Infallible, part 2: Consistency is Insufficient

Kurt GödelMichael, on his way to establish the infallibility of the Catholic Church, makes the claim that consistency is the defining characteristic of truth:

The hallmark of truth is consistency. Error can always be shown, at the core of the argument, to be logically inconsistent and ultimately self­refuting. Ergo, consistency is contingent to any claim of truth.

This is of course an error of monumental proportions.

Consistency is necessary but not sufficient. Sagan's dragon in the garage is perfectly consistent, but still untrue. Alchemy was, as far as I can tell, logically consistent, and turned out to be false nonetheless. Galilean relativity is consistent, but it’s Einstein’s Relativity that coincides with observation.

In physics, consistency is not even achieved as a whole, but only within theories (quantum field theory is incompatible with general relativity for example, although each is self-consistent), which should tell you something about the usefulness of the concept. Second, nothing is ever accepted in physics based only on consistency. You need confrontation to reality. That is the real test. Superstrings are consistent, and even plausible and compelling, but as long as we haven't obtained solid evidence for them, they are not going to be accepted. The graveyard of physics is full of failed hypotheses that were consistent but did not pass the test of reality.

Even in mathematics, consistency is not proof. As Gödel has shown, no non-trivial formal mathematical system can prove its own consistency.

I'll also point out that mathematical truth is essentially different from physical reality, and that it is always circumscribed by the axiomatic system in which they are expressed. For example, the proposition “only one line parallel to a given line passes through a given point” can be true or false depending on whether we are expressing it for Euclidean or non-Euclidean geometries. The geometry of our universe is not determined by consistency.

Michael makes a stupendous but too common error when he says that “error can always be shown, at the core of the argument, to be logically inconsistent and ultimately self-refuting”. This is the illusion apologists are under when they attempt to prove the existence of God through “logic”. If I claim that if I use a flashlight from a train, the speed of the photons is going to be the sum of the speed of light and of the speed of the train, I am making no logical error, and there is nothing self-refuting here. Still, I am in error, because my claim can be demonstrated to be wrong by experimentation.

Consistency is wholly unimpressive, and saying so is not at all the same thing as saying math or physics are unimpressive. Those disciplines have a lot more behind them than just consistency. Catholic dogma? Not so much. I remain unimpressed, except by the unwillingness of apologists to understand the difference between necessity and sufficiency.

Next time, we’ll examine the claim that the Bible’s cosmogonic myths are unique in describing creation ex-nihilo.


Infallible, part 1: Starting the Gish Gallop

Le papeOver the past few weeks, I had an interesting discussion on Facebook with Michael, a militant Catholic, about the Catholic Church’s claim that it is infallible. Like many arguments with believers, this has rapidly morphed from a single simple problem into a full-blown Gish Gallop. I should know better, but I bit. This series of posts is a compilation of my answers to his claims.

When the discussion started, and after trying unsuccessfully to drive home the point that consistency wasn’t sufficient to prove infallibility, I asked Michael to provide an example of a statement that qualified as infallible and that was also falsifiable: after all, it wouldn’t be very impressive to be infallible and only offer inconsequential and unverifiable claims. I offered an example of what it could look like (knowing, I must confess, that the Church had been claiming exactly that):

For example, if the Church were to claim ex-cathedra that Adam and Eve really existed and were once the only two human beings in existence. That's a factual and falsifiable claim.

I got the standard answer that I was expecting:

[…] the church has taught that Adam and Eve were real people. And science has verified Eve: look up 'mitochondrial eve'.

Mitochondrial Eve is a concept that is only describing a most recent common matrilineal ancestor, not a first ancestor or a unique member of a species. It's a useful concept in evolutionary biology, but not especially relevant in this case, especially as her male analog, Y-chromosomal Adam, was not living at the same time as her (missing her by a few dozen or hundred thousand years). We also know that there has never been less than about 1,200 members in the population we descend from. That's pretty much eliminating all possibility of anything remotely comparable to what's in Genesis, and of the Church’s claim being true.

Michael answered this with a long bullet point answer that you can read here:…/Infallible_Church

In the next few posts, I’ll respond to that, and to the inevitable response to the response.


My heroes are all dead: 1. DNA

And by DNA I don’t mean deoxyribonucleic acid, I mean Douglas Noel Adams, whom you probably know as the author of The Hitchhiker’s Guide To The Galaxy.

There are only two people that I didn’t know, whose death made me cry: Pierre Desproges and Douglas Adams. Both wrote prodigious comedy with surprising depth, but Adams was also an outspoken Atheist, and used science as a foundation of his storytelling. Preferably weird science, like quantum mechanics.

The Dirk Gently’s Holistic Detective Agency series for example can be read as relying on the interconnectedness of the universe’s wave function, quantum uncertainty, and spooky action at a distance.

The Total Perspective Vortex from the Hitchhiker’s Guide series can drive anyone insane by showing them their insignificance. It does so based on the principle that boundary conditions, any boundary conditions, such as the surface of a piece of fruit cake, could contain all the information you need about the rest of the universe. Enough to show it all in its glorious infinity, with you in it, “a tiny little mark, a microscopic dot on a microscopic dot, which says, "You are here."”

One of my favorite passages shows the futility of all arguments based on “pure logic” for or against the existence of God:

`I refuse to prove that I exist,' says God, `for proof denies faith, and without faith I am nothing.'
`But,' says Man, `The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.'
`Oh dear,' says God, `I hadn't thought of that,' and promptly disappears in a puff of logic.
`Oh, that was easy,' says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

Or on fine-tuning arguments, when a puddle thinks:

This is […] an interesting hole I find myself in — fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!"

And finally, this nugget on the role of science:

There are some oddities in the perspective with which we see the world. The fact that we live at the bottom of a deep gravity well, on the surface of a gas covered planet going around a nuclear fireball 90 million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be, but we have done various things over intellectual history to slowly correct some of our misapprehensions.

I miss you, Mr. Adams.


Arguments from authority?

Round-Earth is just a theoryDespite appearances, there is a fundamental difference between arguments from authority (or from majority) and scientific knowledge. That fundamental difference is that attacks, independent verification and repeatability are not only expected but necessary to the whole process.

To dumb it down in the extreme, I know that Thailand exists although I've never been there. Not just because people say so, but because I could go there and verify. I don't need to go there, just being able to is enough.

A fallout of it is that democratization of that knowledge, its diffusion to people who may feel they don't have access to it, is possible. There are good authors out there who can explain scientific theories in ways that you will not only understand but that will give you the keys that you need to trust that it's actual solid knowledge and not just speculations. If you need more than that, there is nothing that is ever inaccessible. Even the experiments at the LHC are accessible if you know where to look. That is by design.

Pseudo-sciences, in contrast, tend to only raise objections to established scientific theories, and do not provide the means to verify their claims. Although they are usually easy to refute, objections to those refutations often do exist. That doesn't give all those objections the same value, nor does it make their truth a matter of opinion. Those things are verifiable and verified. The very fact that you too could (not have but could) verify the validity of knowledge and evidence is what makes it more trustworthy than any argument from authority.

For example, flat-earthers do exist, their objections to a round-Earth are well known, and are easily refuted, but those guys do have refutations for those refutations that could look convincing in a vacuum.

I can show you how to set-up simple experiments to show that the Earth is round, and it should convince anyone in their right minds, but it won't convince flat-earthers, who are not in their right minds, and who will have objections for each of those experiments and objections. Or they will ignore the arguments and keep repeating the same BS. Creationists are doing the exact same thing.

There is an easy way to recognize pseudo-science for what it is though: so-called creation science has not resulted in a single real world application. You don't have to and shouldn't consider creationism or flat-earthism in a vacuum to judge whether they are likely or not to be true. All you have to do is see whether it *works*. Creationism and flat-earthism have produced nothing and just don't work. On the other hand, you need General Relativity for GPS to work, you need Quantum Mechanics for computers to work, and you need Evolution for biology, medicine and genetic engineering to work.


Contraception and Religious Liberty

Reproductive organsYet another response to Ambrose, whose blog doesn’t like that my comments tend to have more than 4,000 characters... He says:

"the underlying argument is that religious freedom is not absolute in the US. There have been Supreme Court cases, such as not allowing polygamy, where it has been limited."

Yes, all freedoms have limitations, which is not a big deal. In the case of religious freedom though, religious people in my experience tend to believe that it means that if their holy book mandates something, it should trump the laws of the state, or that no new law can go against what they believe. This would of course be impossible except in a single-religion theocracy (which eliminates entirely everyone's religious freedom of course). I've written extensively on the subject already so I won't add too much on this here.

"any limitation on our First Amendment right to free exercise of religion should ideally find its justification in the Constitution itself (such as the right to life) or clearly in natural law."

The Supreme Court disagrees with this, as in the specific case of polygamy that Ambrose mentions, it said:

"laws are made for the government of actions, and while they cannot interfere with mere religious beliefs and opinions, they may with practices."

In other words, religious freedom is not a license to act as your book tells you. We should all be glad about that, otherwise people would get punished for apostasy or other imaginary crimes (let's not forget that religions themselves impose the strictest limitations on religious freedom, ironically).

But there are a lot more assertions in Ambrose’s post that I find objectionable. For instance:

"nobody is making me work for [Mormon employers]"

Well, Ambrose has a great privilege, which is to choose where he works. Unfortunately the majority of people in this country have no such choice and accept the jobs they can get. Does he really think that the 16% of Americans who have no health insurance deliberately chose to work a job with no coverage? That they could just have chosen to work where they would get great dental as part of the deal? Come on.

It should be mentioned that it’s not the employer that would have to pay for contraception (which I personally regret), so its religious freedom is hardly touched, even with Ambrose’s liberal definition of it:

"if a woman works for a religious employer with objections to providing contraceptive services as part of its health plan, the religious employer will not be required to provide, pay for or refer for contraception coverage, but her insurance company will be required to directly offer her contraceptive care free of charge."

Ambrose also makes a reference to Planned Parenthood that I find interesting, knowing the campaign of hate that has been unleashed against this institution by the religious right:

Even if we were to agree that contraception should be considered "health care," it is widely freely available through other means via organizations like Planned Parenthood.

Beyond the scare quotes, is he saying that he would advocate for better Planned Parenthood funding?

"All you have to do to avoid it is, duh, not have sex. So if someone is in a position where they it (sic) would negatively impact her health to become pregnant, she doesn't need expensive drugs or procedures to help her with that. Just don't have sex while you're fertile."

Now when comparing the efficacy of contraception methods, one must take into account user failures. Condoms for example (that Ambrose seems to be advocating for, which comes as a surprise to me) are fairly efficient if used properly, but the problem is that they often aren't. The method that he advocate for (sympto-thermal) is way worse. When properly applied, it is efficient (so is complete abstinence), but it still has a catastrophic overall failure rate, comparable to coitus interruptus. Recommending this when we have much better options is just irresponsible. Also, what can Ambrose possibly imply by:

"It's homeopathic! It's organic! It's all natural! It's great!"

Homeopathy is a demonstrated scam, and arsenic is natural too, so I don't see a good argument there.

"let's not forget that STDs are a serious problem, right?"

Yes, they are, but there doesn't seem to be a link between contraception and risk-taking (I'm not a MD but the research that I did in the literature indicates the contrary is true).

If Ambrose is sincere about limiting the spread of STDs, it seems his best weapon would be comprehensive sex education. Would that go against religious freedom?

"Preventing pregnancy is not analogous to preventing disease."

No it’s not, but pregnancy does have a huge impact on women's health. Limiting unintended pregnancy was in fact one of the major factors of progress during the 20th century. It reduced infant and maternal mortality rates, limited the spread of STDs and gave many women better opportunities to contribute to society. In turn, we know that empowering women is the single most efficient factor of human progress. Oh, and also, contraception is a great way to limit the number of abortion, whether those are legal or not.

Of course all that is not even touching on the right of women to enjoy sex without becoming pregnant (a right that men have been enjoying since... forever).

"If people feel strongly that all women should have access to contraception, I suggest that they coordinate and fund clinics and the like who can provide it. Or heck, they can just create a fund to cover it for the women who work for Catholic agencies. We don't need the government to mandate violation of the First Amendment to achieve their ends."

So now we have to pay for the shortcomings of Catholics? It so happens that the 99% of Americans who use or have used contraception do feel that women should have access to contraception (and they are right), and they did coordinate and fund organizations that can provide it. They did it by electing governments that advanced our society and provided Planned Parenthood, among other things.

We all pay for things we disagree with, through taxes and other means. Well, tough. For what it's worth, I'd like to get my Iraq war money back, but that's not going to happen, is it?


Don’t mind us, just continuing our vendetta

Careful thereThis is an answer to Ambrose’s answer to my answer to his post on atheists. Comment fields are just too small, so we exchange blog posts. Feel free to ignore me as I talk to Ambrose…

Hi, "poor Bertrand" here. First, don't worry too much about me, I'll do just fine. Second, no, I am not trying to prove myself smarter, or anything silly like that. Having always been surrounded by people who were clearly smarter than me, I maintain no illusions of the sort. The truth of it is that I actually have (as I've said before) a lot of respect for you, and I think you can do much better than that. I maintain that your post was in a way lazy, relying as it was on one single example, one where the author could quite easily be suspected of not talking seriously, being a writer of mostly comedic books. I do apologize for the general tone of the post though, as it could have been much more centered on ideas rather than personal trolling. I guess your post had the misfortune of being the proverbial straw on the camel's back that day.

So what more could you have done? Well, maybe quote from more than one book (oh the temptation to troll on that one, but I'll be strong, I'll resist), more than one atheist or ask atheists that you know what they thought? I would have no problem with your explaining your readership what atheists think if you were exposing the actual spectrum of opinions or narrowing your target to something more precise than that very wide term.

Unfortunately this new post piles new misrepresentations on top of the previous ones. Involuntary ones I'm assuming: there is a clear call to honest discussion, so again I'll bite.

At no point did I claim to say what all atheists believe, except for the absence of god, which is the definition of the word. What I exposed was my own position, as I thought was made clear by my usage of the words "I", or "me".

The claim that you and the book I linked to make is not just that monism requires faith, but that it requires *more* faith than... faith religion (you said: "it takes a tremendous amount of faith"). I pointed out in my post that the assumptions behind science (not atheism) are quite benign and cannot be meaningfully compared with those of any religion. I have not given up hope on convincing you one day that the flying spaghetti monster comparisons are more relevant than you think. The idea is not (just) to ridicule organized religion, but to explain what most religious claims look like *when seen from the outside*. My talking directly about your beliefs is unlikely to convince you because you have trained yourself to rationalize them. The FSM comparison is intended to shift your viewpoint and show you how your beliefs can look like. The hope is that it may encourage you to take a true outsider's test for faith, of challenging your own assumptions.

I recuse the accusation of scientism. I don't consider science to be a universal and exclusive answer (nor do I "worship" it, that is preposterous). I do not claim to "have a direct line to truth based solely on science". What I do maintain is that science has enabled us to attain some truths with an unparallelled level of reliability. That when a claim is contradicted by science but affirmed by religion, science wins every time. I also maintain that as science progressed, the gaps where the supernatural can hide has been shrinking considerably, and one is warranted to ask whether it exists at all. It certainly warrants one to ask for a precise definition of the supernatural. What does it *do*? If it doesn't do anything, it might as well not exist. If it does something, we can observe that something and put it to the test. Note that I'm not saying it doesn't exist, just that I find it extremely improbable. Is that materialism? Maybe it is. What it is not is a reduction to only admitting the existence of things that have "atoms".

You claim that "in school we are indoctrinated to treat [science][...] as an authority". Well, I don't know what kind of school you attended, but the ones I went to, and the ones where my kids go, have always made it very clear that science was verifiable, not a matter of authority at all but one of experiment. I cannot think of a single example of something being presented in the science classes that I attended without a direct experiment supporting it. The word "indoctrination" is particularly inappropriate as science teachers tend to do a good job at asking their pupils to think by themselves and formulate their own hypotheses, and then confront them to the results of an experiment. And before you ask, yes, even quantum mechanics I've been led to experiment directly, and so can you. I even went into the tunnels of the CERN and visited the colossal machines that observe and measure particle collisions.

Is there "an ability of science to account for reality"? Yes, there is, and we know that because it works, because we have countless verifications that it does, not because we have faith in it. No reification to see here. You say that "unless you personally participate in scientific experiments of EVERYTHING that you want to form an opinion about, then you are de facto forced to take things on authority, including those things purportedly discovered through scientific methods". I have heard that a lot, and it is true to an extent, but that extent is very small, which makes the argument a little dishonest. The *principle* of reproducibility is sufficient to reduce the importance of authority. If someone tells you that there is a teapot in orbit around the sun, he's asking you to believe him on authority, and that is just silly. If the same person tells you there is a teapot in the kitchen, and if there are people in the kitchen who are attesting there is a teapot, and who are reporting how they came to that conclusion (by seeing it, by touching it), if all those people give a consistent description of the teapot and if those persons are inviting you to verify yourself that the teapot is there, you don't need to actually go there to have a much higher degree of certainty that there is a teapot in the kitchen than that there is one in orbit around the sun. So is this still accepting the teapot on authority? Essentially yes, but to such an extent that it becomes irrelevant. That's what I meant when I said that not all authorities are equivalent.

When you say "you can't subject justice and love to scientific experimentation", I would disagree: why not? Both those concepts obviously exist and have an effect on the world. Why couldn't we study that effect? I'm not saying that it would necessarily give us a complete understanding, note. But some understanding, certainly. For example, if those sentiments can be induced realiably, isn't that an interesting insight?

Let me try to explain again now that thing about justice and love as emerging concepts. What I'm recusing is the idea that either requires a source. The idea of a source implies that there is something like a fluid, that is conserved and needs to be injected from somewhere else in order to exist. But when I fall in love, do we really need to believe that Cupid or some other entity had to transperce me with an arrow that had been plunged in the mysterious fluid? It's a poetic image, but not much more than that. There is no need for a reservoir of love, and giving love somewhere does not deplete it from somewhere else. That it's not conserved does not imply either that there is an infinite reserve of it somewhere. It only means that it is not conserved, like many other things, such as entropy or temperature. This leads to an important point: thermodynamics give one of the simplest examples of emerging phenomena. Thermodynamics have been developed without an understanding of the underlying microscopic phenomena. Later, we discovered that it could be *reduced* to the microscopic motion of molecules, but the concepts of temperature, exchange of heat or entropy form a perfectly fine model at the scale where they are valid. One cannot find an atom of heat, but one can understand how heat emerges as a concept from the collective movement of atoms. More than that, the concept of heat has no meaning at microscopic scales, but only makes sense at macroscopic ones, where statistics can be computed. The feeling of love can appear in a sufficiently complex animal's brain, and without resorting to evolutionary psychology, it is pretty obvious to see how it can be beneficial to the species (see Price's equation -and yes I'm aware of Price's religious ideas-). The same goes for justice, which is largely a corollary of the ideas of fairness and reciprocity. All those concepts require no source, only a substrate. This substrate is the brain. There is no need to invent a mysterious external source.

On dualism, not to appear arrogant, but Please note, Ambrose, that I did not categorically reject the possibility of a soul (it may surprise you, but neither do I categorically deny the possibility of a creator god), I just said that it was increasingly improbable as neuroscience progresses. Again, what does it do that a brain can't? I think that at best the answer is that we don't know. Otherwise, the next question has got to be: how do you know?
Finally, I'm all for the benefit of the doubt. Doubt is all I ask in fact.


Learning from a Catholic what Atheists think

Bertrand Russel thinks you are mistakenIf you’re out of the closet as an atheist, there is a number of canards that you will hear a lot. One of them is that Atheism requires more faith than religion. Whole (bad) books have been written on that “idea”. Ambrose has a new post on this entirely unoriginal topic, and he gets everything predictably wrong.

The problem with making blanket statements about atheists is that we are negatively defined. It’s a little like trying to understand how non-philatelists think. With a religion, it’s easy: there are holy books and dogmas. No such thing with atheism or aphilately, as the only common point between us is an absence. However, that doesn’t prevent our theist friends from telling us how we all think.

[Terry Pratchett] says something like "take apart the universe to its smallest particles and show me one grain of Justice" or something like that (sic). It's actually fairly poetic in its own way (I'm not doing the passage justice, no pun intended).
Sadly, I think it does accurately portray what an atheistic, materialistic worldview honestly is left with at the end of the day. No indeed, there is no atomic element of Ju (Justice), nor of Lv (Love), nor any other virtue. In a materialistic philosophy, these things really are lies, and an adherent is forced to have faith in those lies in order to create a reality that is bearable as a human.

No, that does accurately portray no such thing. Ambrose is conflating atheism with materialism, materialism with reductionism, and reductionism with determinism. He also betrays a very common quality of religious thought: a form of materialism that goes much farther than that of most people with any scientific literacy. Why do people think that in order to exist, something has to be reducible to some sort of conserved substance? What a lack of imagination that is. To take a random example, entropy is a very well-defined and real quantity, but there isn’t such a thing as an atom of entropy. A thought is a real thing as well, although there is no such thing as an atom of thought. Even if the substrate of all reality is space and elementary particles, there are innumerable emergent phenomena that are just as real. There is no problem or contradiction here.

It’s theists that make the false assumption here that love, morality or justice are substances that need to be breathed into the world by some magical entity, instead of just emerging from the brains of social animals. One thing that I can tell you is that you will never hear me say that morality or justice are illusions. I do think they are very real, even if they are only meaningful within human or human-like  experience. This makes the following assertion fall flat on its metaphorical face:

one difference is that some atheists may try to deny that they have such faith, if put to the test, saying rather that, for example, Justice is only a handy term to represent a reasoned view of moral behavior in society based on mutual self-interest.  But then ask them what they think about having prayer in schools or not redefining marriage to include homosexual unions, and just listen to them go off on how "unjust" those things are.

Oh, but what’s wrong with a “reasoned view of moral behavior in society based on mutual self-interest”? And how do issues of separation of Church and State, or civil rights contradict such a view of justice?

if I'm going to believe in things like Justice, Love, Freedom, Happiness, and other ideals and virtues, I prefer to have a rational basis for believing in them

Fine, and what would that be?

I think it takes a tremendous amount of faith to believe that my human experience is only the result of material interactions in my body. On the contrary, every fiber of my being tells me that there is more to my existence than the material--my own,observed and reasoned experience (I tend to be fairly self-reflective). So why would I take it on faith from scientists (an Authority) or atheistic philosophers (another Authority) that this is so, contrary to my own observations of life?
For me, that would take a lot more faith than to believe in what seems obvious to me based on my own experience and reason, namely that there is a Prime Mover

What Ambrose is basically saying here is that he trusts his personal experience, common sense and gut feelings more than science, ergo Jesus.

He makes a considerable number of mistakes here.

First, personal experience, common sense and gut feeling are extremely poor indicators of truth. Anyone who has studied quantum mechanics, or who has even seen an optical illusion should know how easy it is to fool the human brain, and how reality doesn’t give a damn about your common sense. You need tools such as science to mitigate your own biases.

Second, even if there is a leap of faith at the basis of all human thought, that does not make the tiny assumption that there is an objective reality equivalent to the huge assumption that there is an invisible flying spaghetti monster whose noodly appendages move all things. It’s a common claim of theists to assert that because nothing is ever absolutely certain (an assumption that is necessary to scientific thought), then all beliefs, no matter how outlandish, are equally legitimate to hold. It’s ironic that they hold their dogmas to be absolutely certain.

Third, the claim that scientific knowledge is a form of argument from authority is infuriatingly ignorant. Scientific knowledge is based on reproducible experiments. No claim is ever accepted before it has been replicated by independent teams. Who makes the claim is almost entirely irrelevant (although not all authorities are equivalent). Another very important difference between religious thought and scientific thought is that science works.

Finally, dualism is getting increasingly indefensible in the light of the progress of neuroscience. Once you know how changes in the brain mechanically cause changes in behavior, sometimes to the point where the identity of the person is radically altered or replaced, it becomes extremely difficult to believe that there is a soul in addition to the brain.

Atheism is a faith? What a joke.


Can God appear in a puff of logic?

Saint AnselmLogic is a tricky thing. Any sound argument must rely on it, but it is easy to build seemingly sound and logical arguments that are still wrong or fail to apply to the real world. Fuzzy or wrong premises, shortcuts in reasoning, as well as plain fallacies such as circular reasoning, are easy to obfuscate, and apologists are kings at this game. It's what they do: take the conclusion they want to reach, and then build the rationalization for it. A prime example of this is the age-old ontological argument for the existence of God, that I will be looking at in details in this post.

The argument is that because we can conceive of a perfect being (defined by the impossibility to improve it), then it must exist for surely existing is better than not existing. Really? We'll see.

But first, let me quote Douglas Adams...

Now it is such a bizarrely improbable coincidence that anything so mindbogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the non existence of God.
The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves that you exist, and so therefore, by your own arguments, you don't. QED."
"Oh dear," says God, "I hadn't thought of that," and promptly disappears in a puff of logic.
"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.

What Douglas Adams articulates so brilliantly here is that with badly defined premises and "pure logic", you can prove anything and its opposite, and that therefore you can prove nothing. There is no such thing as a puff of logic of course, as puffs are physical, and logic is mathematical, independent of the physical world, and therefore utterly unable to puff. Of course, I could have quoted Hume and Kant to pretty much the same effect, but this is a lot more fun, isn't it?

To drive the point home, let me paraphrase a reverse formulation of the argument I found in the comments of Ambrose's recent post on the subject:

We can conceive of maximal evil, for which one cannot possibly imagine anything more evil. Surely, it must exist, as something maximally evil would be quite benign if it didn't exist, and would assuredly be more evil if it existed. Therefore, it exists.

Oops. Putting empirical credibility aside, it doesn't look any more or less logically sound than the original argument. So where's the flaw?

What most people call "pure logic" is actually much trickier to define than they may think. I learned that in France a little more than 20 years ago when I was preparing the entry contest for college. One of the students in my class was an orthodox Jew, convinced that the world was 6000 years old, but also a genius, who had already explored Mathematics way farther than any of us. What he taught me was that words are not appropriate to do mathematics. One must be absolutely formal in order to avoid talking nonsense. Here is the example he used, also known as Russel's paradox:

A mathematical set is a pretty simple entity, right? It is defined by its elements. OK, so now consider the set of  non-auto-inclusive sets, defined as the set of all sets that do not contain themselves. Well, that set cannot include itself, by definition, because all its elements are non-auto-inclusive. Therefore, it must include itself since it doesn't.

Uh? Yeah, exactly. Mathematics don't have paradoxes, they only have reductio ad absurdum. This so-called paradox only proves that the naïve concept of set we used here is inconsistent. In particular, the notion of a set of all sets can't be rigorously defined, although an English formulation of it seems to present no challenge. This is known as the naïve set theory, and it had to be replaced by something much more rigorous, which eventually led to a re-foundation of all of Mathematics by the Bourbaki group. This is an eminently modern idea that  Anselm of Canterbury, Kant, Leibniz, Descartes or Plantinga could not possibly have known. We need to apply formal logic in order to determine what in the ontological argument is valid formal logic and what constitutes its premises and hidden assumptions.

Several people have done exactly that with varying success, but the attempt that I find the most interesting consisted in feeding the argument into a computer algorithm that automatically proves mathematical theorems. If that wasn't awesome enough, the good news is that the algorithm not only showed the logical soundness of the argument, it was actually able to simplify it and reduce the assumptions to a single one. The bad news is that this remaining assumption is not trivial. Here it is:

If the conceivable thing than which nothing greater
is conceivable fails to exist, then something greater than it is conceivable.

Makes sense? Suffice it to say that this still needs independent justification that cannot be reduced to formal logic. Back to square one are we? You can still argue one way or the other, but you are outside of the realm of logic doing so, which pretty much means that the argument, while quite subtle and logically sound, is not a complete proof of the existence of God.

Before I conclude this post, I'd like to point out that such attempts to make God appear in a puff of logic are not only doomed logically, they also constitute poor theology (assuming for a second there is such a thing as good theology). For really, doesn't it degrade the idea of God to reduce it to something that can be described and constrained by mathematical expressions? Doesn't that bring him down to the realm of the natural?


Metaphorical? But why?

Dürer: the fall of manMost modern believers interpret their sacred texts as mostly metaphorical. Only the most hard-core fundamentalists maintain that Genesis for example is an accurate historical account of the origin of Humanity.

In order to maintain such a hard stance, they must reject most of what the modern world has to offer, in particular empirical science and its discoveries.

The myth of Adam and Eve as the two ultimate ancestors for the whole of humanity for instance has been destroyed by genetic evidence and by population genetics in general.

It is unfortunately an extremely important myth as without it there is no original sin, and without original sin there is no need for a universal redeemer.

Faced with the evidence, believers resort to a number of techniques to salvage their faith. Some reject empirical science as a whole, some misrepresent the evidence and twist it to fit their pre-established conclusions, and some revise their interpretation of the text by declaring it "metaphorical".

I'm not too interested about the first two, which have willingly moved beyond reason. The third is more intriguing, but I think not much more consistent.

If the god of the Bible exists, he had the power of making the world exactly as it is described in the books he supposedly inspired. Why didn't he then?


More Aperture Science: the Light Bridge

The Light BridgePortals are not Aperture Science's only remarkable scientific accomplishment. Among their other inventions is the Light Bridge, that provides a stable and seemingly immaterial surface that people can stand on. The bridge can also be turned on or off instantly.

How does it work and is it really made of light?

It certainly emits light but it most definitely isn't made of it. For light to be able to withstand the weight of a person would require an amount of energy that would have to be directed upwards and that would be sufficient to fry them instantly.

There is little information available on Light Bridges but similar technology has been mastered by others. One declaration we were able to get from an Aperture representative is the following:

"If you rub your cheek on it, it feels just like being outside, with the sun shining on your face. It will also set your hair on fire, so don't actually do it."

This is because the bridge seems to be a stationary wave of photinos, the supersymmetric partners of photons. Around the surface of the bridge, there is an evanescent wave that is characteristic of a phenomenon of total reflection.

The tricky part is that what is being totally reflected on the surface is the quantum wave function of all fermions above the bridge. In other words, the force exerted by the bridge on what stands on it is purely quantum mechanical in nature, similar to what keeps electrons in separate atomic orbitals or to what keeps a neutron star from collapsing further. It could even be seen as a sort of reverse-quantum-tunneling effect, where objects cannot possibly move any farther. An anti-portal of sorts.

Now light can still pass through because it's made of bosons, of course, which explains the translucency. The blue color is due to the disintegration of some of the photinos that form the bridge.

There is a cylindrical version of the light bridge that is used as a tractor beam and that is obtained by not making the photino wave exactly stationary.

That is it for today. I'll take questions now.