What’s Wrong with the World

Another point is the way that the metaphysical implications of scientific theories change when the science changes.

The best example is determinism: back in the late 1800s, you could argue that free will had to be an illusion, because science had showed that everything was really just atoms obeyed fully deterministic laws. Laplace thought that if you knew the exact position and motion of every particle in the universe at a given point in time, you could extrapolate the future as easily and completely as the past. Science offered no reason for supposing that he was wrong (except for a few anomalies that researchers were picking at), and the course of history since Newton had actually made this picture increasingly reasonable (Laplace fixed up the math; Maxwell explained light, electricity and magnetism...).

...And then along came the quantum revolution and the whole picture fell apart completely. While some people still maintain physical determinism -- I've seen it -- physics no longer supports them. Indeterminacy is real.

Now: suppose you were listening to a philosophical argument over determinism in the 19th century. One of the participants says that yes, physics does seem to support determinism but that the arguments against determinism are so strong that he still refuses to accept it. Would he be an obscurantist?

I know this will sound amusing: But I tend to be a realist and to believe that quantum theory is incomplete. Of course, I'm emphatically not a determinist about agents.

But your point holds for many other examples. The Big Bang was initially resisted because it was believed, understandably enough, to have theistic implications. In fact, if we're going to get into this meta-induction stuff, any scientist who believes _any_ present scientific theory might well use induction to conclude that it will turn out to have some things wrong with it and maybe even need to be replaced fairly radically. Obviously, this shouldn't lead to scientific skepticism. But the naturalist is being quite selective about his use of meta-induction regarding science when he tries to use this weak argument for naturalism itself.

I think it's also very important to remember this: In the cases I have in mind in the main post, it is not the non-naturalist who is asking us to hold out for some later theory that doesn't presently exist. It's the naturalist. The naturalist is looking at some putative evidence against naturalism for which he has no present answer and is issuing an IOU and asking us to accept the IOU on the grounds of the supposed gradual progress of science in whittling away at the space occupied by the non-natural. But this premise, and the validity of any such IOU, need to be challenged directly.

I've enjoyed those quotes Dr McGrew, I've cut and pasted them. And ones you've called to mind for me:

"For every one hitherto unexplained phenomena our scientific investigations uncover two more mysteries to take its place." - Freeman Dyson

"My thesis is that consciousness depends upon an unknowable natural property of the brain...It follows that physics, construed as the general science of matter, is incomplete, because the general properties of matter that the brain exploits to produce consciousness are currently unknown." He even speculates that there is some humanly unfathomable dimensional structure to space-time and matter that leads to consciousness. Review of McGinn The Mysterious Flame

And Pope Benedict XVI on the spiritual sickness that leads to naturalism; which I think is an Archangel in the scheme below.

". . . this optimism that had been discovered was simply a variant of the liberal faith in continuous progress – the bourgeois substitute for the lost hope of faith.

It dawned on me “optimism” is the theological virtue of a new god and a new religion, the virtue of deified history, of a god “history”, and thus of the great god of modern ideologies and their promise. This promise is utopia, to be realised by means of the “revolution”, which for its part represents a kind of mythical godhead, as it were a “God the son” in relation to “God the father” of history.

Despair is the sin against the Holy Spirit because it excludes the latter’s power to heal and to forgive and thereby rejects salvation. Corresponding to this is the fact that in the new religion “pessimism” is the sin of all sins, for to doubt optimism, progress, utopia is a frontal attack on the spirit of the modern age:

With the rage only sacrilege can call forth people let fly at the denial of the god of history and its promises.

The secular imitation of hope is the virtue in the new religion ‘optimism’. Ideological optimism must be distinguished from the optimism that arises from one’s temperament and nature. In reality ideological optimism is merely the façade of a world without hope that is trying to hide from its own despair with this deceptive sham."

The Dyson quotation is especially apt.

I should make clear that my own versions of the naturalist's argument in the main post are not quotations from anyone in particular, though such quotations could indeed be found.

A correspondent, who unfortunately doesn't have time to participate in another blog thread, points out to me quite aptly that Newton's theory itself was considered "spooky" in its day because it involved "forces" rather than being a percussive theory of causation. He also points out the vaunting ambition of sociology in the previous century and its failure to provide us with the planned complete "scientific" explanation of human behavior in the aggregate.

I don't know that it's a clear case that determinism reigned in the 1800s. Remember that Newton could not solve the problem of the motion of three bodies under their mutual gravitational attraction. This left open to him, I believe, the possibility that the orbits of the planets were unstable, i.e., nondeterministic. If I remember correctly, scholars found that his opinion was that God kept the planets in regular orbits.

Great thread.
All this is just a way for evolutionists or God deniers of nature to use errors of men in the past on points where they saw religious truths revealed TO say this is the present and future.
As a evangelical Christian who believes in Genesis I know of no error that can be found in the bible on any point regarding nature.
In the past it was practical errors or theme errors that some religious establishments or societies had based on the error of man but not God's word.
The existence, acts, and recorded acts of GOD as evidenced by observation, discovery, thought or the bible stand tall and confident in the saddle against any naysayers.

The elephant in the living room for all scientific explanation is that all physical theories entail spooky action at an infinite distance. This has not been news since the Eleatics. And it doesn't matter how many forces or fields or messenger particles or curved spaces one throws into the mix. The basic discontinuity of nature affirmed by quantum mechanics has made the problem harder to avoid - has made the handwaving and the airy dismissal of Zeno much more difficult to carry off. The Big Bang is the least of it, so far as theistic implications of scientific theories go: from a quantum perspective, each new event, no matter how trivial, looks more and more like a creation out of nothing. The ontological distance between an event and its successor is no smaller than the distance between nothingness and something.

Even if you get over that hump, you are faced with regularity, which arises because, um, no idea. And then, once you've surmounted that, there is the problem of explaining how the world system coheres as a system from one moment to the next, rather than the far more probable instant descent into chaos.

Which is what you get with the Many Worlds Interpretation.

Bottom line is that it is very hard to see what the naturalist might mean by "nature," unless he is willing to admit natures in the old-fashioned sense of the word. Once do that, and the rest of the Aristotelian-Thomistic camel is very hard to keep out of the tent.

Sorry to mix up camels and elephants in one post.

Newton explained motion by a Final Cause: tendency of two particles to attract by virtue of their mass.
That it was considered spooky is interesting. Maybe Final Causes were not considered respectable among Natural Philospheres in 17th Cent.

"The four points of the compass be logic, knowledge, wisdom, and the unknown. Some do bow in that final direction. Others advance upon it. To bow before the one is to lose sight of the three." Roger Zelazny Lord of Light

The recent research into the causes of religion are based on a few simple propositions:
A) We have separate cognitive processes formulating our expectations of animated creatures and inanimate objects. This has been demonstrated in infants as young as five months.
B) This dualistic perception allows a tremendous social adaption since it permits us to speculate about minds disconnected from bodies, our own as well as others. In other words, it allows a broad range of anticipation of mental states to improve sympathy and cooperation or to preempt an attack. It also provides a default coping mechanism for consideration of personal death, opening the door to the possibility of an afterlife.
C) In addition, humans have a keenly imaginative sense of cause and effect that can be advantageous. If you see bushes rustle you assume there's something there, if predators are around it may be your only warning sign. Running away when you don't have to is a small price to pay for avoiding danger from a real threat.

That and a couple bucks won't even get you a cup of coffee at Starbucks, Step2. _That's_ supposed to tell us that God doesn't really exist and is just a projection of our instincts? Pay no attention to any putative evidence for the existence of God. Move along. Just instincts operating to help us survive by projecting a Super-consciousness onto the world. Nothing to see here.

That's not a very good argument--and that's putting it mildly.

Isn't Step2's comment evidence of the very kind of thinking criticized in the post?

I take it Step 2's argument is: we have a scientific explanation for religious belief, and that two things follow from this.

First, if anyone thinks that the existence of religion itself is enough to repudiate or count as evidence against naturalism, recent (social or natural) scientific advances rebut that claim.

Second, the fact that we have such a good naturalistic explanation of religious belief should lead us to be somewhat skeptical of religious claims. It's certainly possible that any of them is true, but we should keep an eye open on the biases that lead to religious belief in general.

Now, I have no idea, in fact, how good naturalistic explanations for religion are. From what I know, they seem like just-so stories. Moreover, psychological or naturalistic explanations of the origin and function of religious belief can be played against atheists as well. Atheists rebel against father figures, suffer from narcissism, etc.

However, there is one fact that I think is somewhat startling, which is that religious beliefs have been the norm for every culture that we're aware of on earth. (Assuming, of course, that there is such a thing as "religion"; there may be no category that captures all the various things under the heading 'religion', in which case I would revise my claim to say that belief in non-natural intelligent beings has persisted across all times and cultures of the planet.) There has to be some explanation for that. The naturalistic will have some, and so too will the Hickian who thinks that everyone perceives God (or the Transcendent, the One, whatever) in different ways, which helps to explain the diversity of religions on earth.

What is the Christian explanation? Is it that people all over the world have experienced God but have misinterpreted him? Or have experienced angels and demons? Or are just hallucinating/are deluded? (In a recent essay, Mavrodes says that a good explanation for polytheism is experience of angels and demons.)

Bobcat: "Mavrodes says that a good explanation for polytheism is experience of angels and demons."

Where? Is it online? Thanks.

Some sophisticated Christians would explain this way also SOME allegedly otherwise hardly explainable successes of astrology, occultism, and, of course, also some cases of exorcism. But I don't know how solid the available evidence really is.

Cool Bobcat - did a google but struggling to find the essay: do you have a link? Oh and thank you for the intro to Mavrodes, hadn't heard of him.

One can do the "naturalistic explanation" thing for pretty much anything. Here, I'll do it with e-mail and blog threads: It is adaptive for people to take in as much information as possible, including information from distant sources. Therefore, it is adaptive to believe that one is receiving messages from distant people on one's computer. Therefore, there is an adaptive naturalistic explanation for my believing that I am in communication with distant people on blogs. Therefore, I have no reason to think that any of you really exist...Whooops. Something went wrong there.

What is the Christian explanation for the widespread nature of religion?

St. Augustine: "Thou hast made us for thyself, oh God, and our hearts are restless until they find their rest in thee."

St. Paul: "For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things."

St. Paul also conjectures that demonic influence is involved in pagan religion.

Lydia,

I. The first version of the argument for optimistic naturalism is really problematic: How should we count the problems? If we knew how, could we cross out more than half of them?

II. But what about the second version?

You formulate it as follows: „Science has made and continues to make such great progress throughout history, gradually whittling away at the set of things that were previously not scientifically understood, that whatever it is that you are presently bringing forth as evidence against naturalism, I am sure that science will eventually get to that in time and explain it, as well, as entirely the product of natural causes.“

John Post has it similarly: "Plantinga's underlying strategy proves to be very old: point to a stubborn, strategic explanatory gap, argue that (probably) they'll never be able to close it, then suggest a theistic explanation that does a better job (say by closing it without landing in self-referential incoherence, among other things). Not that Plantinga is invoking a God-of-the-gaps. Rather, he is advancing an anti-naturalism-of-the-gaps. Like all such explanatory-gap arguments, this one is vulnerable to, among other things, a kind of meta-inductive argument: in the past when the science on which naturalism draws was criticized for failing to explain this or that, the gap was eventually closed (or shown to be bogus); what was regarded as an impossibility, or at least an improbability, proved instead to be a lack of imagination or knowledge. Why not here, especially since naturalism continues to be a robustly progressing research program?" http://people.vanderbilt.edu/~john.f.post/natdefndpr.htm

Alex Pruss considers it, too: „We've been able to solve many, many explanatory problems naturalistically. Hence, the many remaining explanatory problems which we do not at this point know the answer to are also solvable naturalistically if they are solvable at all, and naturalism is true.“ http://alexanderpruss.blogspot.com/2007/10/duct-tape-and-naturalism.html

III. The question of truth-values of the core historical premises in these arguments in II. Shortly, isn't (natural) science progressively solving and explaining more and more, things which were not explained scientifically before? (Though, even consequently, new questions are constantly arising. But so what? For instance, people who know more replies than other people could also ask more questions. That would not make them not knowing more.)

IV. The question of validity of the arguments in II.

The logic of the arguments in II is really unclear.

(A) Maybe it goes like this: most problems/evidences which were given due treatment (time, experts, resources) were solved/viably explained scientifically (invoking nothing supernatural or even nothing non-physical). Thus, every problem, were it given due treatment, would be solved/viably explained scientifically.

Of course, „due treatment“ is ambivalent and vague and cries for some explication. If this explication were given, then there would remain the problem of counting the problems/evidences. If this latter problem were settled, we would still have to put forward some historical evidence for the mentioned premise (i.e., most problems/evidences which were given due treatment (time, experts, resources) were solved/viably explained scientifically (invoking nothing supernatural or even nothing non-physical) -- and I’m not sure there is any such evidence available. Maybe Tim could make some hints on this point.

(B) Let’s try another way, best suggested by Pruss’ wording.

Suppose first we know how to assort and count problems/evidences. Then we go on as follows.

There are many, many problems/evidences which are solved/viably explained scientifically (invoking nothing supernatural/non-physical). Thus, in the absence of other relevant information, probably most/all problems are solved/viably explained scientifically.

The trouble here is that we have some other defeating, relevant information – some problems are not solved/viably explained scientifically: how the sodium got into the water, or what caused the beginning of the universe, or why there are natural laws, or why Jenny doesn't love me, or where did the mind come from, or why did Napoleon try to conquer Europe, or why the physical constants are fine-tuned (though I know you doubt the fine-tuning argument), or why the disciples and the St. Paul were willing to die for the claim they met the resurrected Jesus, etc.

(C) So, let’s try once more. There are many, many problems/evidences which are SOLVABLE/viably EXPLAINABLE scientifically. Thus, in the absence of other relevant information, probably most/all problems are solvable/viably explainable scientifically. But the absence condition is satisfied because we don’t know about any problems/evidences which are probably insolvable/viably unexplainable scientifically. (Or, at least, the optimistic naturalist/scientist believes so and takes the opposite view (i.e., we do know about some problems/evidences which are probably insolvable/viably unexplainable scientifically) as problematic, doubtful, and begging the question against naturalism/scientism.) So, for ANY hard problem you mention, that problem is probably solvable/viably explainable scientifically. And if this probability is high enough, then probably even the set of ALL of them is solvable/viably explainable scientifically. (This would could be a response to J. P. Moreland’s and W. L. Craig’s note that „even if the gaps in naturalistic scientific explanations are getting smaller, this does not prove that there are no gaps at all.“ Philosophical Foundations for a Christian Worldview, 2003, p. 363.)

(D) Maybe the argument stated in (C) could be specified using direct inductions, like you and Tim do in your book Internalism and Epistemology, in the ch. on induction.

Suppose we have a sample S of many, many problems/evidences solved/viably explained scientifically. Thus, S is also a sample of many, many problems/evidences solvable/viably explainable scientifically – for what is solved/explained is solvable/explainable. Then we go on the following way.

1. At least a* of n-fold samples exhibit a proportion that matches the population.

2. S is a big, random, n-fold sample of problems/evidences with respect to matching the population of all problems/evidences.

Thus, given the absence of other relevant information,

===== (with probability a*)

3. S matches the population.

Further,

4. S has a proportion of 1 (i.e., 100%) of scientifically solvable/viably explainable problems/evidences.

Thus, given the absence of other relevant information,

5. The proportion in the population of all problems/evidences lies around 1 (+/- some degree of precision e).

6. X is a random problem/evidence from this population with respect to being solvable/viably explainable scientifically.

Thus, given the absence of other relevant information,

===== (with probability around 1)

7. X is solvable/viably explainable scientifically.

Note: Ad (5). I’m not sure it makes sense to say that a proportion of a population is in the interval 1 +/- e, given that e is greater than 0 and no proportion is greater than 1. I’m not very good at the technical stuff.

(E) I suppose Pruss, you, and Tim would all deny that S (in the argument in D) is a random, non-rigged, sample, and that the absence conditions are satisfied.

Pruss says: „The set of problems that we've solved naturalistically is not a random sampling of the explanatory problems. Rather, it just is the set of problems that we've solved naturalistically.“

Similarly Tim elsewhere: “That would be like my arguing that since I have won every footrace that I have ever run against people ages 5 and younger, I can probably beat anyone. The reference class for my sample is rigged in my favor.“

(F) But how, exactly, do we know that S is rigged? I guess because of the existence of the problems/evidences not solved/viably explained scientifically: e.g., how the sodium got into the water, or what caused the beginning of the universe, etc. Right?

(G) But IF such hard problems were rare enough, the sample bias of S would be insignificant. Of course, I’m not good at statistics, but I believe Tim has a specific idea how this suggestion could be fleshed out precisely.

(H) But ARE the hard problems rare enough?

Dyson, cited above by Martin, suggests otherwise: "For every one hitherto unexplained phenomena our scientific investigations uncover two more mysteries to take its place."
Of course, we are still assuming we know how to count problems/evidences.

But it’s noteworthy that Moreland and Craig suggest, on the contrary, that the hard problems for science are rare: „After all, what else would one expect of gaps but that there would be few of them? ... primary causal gaps are God's extraordinary, unusual way of operating; by definition, these will be few ... the evidential or sign value of a miracuous gap arises most naturally against a backdrop where the gaps are rare, unexpected and have a religious context (e.g., there are positive theological reasons to expect their presence).“ (Phil. Foundations, p. 363.)

I suppose many would object here that the hard problems/evidences are not confined to miracles.

V. To sum up, in reaction to the optimistic naturalist/scientist there are at least these replies:

-- How should we count all problems/evidences?

-- If we knew how, could we cross out the (overwhelming) majority of them as solved/viably explained scientifically?

And I add:

-- If we could cross out, maybe we could still point to certain hard problems/evidences, AND then employ a variant meta-induction, a sort of a reversal of the arguments in (C) and (D) above, with the following premise:

most problems/evidences which were unsolved/unexplained viably by a some perspective in spite due treatment (time, resources, etc.) have been shown to have no possible solution/viable explanation on the given perspective. So, the hard problems are not solvable.

But if the premise just mentioned could have a sufficient support in the history of ideas, I don’t know. Another question for a historian of science.

VI. Finally and as for the pessimistic meta-induction (most scientific theories have been refuted, etc.), I suppose Post and Co. would try to make some use of a defense of scientific realism and the concept of approximate truth of certain scientific theories.

I invited Dr Post via e-mail to our discussion, but he's swamped by his current projects.

So Post's argument seems to be:
1. Everything that in the past has been pointed out as naturalistically inexplicable, has eventually been explained naturalistically.
2. Therefore, everything we point as naturalistically inexplicable, will eventually be explained naturalistically.

To make the argument precise, we need to specify what "the past" means, or we have obvious counterexamples, such as the case of the life-friendly constants in the laws of nature, which has in the past (say, thirty years ago) been pointed out as not naturalistically explicable, and which still has not been explained naturalistically. (Except in the weak sense in which a naturalistic hypothesis has been given which, if true, would explain the fact. But that's a trivial thing--for any fact, we can sit back in our armchairs and come up with a naturalistic hypothesis which, if true, would explain the fact. The hypothesis has to be one that we have good reason to believe to be true.)

Maybe, then, "the past" means something like "150 years ago". But again it's easy to find problems that are not solved now, weren't solved then, and were thought then by some not to admit of a naturalistic solution. Say, the problem of consciousness. The question of why there is something rather than nothing.

OK, so maybe in (1) we replace "everything" by "most things". But then the inductive conclusion should be that most things that are now pointed out as not admitting of a naturalistic solution will have a naturalistic solution. And that's not good enough for Post's purposes.

1. As you suggest, Vlastimil, we need to distinguish the category of “problems” or “questions” unexplained by purely physical explanations from miracles, strictly construed. Once that distinction is made, I would strongly question the claim that such problems or questions are rare. It is, of course, a matter of how one categorizes them. For example, if we treated “human motivation” as a _single_ problem, then we would get a much, much smaller number than we would get if we counted all the questions about specific human motivations that could be asked. (“Why does Joe love his wife?” “Why does Joe want to be a fireman?”) On the other hand, by that same procedure, we could categorize all the problems solved by purely physical means in, say, chemistry as a single item: “chemistry questions” If we do count all the questions that could be asked about human motivation _alone_, I think that we will easily match or outnumber the questions that have been answered by purely physical means.

2. We know _for a fact_ that the process of “science solving problems by purely physical means” involvess a non-random process of problem selection. There is nothing even remotely like a process whereby scientists reach into a bag containing all the questions in the world that could be asked about anything whatsoever and select at random their research projects! Scientists quite rationally usually try to tackle those problems that are tractable to their methods--hence, most often, problems concerning physical systems. And indeed the vaunting pronouncements last century about the science of sociology should serve as examples of the _failure_ of purely physical methods once they are taken and applied to persons. So, too, I think, should the attempts to “solve” the problem of criminal recidivism by treatment.

3. Beyond points 1 and 2, the entire inductive naturalism argument is quite simply an attempt to evade evidence. Consider how silly a parallel would look:

Most people cannot jump very high when playing basketball.

You say that Michael Jordan can jump very high when playing basketball.

But any evidence you might want to bring to that effect is probably explainable in some other way, because I already know that most people cannot jump as high as you say Michael Jordan can jump.

The strategy here is to dismiss evidence without reckoning with its actual force, on the grounds that the conclusion the other person draws from the evidence is an unusual conclusion. But that is simply absurd. _Even if_ the phenomenon argued for is a rare one (as excellent basketball players are rare among human beings), the evidence about this particular thing is what it is and must be reckoned with. It is simply folly to dismiss evidence on the grounds that “that sort of thing doesn’t happen very often.” This would be a radical abuse of induction. The whole point of a pure induction is that there is no reason to take the item in question to be different from the other members of the set. But whether the item in question is different from the other items in the set is *precisely what is at issue*. The non-naturalist brings to the table evidence for a miracle, an argument for the irreducibility of the mind, and the like. At that point one must reckon with the evidence. One _cannot_ use induction to dismiss the evidence without begging the question against the non-naturalist. Please notice that the non-naturalist is not raising some bare anti-inductive skeptical worry: “Oh, but _what if_ this item is different from the other items?” The non-naturalist is _arguing_ that this item is different from the questions that have been entirely physically answered.

Hi Lydia, you are displaying quite a presuppositionalist bent IMHO. I wonder about the questions you raise [why does Joe love his wife] and [why does Joe want to be a fireman] and think IF one knows enough about man--like God does, he could explain a cause and effect relationship that would be provable and falsifiable. I wonder if the Biblical references to counterfacutals makes this case. When the TAG argument is used and the "impossibility of the contrary" phrase is pressed, it makes the naturalist seem desperate and foolish--holding an unreasonable faith. Reckoning with evidence is an unending excercise because neutrality, it has been said somewhere, is a myth and evidence doesn't interpret itself.

Don't see any presuppositionalist bent at all. I'm the one calling for examining the evidence. I'm not sure what you mean about God's "explaining a cause and effect relationship," but as I believe in free will, God knows much better than I that the _whole_ story cannot involve cause and effect unless the agent is included as, at some point and among other things, an irreducible cause.

... neutrality, it has been said somewhere, is a myth ...

Hi Tim, yes indeed, with no apologies. Everyone is biased, this doesn't necessarily mean that one's bias is leading them astray. If God IS, a bias toward Christian Thesism is a proper bias in a fallen world.

Hi Lydia, there may only be a slight bent, but I think clarification might help. Presuppositionalism doesn't preclude the testing or examining of evidence at all. The method does take into account prior commitments that interpret evidence. Somewhere along the line, a faulty premise can polute a long line of sound reasoning built upon it. When I see you call out the naturalists and their biased handling of evidence, conveniently passing on embarassing logical conclusions in favor of fallacious reasoning, ala the scientific method, I see you employing a presuppositional tactic.

I wonder if I'm understanding your point on free will. God is an irreducible cause, but men are not. He's necessary and we are contingent. Mans freedom has to be about a cause and effect relationship or God's not sovereign, right? Men are free but not autonomous.

Have you considered the Augustinian "Logos Doctrine"? Or, "occasionalism"?

Mans freedom has to be about a cause and effect relationship or God's not sovereign, right?

Hmm. Nope, don't see that. God _made_ man, but he made him free, a free agent, really capable of original, chosen action of his own.

You can call it a "presuppositionalist tactic" to point out the fact that the naturalist emperor has no clothes, lousy reasoning, etc., but that's pure co-option. Rampaging evidentialists are fully capable of pointing that sort of thing out without thereby ceasing to be evidentialists. Indeed, I don't see why they shouldn't.

Hi Lydia, this statement:

"God _made_ man, but he made him free, a free agent, really capable of original, chosen action of his own."

is loaded and highly debatable biblically-maybe a lot of term definitions. It most likely would end up being a serious thread hijacking though so some other time maybe.

I didn't mean come off as attacking evidentialism, or arguing for presuppositionalism, but unless I'm misinformed, evidentialists are not normally insistent on taking the evidence on at the presuppositional level. This is what I picked up from the original piece you wrote and comments along the way. I dont think naturalists are vulnerable at all unless you bring the argument back to logical premises/conclusions. In other words, IF non natrualists, [or supernaturalists] dont attack at the first instance of invalid conclusions, they might not find another opportunity--logically speaking.

I understand/agree that science is good at what it does, as far as it goes--as you stated very well. But, it is not the holy grail that the naturalists wants it to be and it's worth attacking especially when the practitioners lead it astray outside of it's capability making claims where it ought not--as you've stated very well. And, you are right, a "rampaging evidentialist" is fully capable of pointing out lousy reasoning, but it could be a waste of time interpreting evidence back and forth when it is prior commitments behind it on both sides. I see you arguing at a presuppositional level, because that is where naturalism is most seriously and obviously vulnerable-at it's presuppositions.

I don't understand why there is so much worrying going on here about evidence, or how to count how many problems have been solved naturalistically, or that sort of thing. Gödel proved that a complete naturalistic explanation is not possible, as Zippy rightly pointed out the other day in Lydia's last thread on this subject (Hear, Hear):

The biggest (though hardly the only) problem for someone like Dawkins is that what he believes in, foundationally, is a complete explanation: his metaphysical house of cards rests on a complete formalization being not only possible in principle, but also on there being reason to believe that such a formalization is near to hand, with just a few gaps left to close, just details to fill in. That is why every invocation of God looks to a "Bright" like a "God of the gaps" argument. The perception of a nearly-complete system with just a few gaps to close is as inevitable as it is question-begging. Modern man has a faith in the possibility of a theory of everything, in the possibility of his own in principle omniscience, a faith stronger than any faith the ancients had in God, and this despite the fact that such pursuits were many decades ago demonstrated to be illusory by the very tools of mathematical formalism themselves.

Isn't that all there is to it? Take any finite natural system, define it as broadly or as narrowly as you like, from a quark to the multiverse. Specify and represent all its elements perfectly in a formal system (tace Heisenberg). That formal system is incompletable; one can express truths using that formal system which cannot be demonstrated using only the elements thereof. This is as much as to say - it may even be exactly to say - that no finite thing can explain itself completely. So science is not completable.

Science cannot discover that there are truths that science cannot discover. But scientists can. And that can be possible only if scientists themselves cannot be fully specified in a formalization of a natural system. So there is something supernatural about scientists. But since scientists are elements of this world, there is something supernatural about the world.

I'm going pretty fast here, but I think I'm on track.

Will advances in physics eventually solve all the problems of grammar too?

"New quantum experiments provide foundation for subject verb agreement"

Why not? Isn't a (spoken) word just as much a part of the natural world, as a sound, as the Doppler effect and the overtone series? But no one thinks grammar could be made better by getting physics involved with it. Physics is not the right tool to analyze sound in that way. For that matter, if one wanted to analyze sound, not as sound, but as a being, natural science would be of no value either.

Why should there be one science for everything? Why would we even want one science for everything? Any hope for such a thing was the pipe dream of the thankfully defunct modern age, which started to unravel after Hegel, gave its last gasp with logical positivism and universal language schemes, and is now nothing but a stuffed head hanging on the wall.

Again, the scientific method is a tool to understand things. Why would we expect that all of reality can be disclosed by a single tool? If it takes so many distinct and irreducible disciplines to understand the thing that is a spoken word (grammar, acoustics, literary criticism, linguistics, etc.) then "all things" or even "all natural things" will require even more tools.

Lydia,

Thanks.

Let me to focus here on the following, general point:

"There is nothing even remotely like a process whereby scientists reach into a bag containing all the questions in the world that could be asked about anything whatsoever and select at random their research projects!"

Now, you and Tim wrote in Internalism and Epistemology, p. 146:
"Hume himself grants that we have experience of bread nourishing us and the sun rising. If we may take our experience to be a sample, then it appears that we possess all the tools necessary to make a rational defense of everyday extrapolations against Humean skepticism."

So, the sample of scientifically solved/viably explained problems/evidences is rigged. And, as you and Tim said, the sample of our experiences of the bread nourishing or the sun rising is not rigged.

Now, is there something like a process whereby we reach into a bag containing all the experiences of the bread nourishing or the sun rising and select at random our experiences? If not, what is the relevant difference between the two samples (for the former being rigged and the latter being non-rigged)?

Secondly, isn't your reply to Hume vulnerable to the counting problem: how to assort and count our experiences? (But maybe this worry can arise only in a too general, loose, and abstract perspective of approaching the reply to Hume you are suggesting.)

Kristor (and Zippy),

I don't see that the naturalist's "metaphysical house of cards rests on a complete formalization."

And IF the impossibility of complete formalization (or whatever is Goedel believed to say) is a problem for the naturalist, why is it not for the non-naturalist/theist, too?

Thirdly, what do you, Kristor, mean by "supernatural"? E.g., would you say that abstract objects like numbers are supernatural?

***

James,

"Will advances in physics eventually solve all the problems of grammar too?"

Some extremely intelligent and educated people for some time (have) thought that something like the wave function theory of Hartle and Hawking could explain everything. Some people still expect a scientific theory of everything to come or take it at least as possible or possibly discovered by humans (though not "fully formalizable"). I do not know their reasons for such hopes (which I do not share) in detail.

But as Tim relatedly noted elsewhere: "Just what is being given up isn't completely clear, but I have a sinking feeling that it's physicalism, or perhaps the Great Naturalist Hope."
http://maverickphilosopher.powerblogs.com/posts/1170529639.shtml#8363
I have no idea what the best experts currently think about such issues, though.

Once I read that even the great theist Leibniz believed that there is "the ultimate law governing the universe, i.e., the general order, which, being infinitely complex, is beyond our comprehension." http://maverickphilosopher.powerblogs.com/posts/1181758079.shtml
I guess, however, this great law would not be scientific but invoking something supernatural or at least non-physical.

Now, is there something like a process whereby we reach into a bag containing all the experiences of the bread nourishing or the sun rising and select at random our experiences?

Epistemically, yes. That is to say, there is nothing in our experience that we have reason to believe biases the sample in favor of nourishing bread or rising suns. The only worries that cd. arise there are worries about possibility: "_Maybe_ our experiences of bread nourishing are atypical."

I have already pointed out that this is not the nature of the problem w.r.t. to "solvable" scientific questions. Not at all.

"The essential characteristics of a mechanistic philosophy in the most general form that it has developed thus far in physics are the following: The enormous diversity of things found in the world, both in common experience and in scientific research, can all be reduced completely and perfectly and unconditionally (i.e., without approximation and in every possible domain) to nothing more than the effects of some definite and limited framework of laws. While it is admitted that the details of these laws may be subjected to changes in accordance with new experimental results that may be obtained in the future, its basic general features are regarded as absolute and final. This means that the fundamental entities that are supposed to exist, the kinds of qualities that define the modes of being of these entities, and the general kinds of relationships in terms of which the basic laws are to be expressed, are supposed to fit into some fixed and limited physical and mathematical scheme, which could in principle be subjected to a complete and exhaustive formulation, if indeed it is not supposed that this has already been done. [...] Thus, the essence of the mechanistic position lies in its assumption of fixed basic qualities, which means that the laws themselves will finally reduce to purely quantitative relationships. The philosophy of mechanism has undergone an extensive evolution in its specific form, all the while retaining the essential characteristics described above, in forms that tend, however, to become more and more complex and subtle with the further development of science." - David Bohm, quoted from The Essential David Bohm by Lee Nichol

IF the impossibility of complete formalization (or whatever is Goedel believed to say) is a problem for the naturalist, why is it not for the non-naturalist/theist, too?

Lydia,

"there is nothing in our experience that we have reason to believe biases the sample in favor of nourishing bread or rising suns. ... this is not the nature of the problem w.r.t. to "solvable" scientific questions."

Why not? I guess because:

"Scientists quite rationally usually try to tackle those problems that are tractable."

But why, exactly, is the sample comprising scientifically solvable/viably explainable problems/evidences rigged?

I guess because they "most often" "concern" "physical systems."

But that seems to be like arguing that the sample of problems/evidences solvable/viably explainable without invoking anything supernatural/non-physical is rigged because ... well because it is a sample of problems/evidences solvable/viably explainable without invoking anything supernatural/non-physical.

But this reading is not charitable to you, so I guess a better explication of your words is similar to what I said above:

How do we know that the sample of the tractable problems/evidences is rigged? Because of the existence of the problems/evidences not solved/viably explained scientifically: e.g., how the sodium got into the water, or what caused the beginning of the universe, etc. IF, however, such hard problems were rare enough, the sample bias of S would be insignificant.
But ARE the hard problems rare enough? No, they are not. There are many, many of them. Of course, this assumes throughout we know how to count problems/evidences.

***

Ad St. Paul to Romans: "the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Because that, when they knew God, they glorified him not as God, neither were thankful"

Could you come with some specific ways to know God or theistic arguments Paul is here alluding to?

Speaking about pagans generally, he is not alluding to a specifically Christian or Jewish apologetics (Christian or Jewish miracles or prophecies). I guess you would not opt for some common vague religious experiences and feelings, which you take as epistemically weak. So, is Paul thinking of some arguments a la Aquinas' Five Ways or from the nature of mind? If so, such arguments should exist among pagans in some epistemically solid form even before the Greek philosophy (and esp. Aristotle) -- which period would be rendered a mere revival of such arguments, not to mention scholastic, or our Dr Feser.

Zippy,

Thanks.

I can't see how fitting of everything into some fixed and limited physical and mathematical scheme entails that: (i) everything is completely formalizable or provable in some stronger sense Goedel had in mind or (ii) humans are omniscient or (iii) capable of discovering such a scheme.

I suspect there are many reflective naturalists, non-theists and searchers for a scientific (physical and mathematical) theory of everything who embrace Goedel's conclusions.

(Note: I'm the devil's advocate here and now but also a Christian at many times and places.)

Vlastimil, I _think_ I've explained this pretty clearly, but I'll try again. If the property of interest is "tractable for physical solution" or "solvable by scientific/purely physical explanation," and if problems are selected even in part _because_ they are tractable or solvable in this way, then _by definition_ this is a rigged sample. It's like talking about a sample of balls from a bag and their color where black balls were chosen even in part _because_ they are black. That's just rigging the sample for blackness _by definition_. If you know independently that the sample was chosen in part _for_ the property in question, then you _cannot_ treat the high proportion of items in the set with the property in question as having been arrived at by random sampling vis a vis that property.

If I choose to run races that I think I can win, or even in part by the consideration that I have some chance of winning them, I can't then reason from the number of races I've won already to the probability that I will win some other race where that other race is _not_ chosen because I have independent reason to think I can probably win it, and where, in fact, other people are bringing serious arguments to bear for the conclusion that I have no chance of winning it.

Lydia,

Yes, you've been clear. I'm just hyper-Cartesian -- or dumb.

My problem is very general (epistemology of induction), not at all specific to the theme of your post (optimistic naturalism/scientism)! But it could shed some light on the theme.

I assume a central, general, inductive question is whether the given sample matches the population.

For some samples we have no good reason to claim that they do not match the population.

Fo some other we do have such a good reason.

You seem to say that: if a sample is created in the intentional way, then, probably, the sample does not match the population (we have a good reason to claim that it does not match the population). But how exactly do we know THAT conditional? A crazy question, but a serious one. How do we know that intentionally created samples generally do not match their populations? By some other induction? If so, is not there a danger that this induction assumes at some point what we want to establish? (I.e., if a sample is created in the intentional way, then probably /we have a good reason to claim that/ the sample does not match the population.) Maybe not. Does the induction consist in this?: many, many intentionally created samples do not match their populations; thus, probably, all such samples do not match their populations; thus, probably, a given intentionally created sample (say, comprising scientifically tractable problems) do not match the population (of all problems).

It's not that we know that the sample probably doesn't match the population. Rather, what we know is that the sample does not, itself, give us good enough reason to take property of interest to be distributed in the same proportion in the whole population as it is in the sample. The sample is not one we can use to tell us what the population is like with respect to that property, because it's rigged. Since it's rigged for the very property we are trying to measure, we cannot treat it as epistemically random, because our knowledge gives us reason to believe that it would have a high proportion of items with the property of interest *regardless* of whether that were the proportion in the sample. Maybe it matches the population; maybe it doesn't. But we can't treat it as if it does, which is what we have to do for purposes of inductive extrapolation. That would be epistemically unjustified, because we know it would have the property anyway in a very high proportion regardless of the nature of the population as a whole.

So, for example, suppose Joe has dated a whole bunch of very pretty girls in his life; perhaps all of the girls he's ever dated are pretty. And suppose that his friends now arrange a blind date for him by picking a girl's name at random from all the unmarried female students on his very large university campus. We cannot extrapolate from, "Joe has dated all pretty girls before" to "Joe's blind date is probably pretty." For we have perfectly good reason to believe that Joe himself has picked his previous dates partly for their looks, whereas he doesn't have the opportunity to do that in this case, and neither do his friends. And of course matters are even worse if someone claims to have seen his blind date and claims that she is _not_ pretty. We cannot override this by saying that all Joe's previous girlfriends have been pretty! And this is very much like the situation with science. The non-naturalist brings _evidence_ that the problem in question is probably explained by non-natural means, and the naturalist claims, on the basis of a sample deliberately chosen for tractability, that this evidence can be ignored or overridden by the previous record of tractability in problems scientists have tackled with purely physical explanatory tools!

I can't see how fitting of everything into some fixed and limited physical and mathematical scheme entails that: (i) everything is completely formalizable or provable in some stronger sense Goedel had in mind or ...

(ii) humans are omniscient or ...

You might find the work of the mathematician Georg Cantor (who, like Godel, eventually died insane) interesting on the analogy.

(iii) capable of discovering such a scheme.

Lydia: That last paragraph was really great.

Vlastimil:

You say:

I can't see how fitting of everything into some fixed and limited physical and mathematical scheme entails that: (i) everything is completely formalizable or provable in some stronger sense Goedel had in mind or (ii) humans are omniscient or (iii) capable of discovering such a scheme.

As to (i): I’m not saying that we really can completely formalize everything. Indeed, I’m suggesting the opposite. But the program of science is to strive for a Theory of Everything, under which every phenomenon of the world can be adequately and completely formalized in just the strong fashion that Gödel had in mind. Anything less would leave some aspect of the world unexplained, mysterious. There's nothing wrong with this effort, any more than there is anything wrong wtih striving for perfect obedience to the Deuteronomic Law. What's wrong is the Pelagian presumption that one can wholly succeed in either of these projects under one's own steam. The humble aphorism, "you can't pull yourself up by your own bootstraps" captures the error quite nicely. Was there ever a more succinct argument for justification by grace? Was there ever a more succinct repudiation of materialist emergence?

As to (ii): If humans were indeed omniscient, they could completely surmount Gödelian incompleteness. We are intellectually adequate to the transcendence of any particular formal system, but – because no formal system, no matter how transcendent, can be completed in its own terms – not to the formal demonstration, and ipso facto to a fully comprehensive and adequate understanding, of all formally demonstrable truths. It would take a mind with infinite computational capacity and reach – an omniscient mind – to do that. Thus only God is capable of fitting everything whatsoever into an absolutely adequate and complete formal system - or rather, into an infinitely deep set of nested formal systems. [Notice BTW that if at any moment it had ever been the case that He had not already completed this job, then for that moment, and for all moments causally dependent thereupon, there would be no complete Logos – which is to say, no Logos at all – and thus no logic to reality. To get any particular formal system, you have to have the whole infinite nested set of them. The necessary truths are a package deal. Thus if we understand anything at all even a little teeny bit, there must be, must eternally have been, a complete Understanding of every possible thing.]

As to (iii): Therefore, because of the paragraph just ended, humans, and any other finite entity, are not capable of discovering a fully adequate Theory of Everything about any natural system, no matter how picayune that system might be. This is just another way of stating Rescher’s dictum that the number of true statements one can make about even the simplest thing is infinite.

You ask:

IF the impossibility of complete formalization (or whatever is Goedel believed to say) is a problem for the naturalist, why is it not for the non-naturalist/theist, too?

Thirdly, what do you, Kristor, mean by "supernatural"? E.g., would you say that abstract objects like numbers are supernatural?

Gödelian incompleteness is not a problem for the naturalist/theist, because he does not presume to a complete Theory of Everything, but rather grants ab initio that a perfectly adequate TOE is possible only to God.

As to what I mean by "supernatural," for the purposes of the Gödelian arguments I have made in this thread, something supernatural to a natural system would be a truth that cannot be demonstrated within an adequate Gödelian formalization of that natural system. A more adequate or general answer to your question would require a major (and fascinating) threadjack. But, yes, I would say that the numbers are supernatural, in the sense that, as necessary, they are prior to any contingency – and what we usually mean by “nature” is “our contingent world.”

I should add that I remembered last evening that I learned these Gödelian arguments against naturalism from JR Lucas.

I should have said,

Gödelian incompleteness is not a problem for the *non*-naturalist/theist, because he does not presume to a complete Theory of Everything, but rather grants ab initio that a perfectly adequate TOE is possible only to God.

Zippy and Kristor,

Just one point.

You say:

"If everything fits into a fixed physical and mathematical scheme, that fixed physical and mathematical scheme is complete."

"the program of science is to strive for a Theory of Everything, under which every phenomenon of the world can be adequately and completely formalized in just the strong fashion that Gödel had in mind."

I have my doubts precisely about that.

"Anything less would leave some aspect of the world unexplained, mysterious."

It seems to like saying that there are no mathematical proofs because Goedel (haven't you heard?) proved ... what? ... that there there are no proofs in some very strong and specific sense. Uh?

Lydia,

Thanks.

You say: "It's not that we know that the sample probably doesn't match the population."

Right. I said:

"You seem to say that: if a sample is created in the intentional way, then, probably, the sample does not match the population (we have a good reason to claim that it does not match the population)."

I should rather say:

"You seem to say that: if a sample is created in the intentional way, then it is not highly improbable that the sample does not match the population (we have a reason to claim that it does not match the population)."

***

Your examples are good, dialectically convincing, and really helpful for illustrating your point against the optimistic naturalist/scientist.

But let's put the optimistic naturalist aside. I'm trying to put my finger on the general, uderlying, pattern of inductive reasoning about intentionally created, designed, samples; a pattern common both to your point against the optimistic naturalist and your examples from ordinary life. So, we are now rather in the area of general epistemology, not of the philosophy of religion or of the philosophy of science.

Suppose we have an intentionally created, designed, big sample, created in the way you suggest by your examples. I don't know how to define such a sample precisely, though.

You claim that our knowledge gives us reason to believe that the sample has the proportion of items with the property of interest regardless of whether it matches the proportion in the population (to the stipulated degree of precision). I'm unclear about the role and meaning of "having a reason" and "regardless" in the epistemology of induction.

Let's try this: how would you translate that claim into the language of the strong probabilistic foundationalist (which you are)? This way?: it is not highly improbable on our basic beliefs that the intentional sample has the proportion of items with the property of interest which does not match the proportion in the population.

If so, which basic beliefs do you have here in mind and how would you show that it is not highly improbable on them that the intentional sample does not match the population?

This, rather a priori, way?:

1. For any property p, at least a* of (distinct) n-fold "intentional" samples exhibit a proportion that does NOT match the population. (An implication of Bernoulli's theorem or something like that?)

2. S is an n-fold "intentional" sample.

Thus, given the absence of other relevant information,

===== (with at least a* probability)

3. S does not match the population.

***

Or would you conceed proceeding in a more a posteriori way of testing statistics empirically and statistically?

We create a random sample S' of "intentional" samples and then empirically observe that they do not, with some proportion P, match their populations.

1'. For any property p, at least a* of n-fold samples exhibit a proportion that matches the population. (An implication of Bernoulli's theorem or something like that.)

2'. S' is an n-fold sample (of n'-fold "intentional" samples).

Thus, given the absence of other relevant information,

===== (with at least a* probability)

3'. S' matches the population (of all n'-fold samples).

4'. S' has a proportion P of unmatching samples.

5'. The proportion in the population of all n'-fold "intentional" samples lies around P (+/- some degree of precision e).

6'. S is an n'-fold "intentional" sample.

Thus, given the absence of other relevant information,

===== (with probability around P)

7'. S does not match its population.

Zippy and Kristor,

Addendum

To keep things simpler, suppose everything explained by some a mathematical equation (similar to the wave function of Hartle and Hawking). The equation is necessary and thus explains itself. The beginning of the universe is probable on the equation, my sitting here and now is probable on it, too, etc., etc.

Suppose we can’t prove the equation a la Goedel. Does it strictly follow that humans can’t know the equation as true?

Suppose humans can’t know; does it strictly follow there is not the equation?

If we balk at my sitting here and now or the beginning of the universe being probable on some necessary equation, as I do, let’s assume something other: there is an infinite causal series of universes, each universe is contingent, the series as a whole is contingent, and it is governed by some contingent physical law, grounded in the nature of the universes, and saying that if a universe has such and such properties, then, probably, it will spawn another universe with such and such properties. Cf. http://whatswrongwrongwiththeworld.net/2009/03/hear_hear.html#comment-51264 and the following debate.

Suppose we can’t prove this scenario a la Goedel. Does it strictly follow that humans can’t know the scenario as true?

Suppose humans can’t know; does it strictly follow that the scenario is not true?

Suppose humans can’t know; does it strictly follow there is not the equation?

"If everything fits into a fixed physical and mathematical scheme, that fixed physical and mathematical scheme is complete."

Only if "everything" includes mathematical reality. But the theory of everything is not meant to include mathematical reality--it is meant to be a complete theory of what goes on in the physical universe.

Now, you might say that there will be Goedelian sentences about what goes on in the physical universe. But our optimistic naturalist can just say: "Yes, but their truth values can be grounded in the conjunction of (a) the basic physical facts, and (b) all the mathematical truths (including the Goedelian ones)."

"If everything fits into a fixed physical and mathematical scheme, that fixed physical and mathematical scheme is complete."

Only if "everything" includes [all of] mathematical reality.

But even if I'm wrong about all that, though I don't think I am, all that establishes is that I haven't deductively proven the nonexistence of a mathematical TOE[p]. That's fine, because again, the claim isn't that we are deductively certain of the nonexistence of a TOE[p]. The claim is that there is no particularly good reason to believe in a mathematical TOE[p] other than through a leap of blind faith in the face of mountains of reasons not to believe in one.

Vlastimil--On induction: I don't think I would say any of those. Rather, I would say that we are not justified in treating the sample as probably matching the population for the property of interest. We are justified in treating it that way only if, epistemically, the various relevant possible properties (including the property of interest) are epistemically symmetrical for us vis a vis the sample. So, for example, if Joe always picked his girlfriends without reference to their prettiness (and if we could be made to believe that he actually did this), or at a minimum if (which is in this case almost inconceivable) we had no reason to think that Joe _does_ take looks into account in choosing to date a girl, we could justifiably treat the proportion of pretty girls in the sample ("girls Joe has dated so far") as representative of the proportion of pretty girls in the population. Since we do have a reason to think he takes looks into account, the properties pretty/ugly/somewhat pretty (or however we decide to set up our predicates) are not epistemically symmetrical for us vis a vis the sample.

If a person tells me he just loves black balls and dislikes all other colors, and if he gets to look into the urn when he's picking out balls, "black balls" are not in an epistemically symmetrical position for me vis a vis other possible colors of balls, so I am not justified in taking a sample chosen (by this person) with replacement of say, 999 black balls to 1 white ball to be representative. It isn't that I have to argue anything about whether his sample _really is_ or _really isn't_ representative. I don't have to get into that at all. The point is just that the sample is _worthless_ for deciding what the population really is like. He could have been picking the same black ball out over and over again on purpose, and what he said to me ahead of time gives me reason to believe that he would have done that if necessary. On the other hand, it _could_ be the case that virtually all of the balls in the urn really are black. The point is just merely and simply that under these circumstances, _that_ sample does not allow me to infer a high proportion of black balls. In fact, it doesn't allow me to infer much of anything about the population at all, except that it contains at least one black ball and one white ball.

Now, you might say that there will be Goedelian sentences about what goes on in the physical universe. But our optimistic naturalist can just say: "Yes, but their truth values can be grounded in the conjunction of (a) the basic physical facts, and (b) all the mathematical truths (including the Goedelian ones)."

Yes, certainly. But this was my point, or rather, Lucas's point. If you need to invoke all the mathematical truths in order to ground the truth value of a Goedelian sentence in the TOE[p], then the TOE[p] is not a completed formal system, even if it is a perfectly adequate and accurate formalization of everything physical. Provided your TOE[p] is adequate to the actual physical world, a demonstration that certain truths it expresses depend for their truth value on other formal systems somewhere in mathematical reality outside of the TOE[p] is ipso facto a demonstration that the actual physical world of which it is an adequate formalization likewise depends upon a transphysical reality.

Vlastimil:

... suppose everything explained by some a mathematical equation (similar to the wave function of Hartle and Hawking). The equation is necessary and thus explains itself. The beginning of the universe is probable on the equation, my sitting here and now is probable on it, too, etc., etc.

Suppose we can’t prove the equation a la Gödel. Does it strictly follow that humans can’t know the equation as true?

No. It follows only that the necessary comprehensive equation – the NCE - can’t be proven true using arguments derived only from the axioms of the formal system – FS[nce] – in which it is expressed. If, for example, we can just “see” that NCE is necessarily true, that apprehension must derive from the operations of a formal system that transcends the domain of FS[nce].

Kristor,

"the necessary comprehensive equation – the NCE - can’t be proven true using arguments derived only from the axioms of the formal system – FS[nce] – in which it is expressed. If, for example, we can just “see” that NCE is necessarily true, that apprehension must derive from the operations of a formal system that transcends the domain of FS[nce]."

That's helpful.

But I suppose most searchers for a TOE, TOE(p), NCE, and the like, would not be bothered for their standards are not set so high as to imply that the TOE, TOE(p), NCE, etc. are proven true using arguments derived only from the axioms of the formal system FS(TOE), FS(TOE(p)), FS(NCE), etc.

A fortiori for the physicalist (one who embraces only particles/fields/strings, and their configurations, and sometimes their inner ontological principles or even the sui generis, supervening sphere of the mental) which does not have to be such a searcher at all.

And a fortiori again for the naturalist (one who rejects supernatural entities and events like God, angels, miracles, minds without bodies) who does not have to be neither a physicalist nor such a searcher.

Shortly,

I suspect you and Zippy are reading into the definitions of naturalism, physicalism, and TOE too much.

Lydia,

Thanks.

First,

"we are ... justified in treating the sample as probably matching the population for the property of interest ... only if, epistemically, the various relevant possible properties (including the property of interest) are epistemically symmetrical for us vis a vis the sample."

Do you have some GENERAL definition of epistemic symmetry?

Second,

"If a person tells me he just loves black balls and dislikes all other colors, and if he gets to look into the urn when he's picking out balls, ... the sample is _worthless_ for deciding what the population really is like."

Right. But HOW do we know THIS common sense conditional as true? What would be its justification? To say that we inductively know that such sampling quite often does not produce a sample matching its population? If so, then we seem to need something like the strategy I set forth in my last comment addressed to you.

Another great example with a urn or dating won't do for I'm trying to find the rationale which is at the basis of all such examples and makes them convincing.

Thirdly,

You could reply: hey, stupid, if (1) a person tells me he just loves black balls and dislikes all other colors, and he gets to look into the urn when he's picking out balls, (2) the sample is worthless for deciding what the population really is like just BECAUSE (1) implies that (3) the sample has the proportion of items with the property of interest regardless of whether it matches the proportion in the population, and (3) implies (2). In sum, (1) only if (3); (3) only if (2); thus, (1) only if (2). Got it?

Well, no.

I suppose (3) means the same as
(3') If the sample did not match the population, the sample would have the proportion it has.

And (2) means the same as
(2') we are not justified in treating the sample as probably matching the population for the property of interest.

But how do you get from (3') to (2')? If by definition, could you please unpack your definitions to make the inference more transparent?

Fourth,

I conceded above: „some problems are not solved/viably explained scientifically: how the sodium got into the water, or what caused the beginning of the universe, or why there are natural laws, or why Jenny doesn't love me, or where did the mind come from, or why did Napoleon try to conquer Europe, or why the physical constants are fine-tuned (though I know you doubt the fine-tuning argument), or why the disciples and the St. Paul were willing to die for the claim they met the resurrected Jesus, etc.“

But „scientifically“ is ambiguous at least between (i) science invoking nothing supernatural and (ii) science invoking nothing non-physical. On the second reading (and assuming we know how to count), it seems there would be many problems not not solved/viably explained scientifically. But on the first reading, and allowing the explanatory aparatus of social and economic sciences, Craig and Moreland (cited above) could be right that there are few such problems.

Fifth,

Maybe you would allude at this point to the decline of ambitions of sociology (suugested by your e-correspondent). Though I majored in sociology (and philosophy), I have never been keen about this particular science and its trends. Still, I’m curious: could you be more specific about the supposed decline? Given the general popularity of epistemological skepticism, could not be the pessimistic views about the success of social sciences biased? (Like the general pessimistic views about the prospects of a/theistic arguments in the current philosophy, given the agnosticism about such "speculative" issues.) I remember my teachers of sociology as skeptics par excellence. Some people similarly say that economical sciences have revealed their epistemic impotency. But did not Peter Shiff predict the crisis in 2006?

Sixth,

As for the counting problem, I conceded above: „How should we count the problems?“

Still, don’t we sometimes need similar counting to defend reliabilities of witnesses (e.g., this witness is reliable because of the much good info he had delivered to us;or this child is justified to believe her parents because they have proved to be worthy of trust many times before) and philosophical, theological and scientific projects (e.g., theism/substance dualism/probabilism/Christian theism/Protestantism/Catholicism/Lorentzian theory of time/stem cell research is promising and worthy of further pursuit because it solved/viably explained many problems/evidences)? Aren’t we then using double standard wrt the optimistic/naturalist, confronting him triumphantly with a problem we have too?

...are proven true using arguments derived only from the axioms of the formal system

I suspect you and Zippy are reading into the definitions of naturalism, physicalism, and TOE too much.

Zippy,

Suppose that X is a mathematical formula wich explains every basic (non-reducible) physical fact (whatever basic, non-reducible physical facts are/n't) and every configuration of basic physical facts. In addition, as Alex noted, if there were true Goedelian sentences about basic physical facts or their configurations, they would be grounded in (and entailed by) the conjunction of all the basic physical facts, all their configurations and all the mathematical and logical truths. Finally, neither X nor any of the true Goedelian sentences about basic physical facts and their configurations could be proven (at least by humans) solely by means of the aparatus of the formal system in which X were canonically and most exactly set forth.

Yet, I guess it would not be eccentric, measured by the standards of current usage, to call X a "TOE."

And I still don't see why the naturalist or the physicalist needs to claim that every truth is provable (by humans) solely by means of some (human) formal system.

Vlastimil--On induction: A rigged sample gives you no reason to think that the population has that proportion of the property of interest, because the probability that the sample would have that proportion given that it is not representative is the same as the probability that it would have that proportion given that it is representative. Since the likelihood is no higher if it is representative than if it is not representative, there is no evidential traction.

Here is an example that may help that is not about induction or sampling but rather occurs in an explanatory context: Every Saturday at 1 p.m. my town tornado sirens go off. (This is actually true.) It's just a test. We all know that in the town. Therefore, if I hear the tornado sirens go off at 1 p.m. on a Saturday, this occurrence is not evidence of a tornado, because the likelihood is no higher for "tornado" than for "no tornado."

Suppose that X is a mathematical formula wich explains every basic (non-reducible) physical fact (whatever basic, non-reducible physical facts are/n't) and every configuration of basic physical facts. ... neither X nor any of the true Goedelian sentences about basic physical facts and their configurations could be proven (at least by humans) solely by means of the aparatus of the formal system in which X were canonically and most exactly set forth.

I guess it would not be eccentric, measured by the standards of current usage, to call X a "TOE."

But „scientifically“ is ambiguous at least between (i) science invoking nothing supernatural and (ii) science invoking nothing non-physical. On the second reading (and assuming we know how to count), it seems there would be many problems not not solved/viably explained scientifically.

If the would-be naturalist wants to admit openly that the human mind is non-physical and hence wants to say that explanations involving *definitely non-physical* free choice, mental states, human desires and preferences, etc., are both admissible and (on his present definition) "scientific," he may be able to reduce the number of problems unsolved by "science" on that definition. But he will also a) have given up all hope of "naturalizing" the mind, which _is_ a project of naturalism right now and therefore b) have called his naturalist credentials seriously into question.

Moreover, such a shifting of ground will still not allow him to use the optimistic induction strategy against putative miracles for all the other reasons I have already given, the biggest of these being that all such strategies are attempts to evade evidence.

Lydia,

Thanks for your last comment on induction. That's what I needed. Sorry for being cumbrous.

What about the counting problem being our problem, too?

As for the evidence for miracles, I'll try to take up via e-mail, in a day or two. (I'll be brief, not lengthy.)

Thanks again.

Zippy,

"I'm not particularly interested in how fashionable certain uses of language may or may not be."

But then, maybe, you attack a strawman.

If my teacher says: "OK, everyone is in the classroom, we can begin," is it fair to say: that's a hogwash because, surely, at least V. I. Lenin is not in the classroom? No, there's an implicit clause in the teacher's claim. Similarly for someone saying: "a TOE is possible."

And to repeat myself, I still don't see why the naturalist or the physicalist needs to claim that every (physical) truth is provable solely by means of one formal system.

I got lost somewhere: Does a mathematical model that purports to be a TOE account for the rules of logic and math by which the mathematical model, ummmm, models? That is, is the reason the logical rules work contained within the confines of the TOE? Are the rules of math that constrains what we mean by the mathematical model also given within the TOE? If not, why is it a TOE?

The problem I see is, as Zippy and Lydia suggest, that if there are rules of logic that somehow rise above the TOE as part of the non-physical framework within which the TOE explains the physical system, then it seems that either (a) humans are aware of these real rules of logic through some transferability (from outside the physical system to us inside), a process that stands at least partly above the TOE, or (b) humans are not aware of the rules and framework that the TOE subsists within, in which case we humans can have no reason to suppose that our TOE (or, to be more precise, our interpretation of it) has any validity whatsoever.

Either the human mind knows universals that are non-physical, or any science we do has no way to claim a connection with the rules of the universe.

If a common use of language is in fact incoherent and equivocal, and I say that it is incoherent and equivocal, I'm not attacking a straw man. I'm attacking something real, a common use of language which is incoherent and equivocal. If folks firmly believe in a mathematical theory of everything (or a mathematical theory of everything Q) when the notion of a mathematical theory of everything (or everything Q) is incoherent and equivocal, when I (or anyone else) point out that incoherence and equivocation we are not attacking a straw man. If I criticize an argument for the existence of four-sided triangles it doesn't address my criticism to retort that when my interlocutors say "four sided triangles" they really mean a square.

There are two basic critical paths to follow here, it seems to me: one, that when people say "mathematical theory of everything Q" they don't actually mean a mathematical theory of everything Q and are using language poetically; the other, that when they say "mathematical theory of everything Q" they do mean it. The latter is straightforwardly incoherent if the mathematical theory requires arithmetic; the former is also incoherent, or at least is polemically useless as a critique of religion, because the whole point of intransigent belief in the elusive mathematical TOE[p] is to banish the poetical and make everything encompassed by the theory fully explicit.

Either the human mind knows universals that are non-physical, or any science we do has no way to claim a connection with the rules of the universe.

Or the human mind filters reality into simpler maps that imperfectly correspond to real connections. That is why falsifiability is such an important device for testing true statements.

Step2, I am having trouble sorting through what that would mean. Can you help?

Take the rule of logic and the universe expressed as "A thing cannot both be and not be at the same time and in the same respect.

Is this falsifiable? How so?

If the mapping our minds use is simpler than the reality and imperfectly corresponds to reality all across the board, then by what standard do we know which elements lost in a simplification are critical; or by what measure can we say that the imperfect correspondence is not simply false? Can we ever know that the correspondence is correct in feature X? If not, what is the difference between your explanation and, say, Hume's position?

Step2:

Or the human mind filters reality into simpler maps that imperfectly correspond to real connections.

If this statement is true of all our apprehensions, then the statement is saying that the statement itself is imperfectly true - i.e., that it is simply false. But if it is not a blanket statement, how is it different from saying that one ought to be careful?

Is this falsifiable? How so?

Take its opposite as a true statement and demonstrate how it could be so.

...by what measure can we say that the imperfect correspondence is not simply false?

If it is critical, the model will break down of its own inconsistency. If it is false, then falsifiability will show that.

If not, what is the difference between your explanation and, say, Hume's position?

I view Kant as the rational response to the absolute skepticism of Hume.

Kristor,
An imperfect expression of a true thing isn't "simply" false, although it could be false in some aspects.

Take its opposite as a true statement and demonstrate how it could be so.

Wow, that was a pretty fast and easy solution to about half of the problems of epistemology and philosophy of mind.

Or, perhaps, maybe not. It is not enough to show how its opposite "could be so" under some hypothetical state of affairs (which might never be actually possible), but rather it is so under a real state of affairs. That's what an experiment does. Could you, possibly, give us an example of doing that with the principle stated?

If it is false, then falsifiability will show that.

Well, not really. That's not how it works in science. If a scientific statement is false and and appears to be given in a mode that provides access to experimental testing, THEN we may be able to discover the right test that proves it is false. If we DON'T find such a test for a given statement, then either we just have not looked under the right rock, OR the statement is false but not falsifiable, contrary to appearances of testability. So it is not always true that "If it is false, then falsifiability will show that."

However, if a scientific statement is true, it will never be "falsified" validly - and operationally, we will never know whether the reason we could not falsify it was because it was true, or because it was false but we failed to look under the right rock for a good test.

But, of course, all of these notions of "falsifying" a theory or hypothesis use the principle of non-contradiction. So it seems more than a little outre to suggest that you could falsify it by an experiment. The validity of the experiment rests on using it.

Step2:

An imperfect expression of a true thing isn't "simply" false, although it could be false in some aspects.

That sounds like the second interpretation I offered of your original statement, which was that you did not mean "the human mind filters reality into simpler maps that imperfectly correspond to real connections" as a blanket statement. If you had meant it as a blanket statement, you would have meant something like, "human knowledge is unattainable," a self-refuting statement.

But the more sensible interpretation you apparently intended, that human knowledge is a tricky thing, does not work against Tony's statement that "Either the human mind knows universals that are non-physical, or any science we do has no way to claim a connection with the rules of the universe," to which you counter-poised it. For the more sensible interpretation does not rule out perfect knowledge of, e.g., mathematical truths.

Could you, possibly, give us an example of doing that with the principle stated?

If a thing could exist and not exist in the same time and the same respect, it would be demonstrated if its total absence produces the exact same properties and effects as its presence.

If you'll look at what I wrote, you'll see I didn't make falsifiability an exclusive means of determining truth, it is just an important method for doing so.

Zippy,

If a common use of language is in fact incoherent and equivocal, and I say that it is incoherent and equivocal, I'm not attacking a straw man. I'm attacking something real, a common use of language which is incoherent and equivocal.

Are biblical claims with implicit clauses incoherent? For instance, if you're a Christian who is said by the Bible that "all people sinned," should you claim that the Bible is incoherent for (as it is arguably at least implied by the Bible, too) Christ did not sin?

Secondly, that popular presentations of TOE's are poetical/metaphorical does not entail that all TOE's are poetical. I have not studied the best current TOE's in detail; have you?

Are biblical claims with implicit clauses incoherent?

Oh, and on your last question, google Lee Smolin and Peter Woit.

Zippy,

How do you know that "TOE," as used by proponents of "TOE," has no relevant implicit clause on "everything"?

Is googling enough to make a serious idea about TOE's? Have you read many (primary, technical) texts (papers, books) on the issue? If not, that's OK. Just want to know how much verse authority you are.

How do you know that "TOE," as used by proponents of "TOE," has no relevant implicit clause on "everything"?

In fact, I don't think you are really criticizing my criticism: you are just suggesting that when certain people say "mathematical theory of everything" they don't actually mean the "everything" part. That is itself one half of what I am saying. The other half is that if they actually do mean everything, the claim is incoherent.

Is googling enough to make a serious idea about TOE's?

But in any case that is all quite irrelevant for present purposes, because I don't need to have studied the specific mathematical theories to know that if they require arithmetic they necessarily are incomplete.

Zippy,

Nice reply. Thanks.

... if they actually do mean everything, the claim is incoherent. ... I've discussed the matter with professional and academic physicists for years ...

So, according to your knowledge (which is much, much better than mine),
1. does the professionals' and the academicians' "everything" sometimes have an implicit clause?,
2. if (and when) it does, which clause it is?,
3. do they (i.e., the professional and academic proponents of TOE's) mean that their TOE (or some TOE) is complete in Goedel's sense?

(If your answer to (3) is "yes," then I ask: don't they know their Goedel?)

And I still don't see why the naturalist or the physicalist needs (by definition) to claim that every (physical) truth is provable solely by means of one formal system a la Goedel or to hope for a "TOE" taken literally (without any implicit clause).

I don't think questions 1-3 get much thought among non-philosophers. Roger Penrose may be an exception, and there are probably a few others. Paul Davies perhaps. You'll find little but contempt for philosophy (including the philosophy of science) among the New Atheists.

And I still don't see why the naturalist or the physicalist needs (by definition) to claim that every (physical) truth is provable solely by means of one formal system a la Goedel or to hope for a "TOE" taken literally (without any implicit clause).

I still think you are being waffly on the notion of a theory of everything, like my imaginary "four sided triangles" interlocutors using triangular terminology to refer to squares. Implicit clauses are all well and good for nonessentials, trivial and explicit exceptions, etc[*]; but believing in the existence of a "mathematical theory of everything physical" which is in fact a mathematical theory of some physical things but not all physical things isn't just a matter of implicit clauses or trivial exceptions. If it is a physical theory, it is a physical theory of some things. If it is a mathematical theory of everything physical, it is laying claim to complete explicit mathematical expression of all things physical. If it isn't, there is no valid reason to use the qualifier "everything" to begin with.

[*] Even in the case of "trivial" exceptions we call explicit attention to them before using a categorical statement like "all". For example, we say that the Riemann hypothesis is that "all non-trivial zeroes of the zeta function have real part one-half". We make it explicit that by the trivial zeros we mean the ones at -2, -4, etc which are trivial to prove. It would make no literal sense (though it might make rhetorical, poetical, or polemical sense) to assert "all zeroes of the zeta function have real part one-half, except for the ones that don't"; and that is exactly what asserting a "mathematical theory of everything physical except for the physical things it isn't a theory of" is like. The "everything" is inserted for polemical purposes, and actually obscures the fact that the theory under discussion - typically, like M-theory, a theory not known to exist but thought to maybe exist and to have certain characteristics - is not in fact a theory of everything physical, and literally cannot be a theory of everything physical.

You'll also find, by the way, a fairly large cultural difference between mathematicians and physicists, as between philosophers and both. The old joke goes:

Physicist to mathematician: "Have you finished that equation I asked you to work on? You've been struggling with it for a week, and I need it for my experiment today."

Mathematician: "No, I got it to work for the trivial case of positive real numbers right after you asked me, but I'm getting nowhere on the nontrivial cases."

When physicists and mathematicians get together it can be as misunderstanding-prone as when men and women get together.

Zippy,
Vlastimil seems to be advocating an approach of different, interconnected formal systems that compose the unity of the TOE. It would be ironic if the Trinity ends up being a close metaphor.

Thanks for providing the name of Smolin, that is a wild theory.

And I still don't see why the naturalist or the physicalist needs (by definition) to claim that every (physical) truth is provable solely by means of one formal system a la Goedel or to hope for a "TOE" taken literally (without any implicit clause).

The naturalist is committed to a complete TOE[p] because he argues that everything in the world can be fully explained without invocation of any extramundane factors.

I suppose it might be argued that one could fully explain the world in naturalistic terms without going so far as to formalize the explanation. But this would leave the explanation open to the criticism that it relied on hand-waving, black boxes, fuzzy terms, just-so stories, and so forth. Worse, it would make the theory vulnerable to the criticism that it relied upon unfounded belief – the very criticism naturalists lay at theism.

To formalize a theory is to state it without equivocation of the sort that Vlastimil has called implicit clauses, so that it can be understood without confusion, making it possible its testing (whether logically, mathematically, or experimentally) and enlargement. I doubt that a theory that is in principle impossible to formalize can be coherent; how could this be, if it is impossible to state the theory without equivocation or confusion?

But never mind all that, and never mind theories of everything. Let’s say that scientists have devised a theory of rutabagas, and it has been fully formalized. It is perfectly adequate to the natural history of rutabagas, to the actual experimental and experiential data. Is the theory wholly naturalistic? I.e., does it involve entities that are extraneous to rutabagas? No, and yes. For the theory cannot be completed. It relies on math because it is expressed mathematically, and it relies on logic because its arguments instantiate the rules of logic. And rutabagas cannot explain math or logic

For “rutabagas,” substitute any congeries of mundane things you like. The result will be the same.

Could you, possibly, give us an example of doing that with the principle stated?

If a thing could exist and not exist in the same time and the same respect, it would be demonstrated if its total absence produces the exact same properties and effects as its presence.

Well, that's kind of fun. I ask for an actual example, and you describe some of the parameters of an experiment that might do the trick, if only we could find something that behaves the way you describe. This is what is known as not providing an example.

But that's all right. I'll work with what you gave me. Except that what you gave me gives us, itself, a small, little problem. If the presence of the thing has all of the results and properties that its absence has, then we would not really be able to say that observationally we actually know that we have the presence of the thing, now would we?

I am now holding in my hand an invisible, weightless, odorless, frictionless, massless, resistance-less, bit of ether (which is actually Leprechaun hair, but don't tell anyone). What, you say you can't tell it's there? Well, of course not - didn't I just say that it is invisible, odorless...? Your conclusion (just like those dang Michaelson-Morley experiments) from the fact that it cannot be observed is that it ain't there. SO how does that leave room for the claim that this could be a situation that a thing both exists and does not exist in the same way at the same time? Do we just posit that it's there?

Zippy,

If it is a mathematical theory of everything physical, it is laying claim to complete explicit mathematical expression of all things physical.

Do you want to imply here that every claim to a mathematical theory of X is/must be a claim to a complete mathematical theory of X? If so, then you hold that there is no mathematical theory because there is no complete mathematical theory. But this conclusion is strange. So you likely mean something else -- but what is it? In other words, why do you embrace the conditional I cited?

I suppose you'd be very interested in my esteemed countryman Luboš Motl (http://en.wikipedia.org/wiki/Lubo%C5%A1_Motl ). I'm going to see him in my town in two weeks at his lecture. He has a critique of Smolin's critique of string theory (http://motls.blogspot.com/2004/10/lee-smolin-trouble-with-physics-review.html ).

***

Kristor,

... it might be argued that one could fully explain the world in naturalistic terms without going so far as to formalize the explanation. But this would leave the explanation open to the criticism that it relied on hand-waving, black boxes, fuzzy terms, just-so stories, and so forth. ... I doubt that a theory that is in principle impossible to formalize can be coherent ...

So, theism, Christianity, Aquinas' metaphysics, deontological ethics and arithmetic are incoheherent because they can't be formalized completely?

... entities that are extraneous to rutabagas ...

But why such entities must be of a non-naturalistic (= supernatural) or non-physicalistic kind? Let’s define naturalism simply as the view that there is nothing supernatural (God, angels, miracles, souls without bodies, and the like). (Cf. SEP on naturalism or Plantinga’s definition of naturalism.) Let’s define physicalism as the view that there are only (i) elementary (basic) physical particles (or fields, or strings) and (ii) their configurations (and in some versions also (iii) supervening mental properties and/or (iv) inner ontological principles, like essences, or parts of (i), (ii) or (iii)).

... rutabagas cannot explain math or logic ...

First, do math and logic need explanation? That's not clear even to the orthodox Catholic theist Trent Dougherty: http://prosblogion.ektopos.com/archives/2008/03/polish-priestph.html Second, if it does, why the explanation must be non-naturalist or non-physicalist?

For “rutabagas,” substitute any congeries of mundane things you like. The result will be the same.

Again, why the extraneous part must always be supernatural or non-physicalistic? Secondly, why does not your objection apply to theism? Why not to say: for “rutabagas,” substitute any congeries of mundane and non-mundane things you like, and the result will be the same?

Tony,
So there is at least one case when a thing can exist and not exist at the same time and in the same respect. Thanks for demonstrating the exception to the original statement.

Zippy,

If it is a mathematical theory of everything physical, it is laying claim to complete explicit mathematical expression of all things physical.

Do you want to imply here that every claim to a mathematical theory of X is/must be a claim to a complete mathematical theory of X? If so, then you hold that there is no mathematical theory because there is no complete mathematical theory. But this conclusion is strange. So you likely mean something else -- but what is it? In other words, why do you embrace the conditional I cited?

I suppose you'd be very interested in my esteemed countryman Lubos Motl (see Wikipedia). He has a critique of Smolin's critique of string theory (see Smolin on Wikipedia).

***

Kristor,

... it might be argued that one could fully explain the world in naturalistic terms without going so far as to formalize the explanation. But this would leave the explanation open to the criticism that it relied on hand-waving, black boxes, fuzzy terms, just-so stories, and so forth. ... I doubt that a theory that is in principle impossible to formalize can be coherent ...

So, theism, Christianity, Aquinas' metaphysics, deontological ethics and arithmetic are incoheherent because they can't be formalized completely?

... entities that are extraneous to rutabagas ...

But why such entities must be of a non-naturalistic (= supernatural) or non-physicalistic kind? Let’s define naturalism simply as the view that there is nothing supernatural (God, angels, miracles, souls without bodies, and the like). (Cf. SEP on naturalism or Plantinga’s definition of naturalism.) Let’s define physicalism as the view that there are only (i) elementary (basic) physical particles (or fields, or strings) and (ii) their configurations (and in some versions also (iii) supervening mental properties and/or (iv) inner ontological principles, like essences, or parts of (i), (ii) or (iii)).

... rutabagas cannot explain math or logic ...

First, do math and logic need explanation? In which sense? That's not clear: http://prosblogion.ektopos.com/archives/2008/03/polish-priestph.html Second, if they do, why the explanation must be non-naturalist or non-physicalist?

For “rutabagas,” substitute any congeries of mundane things you like. The result will be the same.

Again, why the extraneous part must always be supernatural or non-physicalistic? Secondly, why does not your objection apply to theism? Why not to say: for “rutabagas,” substitute any congeries of mundane and non-mundane things you like, and the result will be the same?

Do you want to imply here that every claim to a mathematical theory of X is/must be a claim to a complete mathematical theory of X?

A claim to a mathematical theory of everything is/must be a claim to a mathematically complete theory. That is what "mathematical theory of everything" means, unless (as I've mentioned every time I've commented on it) the person asserting the existence of one doesn't really mean everything.

The following is merely an attempt to explain to the intransigent using a particular kind of language; it is not a signal that I intend to get involved in an infinite regress of discussion and authority citation of the matter, nor is it a sign that I am unaware of the controversiality of certain uses of natural language in expressing the meaning of certain mathematical truths. This is just for the sake of clarification, in case the reader happens to be open to clarification and further that this form of expression is helpful to that open minded reader:

One (controversial) way to talk about the subject is to say that in the case of an intensional mathematical theory, that is, a mathematical theory which is about something other than itself, we necessarily have both the mathematics of the theory and the metamathematics of the theory. The mathematical theory formalizes what is true and what is false about the metamathematical domain, the domain which the theory is about. So in the case of a mathematical theory of physics, we have the mathematical formalism which formalizes truths about the metamathematical domain of physical reality.

A claim that mathematical theory T (which, pace Step2, may be a synthesis of multiple formalisms; that doesn't change anything) is a theory of everything within the metamathematical domain (in this case physical reality) just is a claim that T - the formalism - is complete. And we know that, if T requires arithmetic, that claim is false.

So again, assertions of the existence of (non-trivial[*]) mathematical theories of everything are all definitely false.

[*] Non-trivial just means a theory that requires arithmetic.

Mind you, though perfectly true that is a stronger result than I required in my own earlier comments. My earlier comments just require that it be unreasonable to believe in the existence of a TOE[p], which it clearly is. But Kristor's stronger claims are also valid, as far as I can tell: that is, not only is it an unreasonable leap of blind faith against all evidence to believe in the existence of a TOE[p], it is also deductively irrational (to the best of our knowledge) to believe in a TOE[p].

And just to be clear, in my own comments I make the weaker claim - that positivist belief in a TOE[p] is unreasonable, resting on just the kind of "blind" faith against evidence in a transcendent all-explaining entity that positivists wrongly attribute to theists - precisely because my unreasonableness claim is more defensible than the claim that belief in a TOE[p] is deductively, through a Godelian refutation, irrational. I do in fact think (following 'stronger' interpretations of Godel a la Penrose) that belief in a TOE[p] is deductively irrational, that the criticisms of 'strong Godelianism' I've seen fail; but I fully recognize that defending that claim against all of the usual criticisms is more subtle a matter than just pointing out that there is no good reason to believe in a transcendent all-explaining TOE[p], and there are many good reasons not to believe in one.

And now the Hour on Calvary approaches, so I take my leave for the time being.

Vlastimil:

So, theism, Christianity, Aquinas' metaphysics, deontological ethics and arithmetic are incoheherent because they can't be formalized completely?

No. A doctrine can be formalized exhaustively and adequately, and can completely cover its domain, and can be perfectly coherent and consistent - but if it is consistent, and uses arithmetic (or by implication any higher maths) it cannot be complete. While I am very far from thinking that any of the doctrines you list cannot be formalized fully, consistently, coherently, adequately, and so forth, it is hard for me to imagine that they could be complete.

I think there is some confusion at work here with respect to the meaning of completeness. It refers, not to the scope of the domain of the formal system, or to its coverage thereof or adequacy thereto, or to its consistency or coherence, but to whether there are any sentences that can be generated by that formal system which cannot be proven or disproven by valid argument from the axioms thereof. If there are some such sentences, then the formal system is incomplete.

... entities that are extraneous to rutabagas ... But why such entities must be of a non-naturalistic (= supernatural) or non-physicalistic kind?

Well, they needn't be, I suppose, if your formal system is covering only rutabagas or rototillers. In such cases, we might be able to argue that our extraneous entities came from elsewhere in nature. But the ambition of science - the noble ambition of science - is to arrive at a formalization of everything physical using no preternatural terms. And that can't be done.

First, do math and logic need explanation? In which sense? ... Second, if they do, why the explanation must be non-naturalist or non-physicalist?

I'm catching a whiff of Euthyphro here. But whether or not math and logic need explanation, what I meant to indicate was that they are invoked in the formal system of the rutabaga, while the formal system of the rutabaga cannot be invoked in the formal systems of math and logic, for since the formal system of the rutabaga invokes math and logic, that would be circular. The system of the rutabaga invokes math and logic, but math and logic do not invoke the system of the rutabaga. Math and logic are super-rutabagal, or trans-rutabagal.

Substitute for "rutabaga" the whole realm of the physical or the natural. It invokes math and logic; but math and logic do not invoke it. Math and logic are super-natural, or trans-natural.

why does not your objection apply to theism? Why not to say: for “rutabagas,” substitute any congeries of mundane and non-mundane things you like, and the result will be the same?

Well, we weren't talking about theism, we were talking about the optimistic naturalist's pursuit of theories of everything physical.

But, since you mention it, my objection does apply to theism qua formal system; it applies to any non-trivial formal system. For any such system S, its consistency cannot be ascertained using only the terms of S. To determine its consistency, its axioms must define a subdomain of another formal system S', and the determination of the consistency of S must invoke the axioms of S'. This does not mean theism is incoherent, only that it is incomplete. That it is incomplete is no reproach to it. All non-trivial theories are incomplete. That doesn't make them false.

That this is so of theism should tell us two things: first, that God is unfathomable (except to Himself); second, that despite the pleasure and utility of theology, the proper basic work of man in respect to God is not ratiocination - for, precisely because God is unfathomable, to think so would be to indulge in proud hubris, and to recapitulate the error of Babel - but worship. Thus only is completeness really to be had.

None of this is news:

Where wast thou when I laid the foundations of the earth? Declare, if thou hast understanding. Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it? Whereupon are the foundations thereof fastened? Or who laid the corner stone thereof, when the morning stars sang together, and all the sons of God shouted for joy? Job 38: 4-7

Vlastimil:

If the forms are abstract Platonic objects, from what are they abstracted? You can’t have an abstraction floating there on its own, independent of any actuality. Abstractions are abstracted from actualities.

If God is wholly, utterly different, then yes, the God/World relation would be plagued with the problem of dualism. But such a God could have nothing at all to do with the world. We could not know anything about Him, and He could not affect us.

So theists have usually held that God is being itself, or maximal being, or some such thing; and that creaturely existence is a pale imitation or image of Divine being, or a partial participation therein. This way, God is not utterly different than His creatures with respect to the nature of His actuality, but rather with respect to the degree and extent of His actuality.

I find it interesting when people raise this argument. The assumption is that in the past almost everything from lightening to gravity was attributed directly to God and science slowly replaced every single one of these except for the "few" remaining phenomena today that still evade a naturalistic analysis.

I wonder where these people got their history from? If one turns to the history of theistic argument, for example, one finds medieval philosophers arguing for the existence of God not from lightening or gravity but from the existence of the universe, its origins, the apparent purpose in nature and the existence of moral values. Pretty much the same arguments contemporary philsophers offer today.

I am pretty sure that most of the medieval scholars accepted that many things, if not most, in the natural world could be explained proximately by natural causes; it was called secondary causation.

All this argument does is show up the superficial understanding of the history of Chrstian thought. Many educated people have today.

I completely agree, Madeleine. It's pretty much impossible to get any long list of things that used to be widely attributed to God (as miracles) that "we now know" are attributable to natural causes. So there is a shifting of the ground: "Well, but science has solved so many problems and questions..." etc. But talk about comparing apples and oranges! Physical explanation has told us about lightning and the planets, therefore we should expect...a physical explanation of the origin of the mind? Of the resurrection of Jesus Christ?

It always amazes me that people take this argument seriously at all. But a lot of them do.

Posted my last on this thread mistakenly. It should have, and has now, been posted over at the thread Hear Hear.

The argument does not follow. You cannot make an orange into an apple but apparently we are the ones who reject reason and science?

All this argument does is show up the superficial understanding of the history of Chrstian thought [m]any educated people have today.

It is much more comforting to the New Atheist to treat Christianity as the equivalent of a tribal native lightning-superstition (which frankly itself is probably not as silly as it is portrayed to be) than it is to address Christianity as it actually is.

It was both silly and dangerous.
http://www.cscs.umich.edu/~crshalizi/White/air/rod.html

Of course, the reason planetary motion was important to the theological view was that Earth was the center of the universe and all heavenly motion was explained by circular motion, which had been given a quasi-mystical status as the perfect geometrical shape since Pythagoras if not earlier.

There is indeed something very Pythagorean about modern prostration before the idea of a transcendent mathematical theory of everything.

Zippy,
Sorry about the bold type, I intended to use italics. Note to self: use the preview button, that is what it is there for.

Music of the spheres I suppose, there is a hint of that in the quest for supersymmetry in string theory. Going off-topic, if the Picard topology is right and Smolin's theory is also right there is some symmetry involved.

My view of TOE is that even if there is a limit that makes formal theories intrinsically incomplete too bad, science has no business in predicting 10-sigma events. It isn’t as though Gödel numbers are a large subset of number theory.

Step2: Also, the fact that geometry is inconplete does not make the Pythagorean Theorem false. That a TOE[p] is necessarily incomplete doesn't make it humanly inconceivable or false. All it means, I think, is that while there may be a TOE[p], there is no Theory of Everything whatsoever, or TOE[w] that is finitely conceivable - that, i.e., can be expressed in a finite number of statements. Thus if there be a TOE[w], it is expressible only by, & thus fully known only to, a thinker with infinite computational capacity.

Also, the fact that Hilbert's project is icompletable does not entail that any workstep therein is erroneous. Truth is integral & consistent. So the whole (non-contingent) truth had to have been completed a priori, at least implicitly, in order for any part of it ever to have been found true by anyone.

Lydia,

Blessed Easter days to you.

What about the counting problem being also our problem?

Don’t we, theists and Christians, sometimes need similar counting to defend reliabilities and trustworthiness of witnesses and organizations (e.g., this witness is reliable because of the much good, true info he had delivered to us; or this child is justified to believe her parents because they have proved to be worthy of trust many times before; similarly for a grandma trusting trusting her church or pastor) and philosophical, theological and scientific projects (e.g., theism/substance dualism/probabilism/Christian theism/Protestantism/Catholicism/Lorentzian theory of time/stem cell research is promising and worthy of further pursuit because it solved/viably explained many problems/evidences)?

Hello, Zippy,

A claim to a mathematical theory of everything is/must be a claim to a mathematically complete theory.

I'm unclear on that. Why does a theory which entails everything true (or everything true about a subject X) have to be complete (in Goedel's sense, that is, demonstrable in the specific technical way)? If you reply that just because it entails everything true (about X) it must be complete, I reply: why? How does (P entails Q) entail (Q is demonstrable in the specific technical way from P)?

A claim that mathematical theory T ... is a theory of everything within the metamathematical domain (in this case physical reality) just is a claim that T - the formalism - is complete.

Again, I don't get it. In short, why does "completeness" in the sense of explaining or entailing every truth about X entail "completeness" in Goedel's sense?

Hi, Kristor,

While I am very far from thinking that any of the doctrines you list cannot be formalized fully, consistently, coherently, adequately, and so forth, it is hard for me to imagine that they could be complete.

So, what's the formal advantage of the doctrines I mentioned over attempts at a TOE?

I think there is some confusion at work here with respect to the meaning of completeness. It refers, not to the scope of the domain of the formal system, or to its coverage thereof or adequacy thereto, or to its consistency or coherence, but to whether there are any sentences that can be generated by that formal system which cannot be proven or disproven by valid argument from the axioms thereof. If there are some such sentences, then the formal system is incomplete.

It seems to me Zippy is prone to this confusion, but given his competence I should be wrong.

any non-trivial formal system. For any such system S, its consistency cannot be ascertained using only the terms of S. To determine its consistency, its axioms must define a subdomain of another formal system S', and the determination of the consistency of S must invoke the axioms of S'. This does not mean theism is incoherent, only that it is incomplete. That it is incomplete is no reproach to it. All non-trivial theories are incomplete. That doesn't make them false.

And I still don't see why attempts at a TOE can't similarly manage without being complete.

Let me come back to this:

I doubt that a theory that is in principle impossible to formalize can be coherent

How do you recognize that a theory (or doctrine) can be formalized? Have you formalized all the theories you take to be coherent? Have you read some obviously correct formalization for all of them?

Step2,

It was both silly and dangerous.

Cf. http://web.maths.unsw.edu.au/~jim/medmyths.html Esp. Franklin's book.

planetary motion was important to the theological view

Cf. B. Vallicella: "Whatever significance we have cannot vary with our position in space or with the relative magnitude of the star which is our sun, and like facts. The upshot of the Copernican revolution, roughly, was that the earth went around the sun and not vice versa. True, but so what? How could that possibly diminish our status?" http://maverickphilosopher.powerblogs.com/posts/1196874834.shtml

As C. S. Lewis similarly said in God in the Dock, and as a commenter notes ibid., "the ancients knew quite well that the earth might as well be a mathematical point compared with the vastness of the universe. They believed (many of them anyway) that everything above the sphere of the moon, i.e. the overwhelming majority of the physical world, was made up of a different and more perfect element than this corruptible sublunar world."

So, I wonder whether the planetary motion and position of Earth was really important to the theological view.

NEWS

Lubos Motl, an esteemed scientific proponent of string theory and the author of a weblog awarded as the best in Continental Europe in 2008, promulgates in his fresh post the scientific optimism, citing Feynman:

God was invented to explain mystery. God is always invented to explain those things that you do not understand. Now, when you finally discover how something works, you get some laws which you're taking away from God; you don't need him anymore. But you need him for the other mysteries. So therefore you leave him to create the universe because we haven't figured that out yet; you need him for understanding those things which you don't believe the laws will explain, such as consciousness, or why you only live to a certain length of time -- life and death -- stuff like that.

http://motls.blogspot.com/2009/04/against-religion-of-chaos.html

Huh.

God is always invented to explain those things that you do not understand.

Yeah, you know, Copernicus, Kepler, all those guys. They just kept on inventing God to explain those things they didn't understand.

Sheesh. What unutterable hogwash.

Vlastimil, have you ever considered a career in sales? I understand persistence is an important virtue in that profession. :-)

More seriously, I haven't answered the counting question, first, because I was just back from a short vacation when you first asked it and was catching up, and second, because it doesn't seem to me to be all that crucial. (You will notice that I was willing to waive it, or at least one version of it, in my discussion of the optimistic naturalist.)

Let me distinguish two "counting problems." The first is the problem of coming up with a complete list of items where the list might, in theory, be infinite and where any such list is in any event unbounded and indefinite in length. This is an insuperable difficulty for the first version of the optimistic naturalist argument given in the main post, but it does not have anything to do with ordinary inductions, which work from a finite, bounded set of past instances to predictions about the future. Ordinary inductions don't start by saying something about all the instances of X in the universe and whether they are also Y. In fact, determining what proportion of all the X's in the universe are Y is part of the _question_ in ordinary induction, and one answers it on the basis of the finite number of X's _in one's experience or knowledge_ and the proportion of them that have also been Y.

The second "counting problem" has to do with individuating instances of (in this case) "questions science has answered with reference only to physical entities." Now, here, it seems to me that it is genuinely more difficult to make a non-arbitrary individuation of such questions than it is to make a non-arbitrary individuation of, say, "Things so-and-so has said to me which turned out to be true." The individuation of the latter is given pretty naturally in so-and-so's propositionally contentful assertions. The individuation of the former requires decisions as to level of generality. It would be fatally easy to individuate "questions science has answered with reference only to physical entities" and "questions that have not been answered with reference only to physical entities" in a manner that made the latter seem far less numerous than they are and the former far more numerous in comparison. Here, what I insist on is that one try to the greatest extent possible to list such problems at a comparable level of specificity. So, for example, if one is going to list diseases for which we now know the cause, one could on the other side list human actions and motivations for which we do not have a physical explanation. The whole thing is going to be exceedingly rough and ready, because these things just don't enumerate themselves as naturally as "mornings on which the sun has risen," but I say that any even roughly fair attempt to list them on both sides will find _at least_ as many "questions" or "problems" thus far thought of or encountered (and I actually think far more) that have no purely physical explanation as "questions" or "problems" that do.

Okay, now you can't say I ignored the question!

No, Lydia, I haven't. I'm slow and persistent, like Columbo said about himself, but persistent only in impractical matters of philosophy.

Thanks for the answer!

... it seems to me that it is genuinely more difficult to make a non-arbitrary individuation of such questions than it is to make a non-arbitrary individuation of, say, "Things so-and-so has said to me which turned out to be true." The individuation of the latter is given pretty naturally in so-and-so's propositionally contentful assertions.

That's interesting. Is it treated in some text pertaining to epistemology (of induction) in greater detail? Maybe Tim would know.

I try to communicate with Dr Motl (on the linked page, in the comments). But we're talking pass each other. I haven't figured out what his position (argument) is. He hasn't appreciated the difficulties of scientific optimism you set forth so clearly in this thread.

...why does "completeness" in the sense of [mathematically formalizing] every truth about X entail "completeness" in Goedel's sense?

Vlastimil:

You quote me:

While I am very far from thinking that any of the doctrines you list cannot be formalized fully, consistently, coherently, adequately, and so forth, it is hard for me to imagine that they could be complete.

And then ask:

So, what's the formal advantage of the doctrines I mentioned [theism, deontological ethics, &c.] over attempts at a TOE?

Unlike the optimistic naturalist's TOE, theism explicitly grants its own incompleteness as a matter of principle.

And I still don't see why attempts at a TOE can't similarly manage without being complete.

All formalizable non-trivial theories have to manage without being complete, because none of them are completable. That does not make them untrue.

How do you recognize that a theory (or doctrine) can be formalized?

That's the $64 question. One of the criteria of a formal system is that it is consistent. This means that none of its statements contradict each other. So if the formalization generates contradictions, you know you need to work on it. But even so, every consistent formalization can generate statements for which no such consistency can be validly inferred from its axioms - this is what it means when we say that such statements cannot be proven or disproven in the terms of the formal system under consideration. So we cannot make the determination whether a formalization really is a formal system - is, i.e., consistent - except by recourse to axioms that play no role in that system.

Have you formalized all the theories you take to be coherent? Have you read some obviously correct formalization for all of them?

Heavens, no. I wish. I take theism, for example, to be coherent not because I have completed its formalization - for that cannot be done in any finite amount of time - but only because it generates no first order contradictions, as I think Gödel showed that naturalism does.

Zippy,

Now I seem to get your idea. Your usage of "formalization" is stronger than mine. Thanks for the interaction.

Kristor,

I just still can't see how is Goedel relevant for refuting naturalism per se. It seems your argument against naturalism from math and being being in some sense trans-natural is just the old, metaphysical argument from the independence of universals and logical truths on the physical realm, as we discussed it briefly in the post Hear Hear!!

Typos, there should be: "from math and logic being in some sense trans-natural"

Vlastimil:

I just still can't see how is Goedel relevant for refuting naturalism per se. It seems your argument against naturalism from math and being being in some sense trans-natural is just the old, metaphysical argument from the independence of universals and logical truths on the physical realm.

I guess I don't disagree with that last sentence. Nevertheless, Gödel is relevant because he demonstrates that the argument from the transcendence of the universals is necessarily true - shows that there is no possible escape from transcendence, at least for a thinker who cares about the Law of Noncontradiction. Gödel shows the naturalist that there is no way he can undertake his project of naturalistic explanation except by recourse to a transcendent realm. I cannot but think that the deconstructionist insistence that nothing means what it says - i.e., that nothing means anything, and be damned to the objection that "nothing means anything" entails the meaninglessness of deconstructionist doctrine - is a reaction to Gödel's proof. Gödel shows the liberal nominalist that logically there is "no escape," so to speak, from realism, and from the transcendent. So the deconstructionist, cornered in his last redoubt, rejects even logic, and thus embraces madness.

Vlastimil, since you seem quite interested in this subject, I cannot too heartily recommend JR Lucas's book, The Freedom of the Will, which lays out the so-called "strong Gödelian" argument in great and compelling detail. Indeed, so compelling that I have a hard time seeing why it should be called "strong Gödelianism," rather than, "common sense, given Gödel's discovery." Oxford University Press will print one up for you specially for only about $60. It's well worth it. The book was one of the most thrilling I have read. Beautifully written, too; and one of those rare and precious glimpses into the inner life of a true genius, a polymath and a giant of erudition. Apparently a nice guy, too.

Kristor,
Unlike the optimistic naturalist's TOE, theism explicitly grants its own incompleteness as a matter of principle.

Unless you are referring to deism, no it doesn't. It says that what can be known of God's design is often cryptic, but it describes God as being itself, omniscient and omnipotent, the alpha and the omega. What sense of incomplete is meaningful to those descriptions?

The theism I am familiar with grants at the outset that human beings can know some things about some things, but cannot know everything about everything. Most forms of theism leave space for mystery, in other words, though there are some protestant and Islamic tendencies toward treating sacred texts as complete.

But in general, in my view, as I mentioned before, positivism is not strictly a necessary concomitant to naturalism either. It is just that positivist theories of everything, if they made any sense, would make naturalism more respectable on it's own terms. Any number of atheists have commented for example that Darwinism understood as a TOE with respect to origins makes it possible to be a self-respecting atheist. Stephen Hawking liked his own imaginary-time theory (that is, his theory that such a theory was possible) because it's putative completeness leaves nothing for a creator to do. In general naturalists tend toward belief in formal completeness precisely because that permits them to believe that as an epistemic matter we are merely in an historically contingent state allowing for a "God of the gaps"; a state which will one day, when the Theory of Everything emerges from a burning bush on Mt. Sinai, come to an end, forever banishing God's dominion, allowing the superman to arise and take his place at the summit of Babel.

And a postmodern, in my view, is simply a modern who has the sense to give up his blind faith in formal theories of everything but who doesn't have the sense to give up his modernism. As a result he merely exchanges one form of nonsense for another.

Zippy,
The theism I am familiar with grants at the outset that human beings can know some things about some things, but cannot know everything about everything.

Naturalism, as you point out, isn't required to be positivist, although I will admit the tendency towards that goal. Personally, I find quantum mechanics so alien and counter-intuitive that it suffices as a source of continual puzzlement.

Anyway, if you are going to insist on calling all moderns supermen, I want to have an actual superpower. Besides bad grammar and living in a state of bemusement.

Anyway, if you are going to insist on calling all moderns supermen...

Agreed --

In this day and age, Zippy should cease being so chauvinistic and start talking about all those "superwomen"!

Step2: Theism doesn't even claim to be adequate, much less complete. However many statements it makes about God, it doesn't claim to be a Theory of _Everything_ About Him. Indeed one of the basic doctrines of theism is that God is immense - i.e., immeasurable (for, how does one measure Measure itself?).

A math that is inadequate to its domain cannot be complete. And theism is doomed by those aspects of its domain that can be humanly comprehended (Divine immensity, eternity, infinity, & so forth) - or rather, merely indicated - to a fundamental conviction of its own inherent inadequacy thereto. The Tao that can be named is not the Tao.