actual side length, but we might assume that all values are equally likely and simply pick the mid-value of 4 cm.
The information on the label allows us to calculate that the surface area of the cube is between 54 and 150 cm². We don't know the actual surface area, but we might assume that all values are equally likely and simply pick the mid-value of 102 cm².
The information on the label allows us to calculate that the volume of the cube is between 27 and 125 cm3. We don't know the actual volume, but we might assume that all values are equally likely and simply pick the mid-value of 76 cm3.
However, we have now reached the impossible conclusion that the cube has a side length of 4 cm, a surface area of 102 cm², and a volume of 76 cm3!
In this example, mutually contradictory estimates of the length, surface area, and volume of the cube arise because we have assumed three mutually contradictory distributions for these parameters: a uniform distribution for any one of the variables implies a non-uniform distribution for the other two. (The same paradox arises if we make it discrete: the side is either exactly 3 cm, 4 cm, or 5 cm, mutatis mutandis.) In general, the principle of indifference does not indicate which variable (e.g. in this case, length, surface area, or volume) is to have a uniform epistemic probability distribution.

===

The issue here is that since it's reasonable under various anthropic principles that the various randomizedparameters are not fully independent, we should assume that the probability distributions are NON-uniform.

Papalinton said...

Give it a rest grodrigues. DL has simply put a hole in whatever it is you tout as logic in probability.

The reasoning underlying your proposition is as wispy as the prospect of an existent god. The 'pointing out a flaw in an argument purporting to prove not-P and giving arguments for P', is irrelevant to the argument. Indeed it is immaterial.

Doctor Logic said...

William,

I like your response a lot. At least it takes the question of uniform distributions seriously.

And I agree that, not knowing the relationships between observed parameters, the actual mechanisms that connect the observables might limit the space of possible worlds in ways we cannot predict. Choosing a uniform distribution along one line of observables might result in different answers for the ratio of probabilities.

Let's take the box with the cube in it. The probability that the cube is less than 4cm on a side will vary depending on how we define our uniform distribution. And we don't have a unique way to set up our uniform distribution.

Now suppose the box says the cube inside is white. And I have a second box in which the cube is also 3-5cm on a side just like the first box, but the cube in the second box can be any color. We can imagine more than one way to classify color. We could parameterize over RGB (as in HTML), or randomly pick out a photon energy, and our choice of uniform distribution would give different distributions for likely colors (the latter favoring violets, perhaps). Because we parameterize the colors in different ways, we might get different answers for the likelihood that the cube is white and less than 4cm on an edge, depending on our choice. But are we ever going to conclude that the cube in the second box is going to be as likely to be white as the cube in the first box?

Doctor Logic said...

Yes, I had a typo in my comment to grodrigues, but he should have known what I meant. William figured it out.

cautiouslycurious said...

"REMEMBER! It's **NOT** a fair die! Which number is most likely to come up and why?"

Some people aren't used to using the principle of charity. For those who are so inclined, I've corrected the omission to correctly reflect what DL is arguing.

Papalinton said...

William: "This is why DL's argument fails. He is treating his god as a random variable."

And I say a random variable is an apt description. When one casts one's eyes over the course of the historical conception of the Christian god, one cannot be but impressed with not only the changing and chameleon nature of this [putatively] 'live' entity, from one so actively engaged in one's life in years and centuries past to being 'just life/existence itself' [as Ben Yachov's impersonalist nonsubstance proposition would have it], but the range and scale of his early works, miracles, deeds etc have equally metamorphosed into total inactivity in recent times. Miracles, once the scion of innumerable testaments to God's presence in this world have faded into oblivion. Even the millions upon millions of Lourdes' incapacitated hopefuls have been reduced to '60' something official 'genuine' miracles. Miracles in the time of Jesus were a dime a dozen.

grodrigues, Ben has also simply rendered whatever mathematical argument you put forward moot. I quote:

"Arguments via probability are not philosophical arguments but scientific ones.", and
"Let me save you some time DL. Your argument is "scientific" in nature not philosophical. Thus any "god" you seek to disprove I can assure you I am a strong Atheist toward believing in in the first place."

It seems, grodrigues, that your contention for a mathematical model for the existence of a god seems oddly quixotic. As DL points out in an earlier comment, in effect that mysticism by numbers is still mysticism.

WMF said...

The issue here is that since it's reasonable under various anthropic principles that the various randomizedparameters are not fully independent, we should assume that the probability distributions are NON-uniform.

That and we have no meaningful concept of what a "uniform" probability distribution on an infinite set is even supposed to be.

BenYachov said...

Principle of Charity? Seriously People!

grodrigues already said English is not his primary language and grodrigues cited other problems he read in DL's account.

Talk about Chutzpah!

Zack grow up son.

Paps don't strain yourself.

CC would it kill ya to learn some philosophy?

BenYachov said...

>Yes, I had a typo in my comment to grodrigues, but he should have known what I meant. William figured it out.

By that logic you should have figured out English is not grod's primary language and he can only go by what you say.

Hey my grammer and spelking are god aweful but I own my mistakes and I don't blame the other guy for them.

grodrigues said...
This comment has been removed by the author.
grodrigues said...

@Doctor Logic:

From February 25, 2013 12:27 PM " If I told you that the 6-sided die was loaded, but not in what way, then the odds still come down to 1 in 6 for any roll because you have no information to make you prefer one side to another." If you repeat the same mistake twice, even after I pointed out to you, what exactly am I supposed to guess? I am not a mind reader, so I can only go by what you write. So the corrected version is:

"I roll my loaded die. Based on the information I have given you, what is the probability distribution for rolling each number?

REMEMBER! It's *not* a fair die! Which number is most likely to come up and why?"

We do know that because the dice is loaded the probability is *not* uniform, but without more information not much else can be said. So what exactly is your point by making such a question?

cautiouslycurious said...

Ben,
“Principle of Charity? Seriously People!”

Yes, seriously. But apparently you see nothing wrong with misconstruing what someone wrote to find the least charitable version of it and criticize that while leaving their argument by the wayside as evident by your comment history.

“grodrigues already said English is not his primary language”

If he doesn’t fully understand English, then he should have less hubris when reading someone else’s statement. Either way, he was acting uncharitably.

“CC would it kill ya to learn some philosophy?”

Have any book suggestions? If it’s at the local library, I’ll pick it up.

Doctor Logic said...

grodrigues,

"We do know that because the dice is loaded the probability is *not* uniform, but without more information not much else can be said. So what exactly is your point by making such a question? "

Given this information (or lack thereof), a single roll of the die is equally likely (epistemically) to land on any of the 6 faces. Epistemically, the distribution remains uniform because we don't know the detailed distribution. We have to average over all the distributions, and there's no more reason to think it's weighted for sixes instead of twos.

We know that if we roll the die 100 times, we'll get information about the specific way in which the die is loaded. But given only the information that the die is loaded (and not how), we don't know which faces are more likely to appear than the others. In effect, there's no difference between not knowing how the die is loaded and not knowing the specific physics of a particular roll, even if it was Newtonian and the outcome was certain.

The same principle works when I tell you I just rolled a 6-sided die, and I ask you what I rolled. The die has already been rolled, so, ontologically, the outcome is 100% in favor of whatever I rolled. Epistemically, for you, the distribution remains uniform.

BenYachov said...


>Yes, seriously. But apparently you see nothing wrong with misconstruing what someone wrote to find the least charitable version of it and criticize that while leaving their argument by the wayside as evident by your comment history.

Ah I see so the next time you tell me you "don't believe in God" I should assume what you really mean is "I am a strong believer in God".

Gotcha!

>If he doesn’t fully understand English, then he should have less hubris when reading someone else’s statement. Either way, he was acting uncharitably.

So what you are really saying is "heads I win tails you loose"?

Yes this is the Gnu Atheist standard for "charity". It's also the Left Wing's standard but I don't want to get into politics.

>Have any book suggestions? If it’s at the local library, I’ll pick it up.

I told you to read the THE LAST SUPERSTITION and AQUINAS etc...which you can even obtain from your local library threw INTERLOAD.

But if you want to seach for excuses not to read them that is fine. You just will be totally useless in polemicing any version of Theism slightly above Young Earth fundamentalism.

Seriously CC. Would it kill ya to learn Philosophy or do you want to go the way of Paps?

grodrigues said...
This comment has been removed by the author.
grodrigues said...

@Doctor Logic:

"Given this information (or lack thereof), a single roll of the die is equally likely (epistemically) to land on any of the 6 faces. Epistemically, the distribution remains uniform because we don't know the detailed distribution. We have to average over all the distributions, and there's no more reason to think it's weighted for sixes instead of twos."

If the dice is loaded the probability distribution *cannot* be uniform, well, because that is the *definition* of a loaded dice, so what are you saying? That since we do not know the correct answer, the answer must be the wrong one, is that it?

ozero91 said...

Couldn't there be an infinite number of distributions? For example, the unfair die might be loaded in such a way that 2 shows up only once out of 100 rolls, or it show up only once out of 1000 rolls, or 1 in 10,000, or 1 in 1,000,000,000,000,000. How do you make an average when there's an infinite involved?

ozero91 said...

Er, Ben maybe you should recommend something more neutral first, like The Metaphysical Foundations of Modern Science.

grodrigues said...

@ozero91:

Since I already have the fame of being a pedant, might as well have the profit.

"Couldn't there be an infinite number of distributions?"

The sample space is {1, 2, 3, 4, 5, 6} and a probability distribution assigns a real number r(i) in the closed interval I = [0, 1] to each i in the sample space subject to the condition that the sum of the r(i) is 1. This cuts out a closed 5-dimensional manifold with corners up to codimension 5 embedded in I^6. It is now easy to see that it has the cardinality of the continuum.

"How do you make an average when there's an infinite involved?"

Here is the standard way to introduce a probability measure on the above set of measures. Since it is a 5-dimensional manifold, you can transport the Lebesgue measure to it. The presence of corners complicates an already complicated construction (you have to mess up with the sophisticated device of partitions of unity to patch the local constructions, blah blah blah), but since they make up a subset of measure 0 you can neglect them.

What can you do with this? Nothing useful, really.

BenYachov said...

>Er, Ben maybe you should recommend something more neutral first, like The Metaphysical Foundations of Modern Science.

Works for me.

Karl Grant said...
This comment has been removed by the author.
Karl Grant said...

cautiouslycurious,

Yes, seriously. But apparently you see nothing wrong with misconstruing what someone wrote to find the least charitable version of it and criticize that while leaving their argument by the wayside as evident by your comment history.

Minor problem there in accusing grodrigues of misconstruing Dr. Logic's arguments since this is actually third time Dr. Logic advanced this exact same argument on this blog and we can find almost exactly the same statements in each previous thread.

Dustin Crummett said...

"In contrast, I'm being clear to define what alternatives would look like on both sides of the coin. All the reductive naturalist coins look basically like the one we're observing. The vast majority of design scenarios look nothing like the features of our universe or biosphere."

Yes. All the theism+ coins also look like the one we're observing. What I'm asking you to do is explain why theism+ should be given a lower prior probability than reductive physicalism.

Let's take just one of the constraints built into reductive physicalism--namely, that the laws of nature aren't randomly violated. (This isn't explicitly built in, but it should be if what you're saying is going to make any sense.) There are *at least* as many worlds where the laws of nature are violated arbitrarily as there are worlds where they are not, given that for any given way that the laws of nature can be upheld, there are an infinite number of ways they can be violated. (Incidentally, Alexander Pruss argues that, where a "continuant world" is a world that shares our history, the set of continuant worlds that go on to experience catastrophic violations of the laws of nature is beyond cardinality while the set of continuant worlds where the laws of nature continue to hold is at best of a finite cardinality. (If determinism is true, the set of continuant possible worlds where the laws of nature aren't later violated has only one member!)) What's your justification for excluding all these worlds?

I'm not *really* taking seriously the idea that you can just accommodate any evidence by making your hypothesis specific enough; obviously, as per Bayes' theorem, that will just correspondingly lower your prior probability. I was playing around with you, but I guess it didn't come across. What I'm objecting to is taking only a small subset of physicalist worlds and comparing it to the whole subset of theistic worlds. You need some reason why, if you make your hypothesis some specific form of physicalism, I can't just make mine some specific form of theism.

"It's not an abuse of the anthropic principle. If physics is all there is, then we can only find ourselves in a world where we evolved and in a world that doesn't give a damn about us (as observed)."

Well, that's not true (particularly if we take worries about Boltzmann brains and the like seriously.) But my point about the anthropic principle was that, plausibly, on physicalism there's a pretty decent chance that there wouldn't be any us at all. You have to either argue that no, that isn't true, or else pull a "well, but then we wouldn't be around to observe it" type move--which I regard as an abuse of the anthropic principle (since the fact that we wouldn't be around to worry about it if we weren't here doesn't make it any more or less surprising that we *are* here.) Or just build into reductive physicalism that the universe in question is one that's reasonably likely to give rise to life--which, as we've seen, isn't a helpful move.

Doctor Logic said...

grodrigues,

"What can you do with this? Nothing useful, really. "

You can show that ignorance preserves the uniform distribution. Even when we're very confident that the distribution would be highly non-uniform to an omniscient observer, our lack of information about the non-uniformity leads us to a uniform distribution.

In my example, it is equally likely that I will roll a 1, 2, 3, 4, 5 or 6 on the die because you don't know which outcome it is loaded to favor.

For the same reason, even if you suppose that God (or any other agent) is biased in a non-trivial way, that bias does you no good if you don't know exactly how God is biased. If you don't know that a God would create an evolved world, then you have to consider the variety of worlds God could create. And your ignorance leads you to a uniform distribution.

There's nothing inherent in the concept of God that suggests he would make evolved worlds. As I mentioned, even Christian mythology doesn't anticipate it.

I'll say this again because you don't seem to get it. First, the fact that God is an agent is irrelevant. We're not talking about whether God's mind is governed by ontological randomness or deterministic mechanics. We're talking about our own epistemic point of view. The fact that God is unpredictable and mysterious means we have to take a uniform distribution across all the things God could have done. Ignorance makes the distribution more uniform not less. In contrast, all reductive physicalist worlds will look roughly like our own.

cautiouslycurious said...

Karl,
"Minor problem there in accusing grodrigues of misconstruing Dr. Logic's arguments since this is actually third time Dr. Logic advanced this exact same argument on this blog and we can find almost exactly the same statements in each previous thread."

That was aimed towards Ben.

BenYachov said...

>There's nothing inherent in the concept of God that suggests he would make evolved worlds.

From a Classical Theist point of view that is in fact trivially true. But there is nothing inherent in the concept of God that suggests He wouldn't make worlds that contained evolutionary processes either.

>As I mentioned, even Christian mythology doesn't anticipate it.

Clearly you never read Augustine.

http://www.christianitytoday.com/ct/2009/may/22.39.html

grodrigues said...

@Doctor Logic:

"You can show that ignorance preserves the uniform distribution. Even when we're very confident that the distribution would be highly non-uniform to an omniscient observer, our lack of information about the non-uniformity leads us to a uniform distribution."

Please, refrain from talking about what you demonstrably do not know.

"I'll say this again because you don't seem to get it. First, the fact that God is an agent is irrelevant. We're not talking about whether God's mind is governed by ontological randomness or deterministic mechanics. We're talking about our own epistemic point of view. The fact that God is unpredictable and mysterious means we have to take a uniform distribution across all the things God could have done."

Oh I do get perfectly what you are saying and you are as wrong as wrong can be. Just think for a second about what you are saying: we are ignorant of the situation, so we choose a uniform distribution, choice which is a measure of our ignorance. Then you mistake ignorance for knowledge, and go on deriving facts about reality, what God would or would not do. You are saying that since we are ignorant of such and such then such and such must be this and that. You are literally saying that our ignorance dictates what reality is. Amazing, really amazing.

But at this point, you want to maintain such patent absurd nonsense? Be my guest. Every single point I aimed at your "argument" still stands, so unless you have anything of relevance to say I am done here.

ozero91 said...

The principle of indifference according to wikipedia.

"The principle of indifference states that if the n possibilities are indistinguishable except for their names, then each possibility should be assigned a probability equal to 1/n."

We know that the 6 possibilities are not indistinguishable, because we know it is not a fair die. Therefore, we should not assign each side the probability equal to 1/6.

Doctor Logic said...

ozero91,

"We know that the 6 possibilities are not indistinguishable, because we know it is not a fair die. Therefore, we should not assign each side the probability equal to 1/6."

Which side of the die is loaded?

You don't know. So the system is still invariant with respect to a shuffling of the labels.

Suppose I have 6 dice. Each one is loaded to prefer to bring up a side. One is loaded to preferentially roll a 1. The next is loaded to preferentially roll a 2, and so on.

The problem I described is equivalent to me giving you one of the 6 loaded dice at random. You know that the die I have given you is loaded, but you don't know how it is loaded.

Now, what is the probability that your next roll of this die will give you a 1? Give you a 2?

Given the information you have (and don't have) the distribution is symmetric with respect to shuffling the faces on the dice. Therefore, the probability of rolling any specific outcome on one roll is still 1/6.

grodrigues said...

It seems several people raised concerns about my tone, arrogance, and what not. I confess have very little sensibility for such matters; this is no excuse however, so if I have crossed the lines, my apologies, to Doctor Logic in particular, and to the audience in general.

Let us get one thing straight however. If you demonstrably do not know a thing about mathematics and yet go on about how "Mathematics is an enumeration of consistent systems", I will correct you and knock you off your high horse if I can. If you have never set foot on a lab, demonstrably do not know a thing about justifications of induction and yet prattle how "All inductive reasoning springs from this principle. The thing that makes the 6-sided die the likely culprit are the alternative possibilities (even if they never actually occurred)" I will correct you and knock you off your high horse if I can. If you come, guns blazing, boasting of how your pet argument "demolishes design", I will correct you and knock you off your high horse if I can.

Doctor Logic said...

grodrigues,

Thanks.

"I will correct you and knock you off your high horse if I can."

This whole exercise would be pointless and boring if you didn't do your honest best to correct me when you think I'm wrong. So, please don't stop trying to correct me!

I'm not a mathematician. My background is in physics. I'm sure that my mangling of mathematics is as annoying to you as mangling of physics is annoying to me. I just wish that you would acknowledge that what I'm saying works, even if in limited scenarios.

In the case of the dice game, ozero91 responds with the principle of indifference:

"The principle of indifference states that if the n possibilities are indistinguishable except for their names, then each possibility should be assigned a probability equal to 1/n."

If the die is loaded, but we don't know how, then the n possibilities remain indistinguishable except for their names.

WMF said...

I fail to see why anyone continues to talk about uniform distributions as if they have any relevance.

ozero91 said...

"We don't know which side (or sides) are loaded" still implies that the distribution cannot be uniform. So why are we justified in assuming the PoI?

What are the odds you rolled a 2? Well, since I can't assume the PoI, I would say the probability is 1/x. Six variables, one equation. Thats as far as I can go.

grodrigues said...

@ozero91:

Continuing with my pedantery, on second thought, I am using a cannon to kill a fly in my second response to you in February 25, 2013 5:31 PM. Much easier to simply see that the the constraint \sum_i r(i) = 1 defines a hyperplane in R^6, and thus the intersection with the unit cube I^6 is a closed convex set, even a polyhedra, and thus, by a simple linear transformation, a well-behaved subset of R^5 as far as measure goes. Now take the Lebesgue measure induced on this subspace.

note: there are other, conceptually very natural ways to construct a probability measure on a space of probability measures; but if the above sounds gibberish and as so much gobbledygook, these ways are even more gibberish-y and gobbledygook-y.

Doctor Logic said...

ozero91,

What day of the year is my birthday?

What is the probability that my birthday is today?

If you can answer this, then I think you understand how an epistemic distribution can be uniform while an ontological distribution is highly non-uniform.

To you, my birthday is a random variable. But, to physics (or history, if you like) it's not remotely random.

From your perspective, the distribution is uniform because you have no more reason to assign me a birthday of today than tomorrow or yesterday. Neglecting the effect of leap years, you would say there is a 1/365 chance today is my birthday, but you also know that, for me, the person who has more information, the distribution clumps all the probability on a single day.

Back to the dice. You know that the die is loaded to favor an outcome (birthday), but you don't know which. So you have to spread your epistemic probability over every possible outcome consistent with the information you have, so 1/6 for each possible outcome.

On to God. God, if he exists, has specific biases or natures that will result in a particular distribution of universes (perhaps a single universe). But not knowing the specific biases and natures, you have to weight equally across them all. There are different ways to parameterize this uniformity, but none of them are favorable to theism with respect to my argument.

cautiouslycurious said...

I think the disagreement can easily be summarized as "DL is talking about epistemology, everyone else is talking about ontology." Is it really that hard for both sides to see why they are talking past each other and actually talk about the same thing?

WMF said...

Nobody trying to answer what a uniform probability distribution on an infinite set is even supposed to mean?
No one?
Keep talking to yourselves then.

Doctor Logic said...

WMF,

"Nobody trying to answer what a uniform probability distribution on an infinite set is even supposed to mean?"

Let's talk about it.

Is it even necessary? We do cosmology on a finite horizon, even though the universe might be infinite.

Suppose we only consider some finite intervals of physical constants, parameters of life, etc.

For example, how many ways are there of evolving 10 species, 100 species, or 10 million species without design?

How many ways are there of designing and potentially manufacturing 10 species, 100 species or 10 million species?

How many construction materials and mechanisms (e.g., organic compounds, ATP, DNA) do we expect to be shared among 10 species with common descent, 10 million species with common descent?

And how many variations are possible with design?

How many species do we expect to be manufactured (i.e., have no self reproduction) and in what permutations do we expect under reductive physicalism? (hint: approximately zero)

In design? (unlimited permutations)

This analysis might be artificially small, in the sense that we can imagine more than 10 million species, and potentially an infinite number. We can imagine universes much older than our own, etc. We can imagine more theistic variations on each theme than the few we can jot down on paper in 15 minutes.

But it doesn't matter. There's no way that design theism will ever have fewer permutations unless we get a detailed predictive theory of design that is more specific than reductive physicalism.

As we make the space of consideration larger, design theism just crashes exponentially worse/harder than reductive physicalism because the number of designed alternatives grows faster and faster.

I don't see how making our horizons larger will ever make it more likely (or as likely) that design theism is true.

WMF said...

But it doesn't matter. There's no way that design theism will ever have fewer permutations unless we get a detailed predictive theory of design that is more specific than reductive physicalism.

"There seems to be a fairly simple fallacy at work. As I understand it, the argument is
1) If life were to originate via chemistry in a world where God doesn't exist, then God could create life the exact same way in any world where God would exist
2) In any world where God would exist, there are ways God could create life, that could exist in no world where God would not exist
3) There exists an injective map from the set of ways life could originate via chemistry alone into the set of ways life could originate via God (from 1)
4) This map is not surjective (from 2)
5) No bijection between these sets exists (from 3 and 4)
6) The set of ways life could originate via God is greater than the set of ways life could originate via chemistry (from 3 and 5)

Irrelevant nitpick: we don't know if these are sets.
Serious problem: 5) does not follow from 3) and 4) if both sets are infinite.

However, even if we grant 6, why should this mean anything about the probabilities involved?"

grodrigues said...

@Doctor Logic:

"If the die is loaded, but we don't know how, then the n possibilities remain indistinguishable except for their names."

I have already addressed this more than once; you have not responded. Instead, you keep repeating the same mistakes again and again and never actually address the objections posed.

This is the last time I am going to say this. If the dice is loaded the probability distribution *cannot* be uniform; if we do know that the dice is loaded and nothing else, that is exactly the amount of knowledge we have, no more, no less. To say that "In my example, it is equally likely that I will roll a 1, 2, 3, 4, 5 or 6 on the die because you don't know which outcome it is loaded to favor" as you do in February 25, 2013 10:34 PM, and keep doing in all subsequent posts, *IS A CONTRADICTION*; it is exactly the same as saying that the dice is loaded and fair at the same time.

note: to all the clueless gits that accused me of lack of charity; maybe you should read what people are saying and apply the principle to yourself.

It seems that (repeatedly) pointing out a contradiction is not enough; I am beholden to even stricter standards of proof and have to guess a barely coherent paraphrase of what you are saying. Since the above quoted sentence was in response to the construction of a probability measure in a space of probability distributions let us place ourselves in that scenario. So we can ask the question: what is the probability of hitting the uniform probability distribution. Zero. I will repeat just in case you did not read it right: the probability of hitting the uniform probability distribution is exactly zero. So if you took the above mathematical construction as a get-away escape for you, think again. The (induced) Lebesgue measure is indeed uniform, but uniform has in this context a different, but related and more nuanced meaning than when we say that the dice is fair iff the probability distribution is uniform.

So here is a coherent paraphrase of the question you posed: assume I give you a dice. Assume that the dice is produced by a machine in a random way that is modeled by the measure constructed above. What is the probability of the machine handing you a dice whose probability distribution is uniform? Zero. Fix a countable subset A of probability distributions. What is the probability that the probability distribution of the dice produced by the machine is in A? Once again, zero. You can keep asking this type of questions; the point is that *these* questions, which are indeed meaningful, are *irrelevant* as far as your argument goes, which needs a uniform probability distribution on an infinite set to get going (*not* a probability measure on the set of probability measures on a set), a meaningless and faulty premise for all the reasons already explained and that I am not going to repeat.

Doctor Logic said...

grodrigues,

I appreciate your frustration, but you've grabbed the wrong end of the stick again.

Suppose I have a bag of 6 dice. They are all loaded in some way.

My question is NOT "If I draw a die from the bag, what is the probability that it will be a die that is fair, i.e., a die that will generate equal numbers of rolls on all sides in a suitable series of trials?"

As you say, it would be a contradiction if I were to assert that I could somehow draw a fair die out of a bag of loaded dice.

Similarly, as you say, if we had a machine that produced a smooth distribution of dice with different forms of loading, the odds of getting a die that was perfectly fair is zero.

But this is not at all the point that I was making.

My question is like this: "You get the machine to spit out a 6-sided die. As you know, this die is loaded. Now, you are going roll the die. What is the probability that you will roll a 1?"

The answer is 1/6.

There is no difference between this problem and the case where I hold either a nickel, a dime or a quarter in my hand, and I ask you to guess what coin I'm holding. THE HAND IS LOADED! I've already selected a coin for you to guess, and the distribution has all the probability in either the nickel, the dime or the quarter. But, for you, the probability that the coin is a nickel is 1/3.

There is no contradiction here. As casuallycurious said, this is a difference between ontological and epistemological randomness.

grodrigues said...

@Doctor Logic:

"My question is like this: "You get the machine to spit out a 6-sided die. As you know, this die is loaded. Now, you are going roll the die. What is the probability that you will roll a 1?"

The answer is 1/6."

Followed by:

"There is no contradiction here."

Whatever.

Doctor Logic said...

grodrigues,

Suppose you're going to gamble on the outcome of the first roll of a die produced by the machine in the previous comment.

For example, if he gives you 2:1 odds, he'll pay you $2 if you correctly guess the outcome of the first roll of the die.

At what odds will you break even? Above what odds will you keep taking the bet and keep winning on guessing the first roll from dice from the machine?

I mean, come on, the result of the first roll from any die that the machine makes is a random variable because the loading is random. This isn't that hard.

Doctor Logic said...

WMF,

I am thinking about your comment, not ignoring it.

ozero91 said...

Few quick comments. The birthday case isn't parallel to the die argument, because how can a calender be "unfair?" Also, God is 1 "unfair die," not 6 "unfair dice." Lastly, aren't there more than 6 ways to load a 6-sided die? I'm talking about the extent of loading, or the weight, etc.

ozero91 said...

This is a closer scenario. If I have a coin, and I tell you that for this coin, the odds of flipping heads =/= the odds of flipping tails =/= 1/2. I flip the coin. What are the odds I flipped tails?

Doctor Logic said...

ozero91,

The calendar is fair, but the day of my birth isn't. My birthday was determined when my parents did the naughty, and by the specifics of gestation. Efficient causes, set in motion long ago.

When I fill out medical forms, I don't randomly select a day of the year as my birthday. This is because my birthday is not a random variable, ontologically speaking. But for someone who lacks the detailed information about how my birthday is non-random, they have no more reason to assign one day of the year or another as my birthday. My birthday is effectively (epistemologically) random.

"Also, God is 1 "unfair die," not 6 "unfair dice.""

When the machine spits out a loaded die, there is one loaded die. What matters is that, from our perspective, there was an infinite number of different die loadings that the machine could have produced (in principle, if not in practice), and we have no idea which one was produced.

"Lastly, aren't there more than 6 ways to load a 6-sided die? I'm talking about the extent of loading, or the weight, etc."

Yes, but are there more ways of loading for 1's than for 2's? No. The number of possible loadings for each side is the same, no matter how we shuffle the labels. Principle of Indifference, again.

cautiouslycurious said...

Grodrigues,

"note: to all the clueless gits that accused me of lack of charity; maybe you should read what people are saying and apply the principle to yourself."

I suppose this is targeted to me. I understand what your saying, but you haven't addressed DL's point. I hope it's the language barrier rather than intentional. There is no contradiction in what he says, I wrote a program to model what he says in a simulation and the result is roughly uniform. The problem is that you keep misinterpreting what he says so that you can find a contradiction, which is, as I said before, a violation of the principle of charity.

grodrigues said...

@cautiouslycurious:

"The problem is that you keep misinterpreting what he says so that you can find a contradiction, which is, as I said before, a violation of the principle of charity."

And the problem is that I am not misinterpreting anything; I am well aware of the hatch Doctor Logic wants to open to extricate himself. For the reasons already explained, more than once and in various different ways, it does not work. if there is anyone misinterpreting here, it surely is not me; rest assured I am not going to impugn your charity.

ozero91 said...

grod,

Is your machine example directed at DL's comment at February 26, 2013 7:49 AM? Or is it a general point?

grodrigues said...
This comment has been removed by the author.
grodrigues said...

@ozero91:

"Is your machine example directed at DL's comment at February 26, 2013 7:49 AM? Or is it a general point?"

Both.

The dice is loaded iff the probability distribution is *NOT* uniform. Without more information that is all we know. Period. Saying that Doctor Logic is speaking epistemology while I am speaking ontology, is to not know what these words mean and to unnecessarily obfuscate the matter. Knowledge is knowledge *of* reality, even if said reality is the measure of our ignorance. Transforming ignorance (the dice is loaded, nothing else is known) into knowledge (the probability distribution is uniform) is wrong and self-contradictory, a move of despair to save an argument that has more holes than swiss cheese, *none* of which was plugged in.

The machine example is to give one coherent paraphrase of what Doctor Logic is saying (*). But as I pointed out, it is hardly of any consolation, since even if he opted out for this non-contradictory formulation, it would not help him one iota.

(*) the machine example I gave is not a realistic one, because it implies the existence a machine that picked out a point from a set with the cardinality of the continuum. Here is how a physicist would think: partition the space of probability distributions in little cells of "epsilon width". In each such "macroscopic" cell, the distributions are sufficiently close (within "epsilon distance") that the experimental results are "sufficiently close", so we just "average out" each cell. This spits out a probability distribution for each cell; since there are only a finite number of them, we can construct a machine to pick a cell randomly in a uniform way. Criminally simplifying things, this is how statistical mechanics works.

Doctor Logic said...

grodrigues,

Er, you've just jumped the shark.

Transforming ignorance (the dice is loaded, nothing else is known) into knowledge (the probability distribution is uniform) is wrong and self-contradictory

No, it isn't. There are TWO different distributions, and you're either being obtuse or playing silly games by ignoring this.

The first distribution is the distribution of values we would expect in multiple rolls of a single die spat out by the machine. This distribution of these values is non-uniform (e.g., a die weighted to roll more sixes has more probability in the six bucket).

The second distribution is the distribution of values we would get for the first roll from a randomly loaded die (or from a random selections from the set of all loaded dice). This distribution IS uniform. I have as much chance of receiving a die weighted to roll sixes as I have of receiving a die weighted to roll any other number.

These are two different probability distributions, and having one uniform and one non-uniform is consistent, not remotely contradictory. Indeed, it's the basis of how many gambling games work. Every time you shuffle an individual deck of cards, you get a non-uniform distribution of cards in that deck. But the distribution of first cards from future shuffled decks is uniform. Two distributions. See how it works?

If you don't get it, try playing poker. Maybe you'll understand probability by the time you get down to your underwear.

Criminally simplifying things, this is how statistical mechanics works.

Yes, I'm a criminal. All those scientists in statistical mechanics are criminals, too. I mean, if only statistical mechanics worked. Oh, wait, it works brilliantly.

grodrigues said...

@Doctor Logic:

"Criminally simplifying things, this is how statistical mechanics works.

Yes, I'm a criminal. All those scientists in statistical mechanics are criminals, too. I mean, if only statistical mechanics worked. Oh, wait, it works brilliantly."

I am not exactly sure what you read in my statement, but I am pretty sure it is not what you are implying.

Your background is in physics, you say? So is mine. What can I say? Wow, just wow.

ozero91 said...

"Transforming ignorance (the dice is loaded, nothing else is known) into knowledge (the probability distribution is uniform) is wrong and self-contradictory."

Isn't that an example of transforming ignorance into an assumption/hypothesis?

William said...

WMF"
"
1) If life were to originate via chemistry in a world where God doesn't exist, then God could create life the exact same way in any world where God would exist
2) In any world where God would exist, there are ways God could create life, that could exist in no world where God would not exist
"

Sounds right. But add also, assuming God intends life (DL assumed this above)
2'. In any world where life might exist via chemistry, there are any number of ways life might have failed to exist via chemistry.

SO the denominator is changing. And it would seem grodrigues think's it's probably infinite anyway.

grodrigues said...

@ozero91:

"Isn't that an example of transforming ignorance into an assumption/hypothesis?"

Fine by me. But then you have to defend and substantiate the hypothesis. In the artificial situation of the machine spitting out loaded dices there is nothing to defend because the whole scenario is rigged form the start. One cannot simply say that because you are ignorant than the distribution is uniform; that is preposterous and no scientist worth is salt would do that. When investigating natural phenomena, the way forward is clear; we gather data, then we make an hypothesis to explain the data. But the discussion centers around possibilities (logical, metaphysical, nomological, etc.); there is no data to gather, so what can one possibly appeal to? Quite apart from all the unanswered objections, this is the primary sin in the whole debate, to try to force-fit what is at bottom a philosophical issue to be amenable to the methods of the empirical sciences. It just does not work. As the saying goes, if you only have a hammer, everything looks like a nail.

BenYachov said...

Gee Zacky if only you followed your own advice.....