Monthly Archives: July 2012

Word of the Day: Atheist’s Wager

Posted on by
8

Pascal’s Wager imagines belief in God as a wager.  Suppose you bet that the Christian god exists and act accordingly.  If you win, you hit the jackpot by going to heaven, and if you lose, you won’t have lost much.  But if you bet that God doesn’t exist, if you win, you get nothing and if you lose, you go to hell.  Conclusion: you should bet that God exists.

A thorough critique of the many failings of this argument will have to wait for another post.  But this argument is easily turned around to make the Atheist’s Wager.  If God exists and is a decent and fair being, he would respect those who used their God-given brains for critical thinking.  He would applaud those who followed the evidence where it led.  Since God’s existence is hardly obvious, he would reward thoughtful atheists with heaven after death.

But God would be annoyed at those who adopted a belief because it felt good rather than because it was well-grounded with evidence, and he would send to hell those who misused his gift of intelligence.

Here it is formulated as a syllogism:

  • God treats people fairly and will send honest, truth-seeking people to heaven and everyone else to hell.
  • God set up the world without substantial evidence of his existence.
  • Therefore, God will send only atheists to heaven.

The Atheist’s Wager can be different than Pascal’s Wager in that Pascal is assuming the Christian god, while the Atheist’s Wager can imagine a benevolent god.  The difference is that the actions of the benevolent god can be evaluated with ordinary human ideas of right and wrong, while Christians often must play the “God’s ways are not our ways” card to explain away God’s occasional insanity as recorded in the Bible.  For example, no benevolent god would send one of his creations to rot in hell forever.  Or support slavery.  Or demand genocide.

Of course, if a non-benevolent god exists, and the Christians stumbled upon the correct way to placate him, then the atheist is indeed screwed.  But then we’re back to the fundamental question: why believe this?

Photo credit: maorix

Related posts:

Related articles:

  • Austin Cline, “Atheism & Hell: What if You Atheists Are Wrong? Aren’t You Afraid of Hell?,” About.com.
  • “Atheist’s Wager,” Wikipedia.

Infinity—Nothing to Trifle With (2 of 2)

Posted on by
3

(See Part 1 for the beginning of this discussion in progress …)

We can compare the sizes of two sets of numbers by finding a one-to-one correspondence between them, but in the case of infinitely large sets, strange things can happen.  For example, compare the set of positive integers I = {1, 2, 3, 4, …} with the set of squares S = {1, 4, 9, 16, …}.  Every element n in I has a corresponding n2 in S, and every n2 in S has a corresponding n in I.  Here we find that a subset of the set of integers (a subset which has omitted an infinite number of integers) has the same size as the set of all integers.

Playing with the same paradox, Hilbert’s Hotel imagines a hotel that can hold an infinite number of guests.  Suppose you ask for a room but the hotel is full.  No problem—every guest moves one room higher (room n moves to room n + 1), and room 1 is now free.

But now suppose the hotel is full, and you’ve brought an infinite number of friends.  Again, no problem—every guest moves to the room number twice the old room number (room n moves to room 2n), and the infinitely many odd-numbered rooms become free.

Infinity is best seen as a concept, not a number.  To understand this, we should realize that zero can also be seen as a concept and not a number.  Consider a situation in which I have three liters of water.  I give you a third so that I have two liters and you have one.  I now have twice what you have.  I will always have twice what you have, regardless of the number of liters of water except for zero.  If I start with zero liters, I can’t really give you anything, and if I “gave” you a third of my zero liters, I would no longer have twice as much as you.

Not all infinities are the same.  Let’s move from integers to real numbers (real numbers are all numbers that we’re familiar with: the integers as well as 3.7, 1/7, π, √2, and so on).

The number of numbers between 0 and 1 is obviously the same as that between 1 and 2.  But it gets interesting when we realize that there are the same number of numbers in the range 0–1 as 1–∞.

The proof is quite simple: for every number x in the range 0–1, the value 1/x is in the range 1–∞.  (If x = 0.1, 1/x = 10; if x = 0.25, 1/x = 4; and so on)  And now we go in the other direction: for every number y in the range 1–∞, 1/y is in the range 0–1.  There’s a one-to-one correspondence, so the sets must be of equal sizes.  QED.

(Note that this isn’t a trick or fallacy.  You might have seen the proof that 1 = 2, but that “proof” only works because it contains an error.  Not so in this case.)

The resolution of this paradox is fairly straightforward, but resolving the paradox isn’t the point here.  The point is that this isn’t intuitive.  Use caution when using infinity-based apologetic arguments.

Let’s conclude by revisiting William Lane Craig’s example from last time.

Suppose we meet a man who claims to have been counting from eternity and is now finishing: . . ., –3, –2, –1, 0.  We could ask, why did he not finish counting yesterday or the day before or the year before?  By then an infinite time had already elapsed, so that he should already have finished by then.…  In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will have already finished.

The problem is that he confuses counting infinitely many negative integers with counting all the negative integers.  As we’ve seen, there are the same number of negative integers as just the number of negative squares –12, –22, –32, ….  Our mysterious Counting Man could have counted an infinite number of negative integers but still have infinitely many yet to count.

For a more thorough analysis, read the critique from Prof. Wes Morriston.

And isn’t the apologist who casts infinity-based arguments living in a glass house?  The atheist might raise the infinite regress problem—Who created God, and who created God’s creator, and who created that creator, and so on?  The apologist will sidestep the problem by saying (without evidence) that God has always existed.  Okay, if God can have existed forever, why not the universe?  And if the forever universe succumbs to the problem that we wouldn’t be able to get to now, how does the forever God avoid it?

This post is not meant as proof that all of Craig’s infinity based arguments are invalid or even that any of them are.  I simply want to ask apologists who aren’t mathematicians to appreciate their limits and tread lightly in topics infinite.

Of course, if the apologist’s goal is simply to baffle people and win points by intimidation, then this may be just the approach.

Related posts:

Related articles:

  • “Aleph number,” Wikipedia.
  • Wes Morriston, “Must the Past Have a Beginning?” Philo, 1999.
  • William Lane Craig, “The Existence of God and the Beginning of the Universe,” Truth Journal.

Infinity—Nothing to Trifle With

Posted on by
4

Snowflake curveThe topic of infinity comes up occasionally in apologetics arguments, but this is a lot more involved than most people think.  After exploring the subject, apologists may want to be more cautious.

Philosopher and apologist William Lane Craig walks where most laymen fear to tread.  Like an experienced actor, he has no difficulty imagining himself in all sorts of stretch roles—as a physicist, as a biologist, or as a mathematician.

Since God couldn’t have created the universe if it has been here forever, Craig argues that an infinitely old universe is impossible.  He imagines such a universe and argues that it would take an infinite amount of time to get to now.  This gulf of infinitely many moments of time would be impossible to cross, so the idea must be impossible.

But why not arrive at time t = now?  We must be somewhere on the timeline, and now is as good a place as any.  The imaginary infinite timeline isn’t divided into “Points in time we can get to” and “Points we can’t.”  And if going from a beginning in time infinitely far in the past and arriving at now is a problem, then imagine a beginningless timeline.  Physicist Vic Stenger, for one, makes the distinction between a universe that began infinitely far in the past and a universe without a beginning

Hoare’s Dictum is relevant here.  Infinity-based arguments are successful because they’re complicated and confusing, not because they’re accurate.

One of Craig’s conundrums is this:

Suppose we meet a man who claims to have been counting from eternity and is now finishing: . . ., –3, –2, –1, 0.  We could ask, why did he not finish counting yesterday or the day before or the year before?  By then an infinite time had already elapsed, so that he should already have finished by then.…  In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will have already finished.

Before we study this ill-advised descent into mathematics, let’s first explore the concept of infinity.

Everyone knows that the number of integers {1, 2, 3, …} is infinite.  It’s easy to see that if one proposed that the set of integers was finite, with a largest integer n, the number n + 1 would be even larger.  This understanding of infinity is an old observation, and Aristotle and other ancients noted it.

But there’s more to the topic than that.  I remember being startled in an introductory calculus class at a shape sometimes called Gabriel’s Horn (take the two-dimensional curve 1/x from 1 to ∞ and rotate it around the x-axis to make an infinitely long wine glass).  This shape has finite volume but infinite surface area.  In other words, you could fill it with paint, but you could never paint it.

A two-dimensional equivalent is the familiar Koch snowflake.  (Start with an equilateral triangle.  For every side, erase the middle third and replace it with an outward-facing V with sides the same length as the erased segment.  Repeat forever.)  At every iteration (see the first few in the drawing above), each line segment becomes 1/3 bigger.  Repeat forever, and the perimeter becomes infinitely long.  Surprisingly, the area doesn’t become infinite because the entire growing shape could be bounded by a fixed circle.  In the 2D equivalent of the Gabriel’s Horn paradox, you could fill in a Koch snowflake with a pencil, but all the pencils in the world couldn’t trace its outline.

Far older than these are any of Zeno’s paradoxes.  In one of these, fleet-footed Achilles gives a tortoise a 100-meter head start in a foot race.  Achilles is ten times faster, but by the time he reaches the 100-meter mark, the tortoise has gone 10 meters.  This isn’t a problem, and he crosses that next 10 meters.  But wait a minute—the tortoise has moved again.  Every time Achilles crosses the next distance segment, the tortoise has moved ahead.  He must cross an infinite series of distances.  Will he ever pass the tortoise?

The distance is the infinite sum 100 + 10 + 1 + 1/10 + ….  This sum is a little more than 111 meters, which means that Achilles will pass the tortoise and win the race.

Some infinite sums are finite (1 + 1/2 + 1/4 + 1/8 + … = 2).

And some are infinite (1 + 1/2 + 1/3 + 1/4 + … = ∞).

(And this post is getting a bit long.  Read Part 2.)

Photo credit: Wikipedia

Related posts:

Related articles:

  • “Zeno’s paradoxes,” Wikipedia.
  • “Zeno’s Advent Calendar,” xkcd.com.
  • “Paradoxes of infinity,” Wikipedia.
  • “Is God Actually Infinite?” Reasonable Faith blog.
  • Peter Lynds, “On a Finite Universe with no Beginning or End,” Cornell University Library, 2007.
  • Mark Vuletic, “Does Big Bang Cosmology Prove the Universe Had a Beginning?” Secular Web, 2000.
  • Wes Morriston, “Must the Past Have a Beginning?” Philo, 1999.
  • William Lane Craig, “The Existence of God and the Beginning of the Universe,” Truth Journal.

Gay Marriage Inevitable?

Posted on by
21

Jesus and God and apologeticsA century ago, America was immersed in social change.  Some of the issues in the headlines during this period were women’s suffrage, the treatment of immigrants, prison and asylum reform, temperance and prohibition, racial inequality, child labor and compulsory elementary school education, women’s education and protection of women from workplace exploitation, equal pay for equal work, communism and utopian societies, unions and the labor movement, and pure food laws.

The social turmoil of the past makes today’s focus on gay marriage and abortion look almost inconsequential by comparison.

What’s especially interesting is Christianity’s role in some of these movements.  Christians will point with justifiable pride to schools and hospitals build by churches or religious orders.  The Social Gospel movement of the early 20th century pushed for corrections of many social ills—poverty and wealth inequality, alcoholism, poor schools, and more.  Christians point to Rev. Martin Luther King’s work on civil rights and William Wilberforce’s Christianity-inspired work on ending slavery.

(This doesn’t sound much like the church today, commandeered as it is by conservative politics, but that’s another story.)

Same-sex marriage seems inevitable, just another step in the march of civil rights.  Jennifer Roback Morse, president and founder of the Ruth Institute for promotion of heterosexual marriage and rejection of same-sex marriage, was recently asked if she feared being embarrassed by the seeming inevitability of same-sex marriage.  She replied:

On the contrary, [same-sex marriage proponents] are the ones who are going to be embarrassed.  They are the ones who are going to be looking around, looking for the exits, trying to pretend that it had nothing to do with them, that it wasn’t really their fault.

I am not the slightest bit worried about the judgment of history on me.  This march-of-history argument bothers me a lot. …  What they’re really saying is, “Stop thinking, stop using your judgment, just shut up and follow the crowd because the crowd is moving towards Nirvana and you need to just follow along.”

Let’s first acknowledge someone who could well be striving to do the right thing simply because it’s right, without concern for popularity or the social consequences.  I would never argue that someone ought to abandon a principle because it has become a minority opinion or that it is ridiculed.  If Dr. Morse sticks to her position solely because she thinks it’s right, and she’s not doing it because of (say) some political requirement or because her job depends on it, that’s great.

Nevertheless, the infamous 1963 statement from George Wallace comes to mind: “I say segregation now, segregation tomorrow, segregation forever.”  That line came back to haunt him.  To his credit, he apologized and rejected his former segregationist policies, but history will always see him as having chosen the wrong side of this issue.

Christianity has similarly scrambled to reposition itself after earlier errors.  Christians often claim that modern science is built on a Christian foundation, ignoring the church’s rejection of science that didn’t fit its medieval beliefs (think Galileo).  They take credit for society’s rejection of slavery, forgetting Southern preachers and their gold mine of Bible verses for ammunition.  They reposition civil rights as an issue driven by Christians, ignoring the Ku Klux Klan and its burning cross symbol, biblical justification for laws against mixed-race marriage, and slavery support as the issue that created the Southern Baptist Convention.

Mohandas Gandhi had considerable experience as the underdog.  He said, “First they ignore you, then they ridicule you, then they fight you, then you win.”

(And then they claim that it was their idea all along!)

The same-sex marriage issue in the United States has almost advanced to “then you win” stage.  Check back in two decades, and you’ll see Christians positioning the gay rights issue as one led by the church.  They’ll mine history for liberal churches that took the lead (and flak) in ordaining openly gay clerics and speaking out in favor of gay rights.

If someone truly rejects same-sex marriage because their unbiased analysis shows it to be worse for society, great.  But it is increasingly becoming clear how history will judge that position.

Truth never damages a cause that is just.
— Mohandas Gandhi

Photo credit: Spec-ta-cles

Related posts:

Related links:

  • “Dr. Jennifer Roback Morse, Are Defenders of Natural Marriage on the Wrong Side of History?” Issues Etc., 5/25/12.
  • “Pure Religion: Revivalism and Reform in Early 19th-Century America,” The Dartmouth Apologia, Spring 2010, pp 20–24.

Witch Hunts, Sex Scandals, and the Atheist Community

Posted on by
Reply

I attended The Amazing Meeting 2, the skeptics conference organized by magician James Randi, in 2004.  I’ve been to many conferences before and after, but this one was a big deal for me.  Though not actually an atheist conference, I think it was the first chance I had to publicly kick around my embryonic interest in atheism.  A year later, I heard Sam Harris lecture on his new book, The End of Faith, and my interest in Christianity and atheism was ignited.

I bring this up because of dark clouds gathering over The Amazing Meeting.  I don’t pretend to understand the issue, but an Elevatorgate-like discussion has blown up about an incident of sexual harassment at a previous TAM, how it was handled, and then the inevitable recursive discussions about the descriptions of those incidents, critiques of those discussions, analysis of those critiques, and so on, seemingly to infinity.

Are women welcome and safe at TAM?  That the question is even being asked is incredible to me, but early evidence suggests the fraction of attendees who are women will be half of last year’s 40% because of concern over this story.  It must be an unintended consequence to all sides for a conference that is accused of being unfriendly to women to now become even more populated by men.

Some good has come out of this in that it has encouraged conferences to adopt anti-harassment policies.  That sounds like a positive step to restore confidence, assuming that they’re not extreme by, say, prohibiting a handshake or tap on the shoulder.

I’m amazed at the byzantine turns this topic has taken and the hold it has on some atheist bloggers.  It would take me days to read all that has been written, and let me say again that, not having done that, I don’t pretend to be well-informed about the issue.  But let me summarize an event that happened in my part of the country about 15 years ago that, while much more extreme, may have parallels to today’s anxiety about TAM.

Perhaps you remember the story about the Wenatchee child sex ring, what has been called history’s most extensive child sex abuse investigation.

It began in 1992, when, after much questioning, the 7-year-old daughter of poor and uneducated parents accused a family acquaintance of molesting her.  After repeated encouragement by the Wenatchee police lieutenant who was acting as foster parent to the girl and her sister, the girls eventually named over a hundred abusers and many child victims.

Local Pentecostal pastor Robert Robertson tried to do the right thing and talk sense to the investigators.  For his troubles, he and his family were sucked into the investigation, and the story was rewoven to include his church as a center for orgies with the children.  Others who also tried to rein in the crazy were also charged or fired.  (What explains a defense of the accused but that that person is similarly guilty?)

Child witnesses, mostly from 9 to 13 years old, were often taken from their families and placed in foster care. Many said later that they were subjected to hours of frightening grilling and if they didn’t believe they had been sexually abused, they were told they were “in denial” or had suppressed the memory of the abuse. They were also told that siblings and other children had witnessed their abuse, or that that their parents had already confessed.

Interrogators called some children who denied abuse liars. Children were told that if they agreed to accusations they wouldn’t be separated from parents or siblings. Many of them later recanted. [The police lieutenant] neither recorded nor kept notes of his interrogations.

Recantations were ignored. “It’s well known that children are telling the truth when they say they’ve been abused,” [the] Wenatchee Child Protective Services [supervisor said.] “But (they) are usually lying when they deny it.”

In all, “43 adults were arrested and accused of 29,726 counts of sexually abusing 60 children….  Eighteen pleaded guilty, mostly on the basis of signed confessions.  Ten were convicted at trial.  Three were acquitted.  Eighteen went to prison.”  All confessions were later recanted, all felony convictions related to the sex ring appear to have been overturned, a third of the children claimed to have been abused were at one point taken from their parents and put up for adoption, and the city of Wenatchee had to face lawsuits claiming millions of dollars in damages.

It was a modern-day replay of the 1692 Salem witch trial in which several girls’ accusations resulted in 19 people being hanged and one more pressed to death.

No, just because there’s smoke doesn’t mean there’s fire, and someone encouraging restraint isn’t necessarily part of the problem.  I hope the Wenatchee example of good intentions gone horribly wrong highlights some potential parallels with the TAM situation and that all parties analyze the evidence dispassionately.

Photo credit: Wikipedia

Links about the Wenatchee sex case:

  • “Wenatchee Witch Hunt: Child Sex Abuse Trials In Douglas and Chelan Counties,” HistoryLink.
  • “Wenatchee child abuse prosecutions,” Wikipedia.

Links about charges against The Amazing Meeting:

  • “‘Dogmatic Feminism’ Discussion Podcast (part 1),” Ask an Atheist blog, 6/12/12.
  • “‘Dogmatic Feminism’ Pt. 2, and Some Other Things,” Ask an Atheist blog, 6/14/12.
  • Jason Thibeault, “Harassment policies campaign – timeline of major events,” Lousy Canuck blog, 6/15/12.