Logic for the Complete Idiot

"Logic is the beginning of wisdom, not the end." - Mr. Spock

Recently I heard someone declare that liberals are incapable of logical thought. But that same day, I saw a meme floating around Facebook making fun of "Republican Logic 101." So clearly some liberals think the conservatives are the illogical ones. You can find similar memes attacking atheist logic, or Christian logic, or creationist logic, or "evolutionist" logic. Everybody thinks their side is logical, and the other side isn't. The world is full of people who think they understand logic. What it is not full of is people who really do. 

The truth is, most people have barely a clue how logic really works. Take me, for example. I've always tried hard to think logically, and I tell myself I'm pretty good at it. I've even read a couple dozen books about critical thinking and informal logic. I can spot a straw man, a red herring, and many other fallacies (at least when other people commit them), and I can tell you about a multitude of cognitive biases that keep us from being as smart as we think we are. So you can imagine my horror when I recently picked up a book called Logic for Dummies, started reading it, and thought, "Maybe I should start with the Complete Idiot's Guide." 

My only consolation is that Logic for Dummies is all about formal logic. It's full of Venn diagrams, truth tables and strings of symbols that look like some kind of alien algebra. It's more mathematical than linguistic. And it's not easy. Well, it's not easy for me...few things involving the word "formal" are. Still, in this post I want to explore what I've learned so far. For one thing, maybe I can save someone the initial bewilderment I had when I started trying to learn about formal logic. Beyond that, though, I want to explore how useful formal logic might be in everyday debates. 

What is Formal Logic?

First the basics. Formal logic is a way of putting some arguments people make in ordinary language into a precise, standardized form, in order to determine unambiguously whether they're valid or not. I say "some" arguments because formal logic is mostly concerned with deductive arguments--arguments where the truth of the conclusion depends on the structure of the argument, not the content of the premises. If a valid deductive argument has true premises, it can't help but have a true conclusion. That's what valid means. With invalid arguments, it's possible for the conclusion to be false even if the premises are true. 

For example:

If Bubba ate that green porkchop yesterday, he will be sick today.
Bubba is not sick today.
Therefore, Bubba did not eat that green porkchop yesterday.

That's a valid argument, of the form called modus tollens. If both premises are true, the conclusion can't help being true, just by virtue of the structure of the argument. However:

If Bubba ate that green porkchop yesterday, he will be sick today.
Bubba is sick today.
Therefore, Bubba ate that green porkchop yesterday.

That's not a valid argument--it's the fallacy called affirming the consequent. Bubba could have passed on the porkchop but gotten sick for other reasons. The conclusion might be true if the premises are true, but it isn't necessarily true. Validity and truth are connected, but they aren't the same thing. An argument can have totally ludicrous premises and an equally ludicrous conclusion, and still be valid. For example:

If lizards play fiddles, then frogs will dance jigs.
Lizards play fiddles.
Therefore, frogs will dance jigs. 

That's a valid argument, with a form known as modus ponens. But valid doesn't mean true. It's just that if the premises were true, then the conclusion would be as well. Lizards, alas, do not play fiddles. Conversely, an argument could have true premises and a true conclusion, but still be invalid. Even if Bubba ate that porkchop and then got sick, the second argument above still isn't valid. If an argument is both true and valid, it's said to be sound. If it's valid but not true, like the one about lizards and frogs, it's unsound.

Formal logic, then, is concerned with deductive validity, not truth. It's the study of what conclusions can be validly drawn based on certain arrangements of premises. That makes it limited when it comes to everyday arguments, because many of those are inductive, not deductive. An inductive argument is any argument where the premises may support the conclusion, but the conclusion doesn't necessarily follow from the premises by virtue of the argument's structure. Analogies, generalizations, predictions based on past observations--those are all inductive. The second Bubba syllogism above might be a decent inductive argument. You might hear that Bubba is sick and correctly guess that it's because he ate that porkchop. But the premises only support the conclusion inductively, not deductively. 

So far, none of this seems all that hard. But the devil is in the details. If you want to learn how to translate ordinary arguments into the symbols and structures of formal logic, it gets really complicated. For one thing, there are several kinds of formal logic, and logicians can't seem to agree on what to call them. There's propositional logic, which is sometimes called sentential logic, sentence logic, or truth functional logic. Then there's predicate logic, which is sometimes called quantifier logic. So, the first thing we have to do is get the different types of logic sorted out. 

Most introductory textbooks on logic cover three branches: categorical logic, propositional logic, and predicate logic. Categorical logic is concerned with classes of things, and is based on statements like "All cats are mammals" or "Some mammals are not quadrupeds." Categorical logic is a way of reasoning about which things belong in different classes, and it's the kind of logic that uses Venn diagrams--the little conjoined circles that show which classes do and don't overlap. It's also the oldest kind of logic. It was basically invented by Aristotle. It looks the simplest, but don't let that fool you. When you actually try to use it, it's a lot tougher than it looks. 

Propositional logic developed later, among the Stoics. Unlike categorical logic, which is concerned with terms inside phrases, propositional logic is concerned with the relationship between whole phrases, each containing a subject and a predicate. To see the difference, consider the phrase "Lassie is a collie" In categorical logic that would be an entire line in a syllogism. It's concerned with two terms, or classes of things: things identical to Lassie (in logic jargon), and collies. It might be symbolized as "All L are C." In propositional logic, that phrase would just be one part of a line, for example, "If lassie is a collie, then she is smart." Now the whole phrases on either side of the comma can be turned into single symbols, so we might have "If L (lassie is a collie) then S (she is smart)." The "atoms" of categorical logic are smaller parts of sentences than the atoms of propositional logic. 

Propositional logic can be completely expressed in symbols, so it looks almost like algebra. Here are the five basic symbols it uses.

⊃ means "implies" or "if, then"    Example: "If L then S" becomes "L ⊃ S"

~ means "not"                             Example: "It is not the case that L" becomes "~L"

• means "and"                             Example: "L and D" becomes "L • D"

˅ means "or"                               Example: "L or D" becomes "L ˅ D"

≡ means "if and only if"              Example "L if and only if D" becomes "L ≡ D"

Propositional logic lets you write complicated statements using efficient little symbols that can then be manipulated according to a set of standard rules, similar to algebra. Whereas in algebra you swap symbols around to find the value of a variable, in propositional logic you swap symbols around to see what conclusions follow from a set of premises. Each statement is said to have a certain truth value: either true (T) or false (F). Compound statements linked together with the symbols above also have truth values, which depend on the truth values of each statement they link. For example, L • D is true if both L and D are true. If one or both are false, then the whole statement is false. This can be represented in a table, called a truth table:

L	D	L • D
T	T	T
F	T	F
T	F	F
F	F	F

All the other logical operators have particular truth tables, and they can all be combined into a single table, like so: 

L	D	~D	L • D	L ˅ D	L ⊃ D	L ≡ D
T	T	F	T	T	T	T
F	T	F	F	T	T	F
T	F	T	F	T	F	F
F	F	T	F	F	T	T

You can check to see if a syllogism is valid by putting the premises and the conclusion in a truth table. If there's any row where the premises are true, but the conclusion is false, then the argument is invalid. In other words, the truth of the conclusion doesn't always follow from the premises. 

Obviously, categorical logic and propositional logic are two very different animals, useful for different things. A third kind of logic, called predicate logic, is a way of combining their respective strengths into a single symbolic system. It starts with the same symbols and rules as propositional logic, but expands on them with two more symbols: ∀ for "All" and ∃ for "some" (or more precisely "at least one"). I won't get into predicate logic, because I'm just starting to get the hang of it myself, but it's a very powerful system for figuring out both categorical and propositional questions. It's also a pretty tough to understand, at least for my kind of brain.

What's also tough, with all three branches of logic, is translating the arguments people make in everyday life into formal logic. People don't speak in formal syllogisms. They put conclusions before premises, leave premises unspoken, and use language that can be interpreted multiple ways. Another problem with translation is that logical operators like "some", "or", and "if, then" have very precise meanings in formal logic that may be different from their meanings in everyday speech. For example, in logic "some" means "at least one". There's no way to make distinctions like "most", "almost all", or "just a few". It sacrifices nuance for precision. "Some" is also confusing because if you make a statement like "Some plumbers are redheads", that doesn't imply that "Some plumbers are not redheads" The first statement makes no such claim, even though in ordinary speech people often use "some" to mean "some are and some aren't."

Then there's "or". People use that word in two different ways: 1. "One or the other, or both" or 2. "One or the other, but not both." In logic, "or" only corresponds to the first statement. That's why in the truth table above, L ˅ D is true if either or both L or D are true. It's only false if neither are true. 

For my money, though, "if, then" is the most confusing logical operator. When you were a kid and your mom told you, "If you do your homework, then you can watch TV", you knew she meant "if and only if." But that's not how it's interpreted in logic. Let's symbolize mom's statement as H ⊃ T. All that means is that if it's true that you do your homework, then it's also true that you can watch TV. It doesn't mean that if you didn't do your homework, you can't watch TV. As the truth table above shows, if H is false and T is true, H ⊃ T is still considered true. It's only false if you did do your homework, but still can't watch TV; in other words, if H is true and T is false. Doing homework is sufficient, but not necessary, for watching TV. If you want to say, "Only if you do your homework can you watch TV", you would have to symbolize that as T ⊃ H. In other words: "If watch TV, then it must be true that you did your homework." Counterintuitive, isn't it? If you want to make it clear that you can watch TV if and only if you do your homework, you have to symbolize that as (H ⊃ T) • (T ⊃ H), or simply H ≡ T.

What's it Good For?

I started learning about formal logic because I realized that if I really want to understand critical thinking and informal logic in any kind of deep way, then I'm going to have to get at least a basic grasp of formal logic. But I was also curious about something else. In the late 1600's, Gottfried Wilhelm Leibniz envisioned a system of formal logic so complete that it could settle any debate. As he put it, "if someone would doubt my results, I should say to him: 'Let us calculate Sir': and thus by taking to pen and ink, we should soon settle the question."

To what extent, I wondered, does formal logic live up to Leibniz's dream? Does let us settle questions just by calculating? Well, sometimes, but not always, or even usually. Formal logic obviously has severe limitations, or there wouldn't be so many disagreements today between philosophers who are fluent in it. But surely formal logic could help us resolve some everyday arguments, by putting them into a more precise form and identifying the ones that turn out to be invalid? Of course, this would only work if both parties to the argument could follow formal logic. If I'm debating someone, and I try to prove my point by converting it into symbols and writing proofs, my opponent won't have any reason to take such odd behavior seriously unless they also understood what the symbols mean. For all they know, I could just be making them up. So, for formal logic to be really useful in day to day discussions, people would have to learn it in school, the way they learn algebra. It's not really any more complicated, and it could be far more useful on a daily basis.

At least, I think it could. I'm honestly not sure. After all, valid deductive reasoning is just one aspect of rationality. It can't tell us which premises are true, and it can't help with inductive arguments, which are probably far more common anyway. But I still wonder--what would happen if we started teaching everyone the basics of formal logic? Would it makes us clearer thinkers? Would it help settle debates? I don't know. Maybe I'll have a better idea when I understand it better myself.

Poultry Wars: Moral Misunderstandings in the Duck Dynasty/Chick-Fil-A Controversies

The culture wars in this country have become downright surreal the last couple of years. Most notably, two of the biggest flair-ups between red state and blue state types have revolved around, of all things, poultry. First there was the great Chick-Fil-A pie fight of 2012, which broke out after president Dan Cathy expressed opposition to same-sex marriage, saying, among other things:

"I think we are inviting God's judgment on our nation when we shake our fist at Him and say, 'We know better than you as to what constitutes a marriage'. I pray God's mercy on our generation that has such a prideful, arrogant attitude to think that we have the audacity to define what marriage is about."

That one blew up on the social media sites, led to protests, counterprotests, boycotts, and widespead de-friending and hurt feelings. The main issues in that debate were gay rights and free speech for people who don't support those rights. It got surprisingly nasty.

The other free speech/gay rights/poultry bomb went off a few days ago, when the country's most famous duck hunter, Phil Robertson, was interviewed in GQ (pretty surreal in itself). When he started talking about how sinful modern society is, the reporter asked him what he considered sinful. He responded:

“Start with homosexual behavior and just morph out from there. Bestiality, sleeping around with this woman and that woman and that woman and those men,” he says. Then he paraphrases Corinthians: “Don’t be deceived. Neither the adulterers, the idolaters, the male prostitutes, the homosexual offenders, the greedy, the drunkards, the slanderers, the swindlers—they won’t inherit the kingdom of God. Don’t deceive yourself. It’s not right.”

You probably know the rest of the story. It's been a kerfuffle of tremendous proportions. Some people think the controversy has been overblown, and that it's silly to spend this much time on it when there are people starving and dying in other parts of the world. It's true that it isn't that important, and it's undeniably ridiculous that this debate centers around a TV show about a family of rich, bearded duckhunters, but still, the issues are real. Free speech and gay rights are both very important. As for free speech, while I found Robertson's comments repulsive, I'm not sure I want to live in a society where people with those kind of views--which are held by a whole lot of people in this country, after all--are censored on mainstream channels. Honestly, I would rather know what people think than see those opinions driven underground, and be surprised by them later. But I see points on the other side, too. It's tricky.

Gay rights are also an important and tricky topic. Gays are one of the last groups still explicitly discriminated against in this country, in laws that are still on the books. In many states it's still legal to deny service to gays in restaurants, fire them for being gay, arrest them for having sex, and deny couples the same legal rights that straight couples have. Attitudes are changing, but still deeply divided, so gay rights are one of the defining civil rights issues of our time. It's also a very important issue to me, as people who read this blog will know, because many of my good friends are gay. I've seen what they go through--coming to terms with their sexuality, finding the tremendous courage required to come out to family and friends who may reject them for it, wondering whether they can kiss or hold hands in public without being accosted or even assaulted...they don't have an easy time of it, especially in conservative areas. Seeing the things they go through makes me very angry, and...well...you mess with my friends, you mess with me.

So, in spite of the beards and the ducks and the essential goofiness of reality TV, this squabble is over real issues. It's also been interesting to me because of the light it casts on public debate and ethical thinking in this country.

First, public debate. As usual, there's been a lot of misunderstanding, simplistic thinking, and sweeping generalizations on both sides. On the conservative Christian side, I've seen several people say things like, "A & E is trying to suppress the Christian viewpoint." Well, it's not the Christian viewpoint--it's the viewpoint of one subset of Christians. Not all Christians have a problem with homosexuality, and conservative Christians need to realize they don't speak for all Christians. Not by a long shot.

But something else I've seen conservative Christians say points out a common misconception on the liberal side. I keep hearing people say, "Just because we don't agree with homosexuality doesn't mean we hate homosexuals." While there is some real hatred out there, I do believe these people. Hate is not their motivation. Here I'm in danger of getting in hot water with my fellow liberals for defending the anti-gay crowd, but it's not so much that I'm defending them as trying to accurately see what's going on in their heads. To say they are all driven by hatred or fear of people unlike them is simply inaccurate, and there's no point in unnecessarily demonizing people or misconstruing their motives. Let's try to see people as they really are, instead of as we want to paint them.

This brings us to ethics. People on either side of this issue are thinking about morality and ethics in completely different ways; basing their ethical codes on almost totally different foundations.

We can get some insight into the conservative Christian way of looking at morality by looking at a statement Phil Robertson released in the wake of the controversy:

"I myself am a product of the 60s; I centered my life around sex, drugs and rock and roll until I hit rock bottom and accepted Jesus as my Savior. My mission today is to go forth and tell people about why I follow Christ and also what the Bible teaches, and part of that teaching is that women and men are meant to be together. However, I would never treat anyone with disrespect just because they are different from me. We are all created by the Almighty and like Him, I love all of humanity. We would all be better off if we loved God and loved each other."

Now, in his case I'm not sure I believe him. A video has since come out that shows him saying things about gays that seem awfully disrespectful and not at all loving. But when it comes to many other conservative Christians (though certainly not all), I think the statement above describes their outlook pretty accurately. When Christians talk about the sins of others, what secular types like me tend to miss is that a central part of their view is that they are sinners themselves. Sin is seen as an essential feature of humankind. The only thing that can redeem people is God's grace, which lets Christians escape the hell they feel they deserve by accepting Jesus as their savior. So, the fact that they're saying someone is a sinner doesn't mean they hate them. They think they're sinners themselves, and may actually be trying their best to love all the other sinners--i.e. all of humanity. After all, many conservative Christians agree with more liberal Christians that the essence of Christian ethics is captured in Matthew 22:36-40. In these verses, Jesus is asked by a Pharisee what commandment in the law is the greatest. He replies:

³⁷ He said to him, “‘You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.’ ³⁸ This is the greatest and first commandment. ³⁹ And a second is like it: ‘You shall love your neighbor as yourself.’ ⁴⁰ On these two commandments hang all the law and the prophets.”

You often hear Christians paraphrasing St. Augustine's phrase, "Cum dilectione hominum et odio vitiorum" as "Love the sinner, hate the sin." Lots of them really mean that (though you wouldn't know it listening to some religious right politicians).

OK, but why do they see homosexuality as a sin? Because several verses in the Bible say it is, and conservative Christians tend to take the Bible literally. Someone who believes the earth was literally created in six days is not likely to write off the verses about homosexuality as the antiquated views of an ancient culture, as many liberal Christians and secularists do. They're going to look at those verses, and the ones about Adam and Eve (not, as the bumper stickers say, Adam and Steve) and conclude that God created men and women to be together; not men and men or women and women. That's what liberals need to realize--if we believed those premises, we would probably draw similar conclusions. It's not so much the logic we disagree with as the axioms it's based on.

In the more technical terms of ethical philosophy, conservative Christians base their ethics on a blend of Divine Command and Natural Law theory. Divine command is the idea that what's right is what God says is right, and natural law is the idea that what is right is determined by what is natural (many liberals also engage in natural law thinking, but in different ways, and not usually about sexuality). Since Christians believe natural laws were created by God, the divine command and natural law views blend together. Of course, most people don't know these labels, but their thought processes tend to follow those theories anyway. Ask a Christian who believes homosexuality is a sin why they think that, and you'll probably hear something like, "It's not natural" or "It's against God's law."

Professional philosophers, including Christian ones, know there are serious problems with both of these ideas; the Euthyphro Dilemma in the case of Divine Command theory, and the Appeal to Nature and Naturalistic Fallacies in the case of Natural Law. But many Christian philosophers still believe in natural law (divine command less often, as far as I can tell), and make quite sophisticated arguments in its favor. Thomas Aquinas, for example, was well aware of the Euthyphro Dilemma, and accounted for it in his natural law theories.

As psychologists like Jonathan Haidt have shown, conservatives are more likely than liberals to see ethics in terms of respect for tradition and notions of sanctity and degradation; points of view that philosophers have mostly overlooked. Conservatives are more sensitive to the perceived purity or sacredness of things than liberals are. Maybe that's why morality for them is so bound up with sex (I'm guessing here, since I'm a secular liberal who finds it hard to think in those terms). Whoever first used the word "dirty" to describe sex was probably not by nature liberal.

Many conservatives think liberals are unconcerned with morality. But that's not true. We just base morality on completely different foundations. While a conservative may see outlawing gay marriage as the moral thing to do, liberals see it as immoral, because it gives gays fewer rights than straights, and makes them unhappy. When liberals set out to determine whether something is moral or not, the main questions they tend to ask are "Is it fair?" and "Does it hurt anyone?" They tend to subscribe to an ethic based on harm and happiness. Ask them if an unusual sex act is OK, and they'll probably say, "Well, are they consenting adults, and does it it hurt anybody?" If the answers are "yes" and "no" respectively, then they probably think it's OK (though perhaps not for them). In other words, there's more emphasis on the consequences of an action in terms of human happiness, not whether it conforms with some divine or natural law.

Of course, both conservatives and liberals can talk about consequences. When it comes to homosexuality, conservatives often maintain that homosexuality has negative effects. For example, they'll start talking about how if it becomes too common, the human race won't be able to reproduce itself (this kind of "what if everybody did it" argument is related to Kant's duty-based ethics as much as consequentialism, but let's not get into all that). Notice this argument is predicated on the belief that being gay is a choice. That's the only way more and more of the population could decide to be gay over time. The choice issue is an interesting gulf between conservative Christian and liberal views of homosexuality--the conservatives almost always think it's a choice. Liberals (and every gay person I've ever asked) think they had no more choice in being gay than straight people had in being straight.

So why do conservatives think it's a choice? One line of reasoning I've heard is that if being gay is against God's law, yet some people are born gay, that would imply that God makes mistakes. So it being must be a choice, because God doesn't make mistakes. I suspect that another reason anti-gay Christians want to think people choose to be gay is that if they are born gay, then it wouldn't be very nice to blame them for something they have no control over. It would be like blaming people for their eye color. Therefore, being gay must be a choice. That's not a valid argument, of course, but I really do think it's how many people are reasoning, at least implicitly.

Those who think being gay is not a choice, on the other hand, will still admit that we can't have everyone be gay. But then, you can't have everyone be a firefighter, either, yet that doesn't mean nobody should be. Anyway, most liberals think a certain percentage of people simply turn out gay, and that percentage is probably more or less constant. That's why there's no reason to worry that everyone will turn gay. I've hung around gay folks most of my adult life, and never had the slightest urge to switch teams. That's not how it works, at least for me. People who think you can just choose to be gay must find that choice easier to imagine than I do.

Another gulf in moral reasoning is that moderates and liberals are far more likely than conservatives to accept the idea that humans evolved by natural selection, instead of being created in one fell swoop--man and woman--by God. That means they see more arbitrariness in the human condition. It could have turned out differently if you rewound everything and started again. That lends less credence to the idea that there are laws of ethics somehow written across the sky. Consequently, they tend to see ethics as coming from the fact that humans are conscious beings capable of pleasure, pain, and preferences. It's about how people should live together without hurting or exploiting each other.

Of course, people think about ethics in all kinds of different ways, and I've just talked about some broad outlines that characterize conservative Christians, on the one hand, and moderate/liberal Christians and secularists on the other (as I see it). It's still too simplistic, and I'm probably wrong in significant ways. But my point is that in order to get through the impasse our country has arrived at on these issues, both sides need to try to understand each other better, instead of relying on simplistic caricatures and demonization. I think most people are basically decent, and want to know and do what is right. They just have completely different ways of figuring out what that is.

For the Bible Tells Me So

Castle of the Pyrenees. Rene Magritte

The other day I came home to find a pamphlet the Jehovah's Witnesses had tucked into my door frame. It's entitled Can the Dead Really Live Again?, and it's answer is a resounding yes. I normally just throw those pamphlets away, but I've kept this one because of an interesting argument it uses to defend its position on life after death. It starts with a rhetorical question: "Can we really believe what the Bible says?" Then it answers, "Yes, for at least three reasons." And here's the striking thing: all three reasons are supported solely with Bible verses.

Now, I'm no logician, but I'm pretty sure that's circular reasoning. It's basically saying, "We can believe what the Bible says because of what the Bible says." In other words, it tries to support its conclusion with statements that assume the conclusion is true. The argument hovers in midair. What's needed to connect it to the firmament of credibility is firm, verifiable evidence that the Bible is true, beyond what the Bible itself says. But no such evidence is offered.

My point here isn't to debate whether there's life afer death or to bash Jehovah's Witnesses. I've known many of them, and they're usually very nice people. Nor do I want to stomp on an easy target like a cheaply-printed pamphlet. I know there are lots of Christians out there far more logically sophisticated than whoever wrote that. What I'm trying to do is point out this kind of circular reasoning, and the real harm it can do.

I don't just see such reasoning in throwaway pamphlets. I see it used all the time by certain conservative Christians to justify attitudes and laws that hurt real people in real ways. The clearest examples these days are assertions that homosexuality is immoral and that gay marriage should be illegal (or remain illegal). This country is full of people who think it's fully justified to tell two consenting adults they shouldn't be able to love or marry each other. They're willing to deny them what most people consider one of the main sources of happiness and meaning in life, and they justify this attitude, and those laws, by citing Bible verses.

That's a pretty serious stance to take. So when I hear people taking it, I always try to ask, as nicely as possible, "OK, but how do you know the Bible is right?" Responses vary, but one I've heard several times is, "Because it's the word of God." So then I ask, "But how do you know that?" Once again, responses vary, but I've actually heard people say, "Because it says so in the Bible."

So we're back to circular reasoning; to arguments built on floating boulders instead of bedrock evidence. And that's just not good enough, especially if those arguments are being used to dictate how people can live their lives. Unless there's clear and undeniable proof that: 1. There is a God. 2. God is the ultimate judge of what is right. 3. God dictated those Bible verses; then pointing to them doesn't count for much. If there isn't clear evidence for number 3 in particular, the simpler explanation for those verses is that they were written by plain old human beings...people just like you and me, except that they lived in a far more violent, sexist, ignorant, and superstitious time. If they were written by such people, without divine inspiration, why should we listen to them? Haven't we made some intellectual and moral progress since then? After all, it's no longer considered acceptable to massacre whole cities, to stone people to death for adultery, or to attribute mental illness to a legion of demons. Why should we put stock in ancient opinions about other things?

Of course, the ancients were probably right about some things. "Thou shalt not kill" seems like a pretty good moral maxim (even if it's widely ignored.) So, I'm not necessarily saying they weren't right. I'm just saying that if they were, you can't prove it by saying, "It's written in this book." Anybody can write a book. If you add, "and God wrote or inspired that book" that would certainly add more weight to the argument, but only if it's true. And if someone says it's true, then they should be able to tell me how they know that. "Because the Bible says so" is not an acceptable answer, because it just takes us back where we started. What's the evidence that takes us outside the logical circle? If you ask an astronomer why she thinks the universe began in a Big Bang, she'll start citing measurable, independently verifiable evidence: leftover radiation predicted before it was discovered, galaxies flying away from each other, predictions from general relativity and particle physics, Hubble observations of young galaxies, and so on. If she couldn't offer any such evidence, we would have no reason to take her seriously. Why should it be any different for someone quoting the Bible?

Another assertion that can't stand on its own is, "God says this is wrong." If someone says that, then surely it's fair to ask: Why? Why does God say it's wrong? Does it cause harm? If so, what? If not, then what else is his reason? Surely God doesn't disapprove of things for no reason? If someone can explain why something is wrong--by saying what harm it does, for example--then they're actually giving me a reason to consider their argument. Alternatively, if they say, "I don't exactly know why God says it's wrong, but I know he says so," then we're back where we were before, and  they should be able tell me how they know he actually says that.

If people can offer evidence for those things, then they're making an actual argument. It's not necessarily a valid one, if the evidence is unconvincing or doesn't logically support their conclusions. But at least its an honest effort. What isn't a real argument is saying, "it says it in the Bible," or "God says it's wrong." Such statements might possibly begin a convincing argument, but they certainly can't end one, despite what the bumper stickers say. By themselves, they just hover in mid-air, resting on nothing.