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Posts tagged as “Jesus and Godel”

The Total Depravity of the No Free Lunch Theorem

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wolpert headshot Many Christians believe that we can only do good by the grace of God. In its most extreme form, this theory of "total depravity" suggests that we are literally incapable of choosing the good, choosing to follow God, or to even believe in Him without His direct supernatural aid, offered as a free gift. Total depravity is false, but it contains an important truth about why we need God's help not to screw up. In artificial intelligence, we model smart things like people as "intelligent agents". An agent, broadly stated, is something that exists in a larger environment, observing situations, taking actions, and receiving rewards - a bit like the entities navigating through Markov decision processes last time. But agents are a broader concept, not strictly tied to the Markov property: anything that makes decisions about actions in a larger environment can be an agent. The line between agent and environment can be clear, as with humans contained within our skins; or it might be fuzzy, like a control system for a factory. While the idea of "intelligence" is fuzzy, one of the things that makes an agent smart is rational behavior - making the right choices. Another thing that makes an agent smart is learning - improving your behavior in the future based on the experiences that you've had in the past. The field I work in, deep reinforcement learning, focuses on building learning agents that improve their rationality based on their experiences, generally within a partially-observable Markov decision process in which it's reasonably clear what counts as rational, even if the agent can't clearly see the whole world. This "partial observability" is one real-world limitation that virtually all agents in Creation share. Robot sensors have a limited range, the factory controller doesn't have a sensor on all its circuits, and we can't see behind our own heads (hey, there's a creepy man standing behind you right now - don't look!) Partial observability means we need to make the best decisions we can based on the information that is available to us. We look both ways at a crosswalk to try to reduce our uncertainty, waiting if a car is coming, and we call out "corner" in a restaurant kitchen to try to reduce the uncertainty of others. Obviously, if you don't know which door holds the lady or the tiger, it's hard to pick. But even if an agent had perfect knowledge of the current state of the world around it - not that current state is well-defined in general relativity / quantum mechanics, but nevermind - making perfectly correct decisions is impossible. Well, not necessarily impossible: a perfectly omniscient agent could make perfectly optimal decisions, because it would know the true value of each action, not just its immediate reward. But without that kind of revelation of information from the future, we can only learn from our past experiences. And that's where the no free lunch theorem comes in: there is no guaranteed way to learn correctly. Imagine a simple decision problem: to turn left or right on a forking path in a garden. (Perhaps only one of those directions leads to the "straight and narrow" - sorry, this is a Lenten series, gotta bring that in somewheres). At each fork in the road, there are two more potential paths than there were before. A path that forks at each stage is like that problem where you double the number of pennies you give someone each day for a whole month. It starts with small change - first day a penny; the second, two, the third, four, and so on - but last day of the month, you're shelling out ten million bucks - a billion pennies. In this garden of forking paths, there are a billion possible destinations. But in the mind of an agent trying to learn what to do, the problem is even harder: there are also a billion intermediate steps, and at each point, the agent must make a decision, with two possible choices. If you perfect knowledge and tried to write down a guidebook, it would have a billion entries, with a recommended decision at each point. But if you don't have perfect knowledge, if you're a learning agent, then your best option is to go into the garden and fill out that guidebook yourself. This is almost inconceivably hard. If you imagine a library with every possible guidebook, one in which each book differed from every other by at least one decision out of those billions, then there are two to the power of a billion possible books - that's a number with roughly three hundred million digits. The only way to fill out the guidebook correctly is to visit all billion possible paths. If you can't do that, then at some point, you're going to need to guess the entries for the parts of the garden that you haven't visited. And then it gets tricky, because there are two to the power of a billion possible gardens. If you're in a garden where the straight and narrow can be approximated by alternating left and right to stay near the middle, you might guess that outer entries of the table should turn inward, the far left turning right, and the far right turning left. But for all you know, more reward can be found further out. The no free lunch theorem says that there is no principled way to fill in parts of the book you haven't seen. At best, you can assume that parts of the garden you've seen are similar to the ones you haven't, but if you could be in literally any possible garden, then those assumptions will inevitably fail. What does this all mean for free will versus total depravity? Well, first off, if you are an intelligent agent, then you can sample actions from your action space. The actions you can take aren't good or evil, they're decisions in your brain and actions of your body. Some of those actions can, by chance, be good ones; God has not so ordered the world to exclude the good. And if you do good works and see that they are good, why, then, you could learn to do them again. There's nothing preventing this; again, God has not so ordered the world to exclude the good. But there's no guarantee that you're going to learn the right lessons, and there lies the problem. In deep reinforcement learning, we see this problem writ large. I teach robots the size of people how to navigate buildings meant for people, and while you think that would be simple, we often observe robot control policies that have completed thousands of successful runs suddenly run straight into a wall. Deep learning systems do not generalize the way human beings would. While a human that learns to drive without hitting things in their hometown will often be able to transfer this skill when they go off for college, a robot moving to a new environment may expose strange "pathologies" in its behavior. This is the meaning of "my thoughts are not your thoughts, neither are your ways my ways" in Scripture: even if a human being honestly chooses to believe in God, sincerely tries to do good, and accidentally gets it right, there is no guarantee that what they've learned from that experience will transfer. In fact, it's more likely to not transfer. Sins of pride, self-righteousness, scrupulousness, and intolerance lead us astray as much as temptations to indulge in things that are "lawful but not expedient". We can turn to Scripture, to church Tradition, or to our own Reason to try to improve, but we'll likely screw up. This is why God's grace is so important. God is actively and spiritually trying to help us come to believe, know and love him, and hopes that this love will prompt us to do the right thing, bringing the Kingdom of Heaven into being here on this Earth. But across a broad spectrum of possible universes, it's mathematically impossible for us to always get it right even if we're trying really hard - literally the only way that we could actually be consistently good is to have perfectly omniscient knowledge of the entire future of the Universe - to actually be God. We can't be God. The position is taken. We don't know what He knows, and we are going to screw it up. Fortunately He's ordered the universe so it's possible to get it right, He's sent his Son as an example of how to get it right, and His Spirit acts in the world to give us the grace we need to actually get it right. -the Centaur Pictured: David Wolpert, who discovered one of the depressingly many No Free Lunch theorems.  

Make Holy the Lord’s Day

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make holy the lord's day To make sure my Sabbath remains a Sabbath, and since responsible people are still working remotely because of the pandemic, in lieu of writing an essay, I'll use that time to watch recorded services from Saint Stephen's in-the-Field instead (note these were filmed at our sister parish St. John the Divine). If you haven't "gone to Mass" today, I encourage you to take a devotional. Stay safe, seek rest, and God bless. -the Centaur Pictured: a graphic. Wow, Illustrator is ... so unnecessarily hard to use, and the Illustrator community seems filled with a small contingent of strangely unhelpful people who can't seem to realize there are other drawing programs out there and legitimate reasons to question why Illustrator does Illustrator.

Pascal’s Wager and Purchasing Parsley

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pascal headshot Hang out with philosophers or theologians long enough, you're likely to run into "Pascal's Wager": the Blaise Pascal's idea that you should believe in God, because if He exists, betting on Him wins you everything and betting against Him loses you everything, whereas if He doesn't, you lose nothing. Right off the bat, we can see this original version of the wager is an intellectually dishonest argument: you don't "lose nothing" if you choose to believe that God exists and He doesn't. At best, you're being credulous; at worst, if you're being cynical about your belief, you're sacrificing your intellectual integrity. Pascal backs off from all or nothing a bit as he's trying to dig himself out of the hole, claiming that he's comparing infinite gains of eternity in heaven against finite losses you can experience here on Earth. Some may have sincere trouble in believing, but he argues they should try to convince themselves. Now, let's be fair to Pascal here: if you read his original text, he wasn't actually trying to convince atheists to believe per se, but instead, trying to show that the world is too uncertain for logical proofs of the existence of God, but we're probably better off acting like God exists, in case it moves us to faith. Unfortunately, Pascal died before he could fully explain himself: the wager appears to be the introduction of a book on the value of faith that he never finished. But, like a philosophical zombie, the argument has continued its life, hollowed out from its original intent, eating brains in every new generation. Let's slay this zombie, shall we? Pascal's wager first appears to be an exercise in game theory: a mathematical formalism for analyzing the best choices in games. In this case, you are playing a game against the Cosmos. Your move is to believe, or not, and the Cosmos's "move" is whether God exists, or not. [Now, the theologically savvy among you might feel like pointing out that God created Creation, and is not a part of it - which is why I used Carl Sagan's more inclusive formulation of the Cosmos as "all that is, was, and ever shall be," and I'm going to run you off with a broom if you argue about what "is" means]. This leads to a simple table: your choice of belief times the existence of God. If He is, and you choose to believe: payout plus infinity; choose not to believe: payout minus infinity. If He is not, whether you choose to believe or not, the payout is zero, or at least finite. Pick the cell with the highest value. The emotional force of this argument is strong - for the believer - for, in decision theory, we should weigh the probability of one cell against the other, and intuitively, unless we judge the possibility of God to be literally zero, the infinite payout of the God-exists column dominates finite payouts of God-doesn't. Mathematically, that's, um, specious at best - it looks true, but it's not a valid decision-theoretic argument. First off, Pascal put infinity in the God column specifically to outweigh any possible finite payout, but technically, we can't multiply infinite quantities by finite quantities this way. Now, when it comes down to the question of whether infinities are actually real, or just a bad metaphor that leads people astray, I'm firmly ready to go to infinity - and beyond! But, technically mathematically, most of the time "infinity" is just a stand in for "this process can go on indefinitely without a limit." As soon as you admit that the payout of Heaven might be finite for the purposes of modeling, then the probability assigned to the "God exists" column can be set so low that the "God doesn't" column becomes attractive. But that gets us no further than Pascal and his strict (zero-probability) unbelievers. To me, the key flaw in Pascal's wager is what physicist E. T. Jaynes called the "mind projection fallacy": assuming that the constructs you're using in your mental models exist in reality. That's how Pascal can even put the wager to someone in the first place: he sets up the board and says "you must wager". But the gameboard Pascal sets up doesn't exist in reality, and there's no reason for someone else to model the problem the same way. A student of religion might add columns for different views of God: Jesus who saves, Zeus who's a jerk, the Great Electron, which doesn't judge, but just is, whoa whoa. Equally well, a student of epistemology might add many columns for belief: strict disbelief, partial belief, certain belief; an evangelical might add columns for "the hope so's" and "the know so's". Even the probabilities of columns are up for grabs. We've got a matrix of confusing possibilities. This flaw in the wager, like the flaws in much science and folk psychology about belief, is that we do not reason about facts provided by others according to the models in the other's head: we reason about the claims that others make about facts, which we internalize based on own beliefs - and trust of the other. Even in the simplest form, moment you start counting the columns of the wager as beliefs, the infinities disappear: there's only a claim of infinite goods in heaven, and a claim of infinite punishment in hell - and a claim that the alternative yields you only finite rewards. And those claims are mixed in with everything else we know. As a mathematical exercise, the self-contained four-cell version of the wager has a maximum payout in the "believe in a God who exists" cell; as something that corresponds to reality, the cells of the wager start to leak. Mathematics is an abstraction of reality - an act of creative human imagination to create repeatable forms of reasoning. I'm on the side that there is an actual reality behind this repeatability of mathematics, or it would not work; but applying mathematics to any particular problem must leave out certain details. This is leads to the law of leaky abstractions: the notion that, no matter how good the abstraction, sooner or later it is going to fail to model the world. Forget game theory, decision matrices, and probabilities: even something as simple as the mathematical concept of number can break down. One of the reasons I haven't published my tabbouleh recipe is that it's hard to quantify the ingredients - two bunches of parsley, four bunches of scallions, six tomatoes, two cups of fine bulgur, the juice of a lemon, etc - but since tomatoes are of different sizes, that "six" is a messy number. But at least tomatoes come in integral quantities. Parsley comes in bunches, which are not just of different sizes; they're composed of individual stems, picked from different plants, which have different degrees of growth, freshness and wilt. Parsley needs to be cleaned and picked to use in tabbouleh. Sometimes, you need to buy three bunches of parsley in order to end up with two. That's the law of leaky abstractions for you: you have to purchase parsley in integral units of bunches, but the bunches themselves don't correspond to the quantities that you can actually use in your recipe. Picking beliefs for use in our minds is far more complicated than assembling a heritage Lebanese salad. There are thousands of potential facts affecting any given problem, more intertwined than the branching leaves of those leafy greens; but like them, some are fresh and edible, others black and wilted. This was the actual point of Pascal's argument, the one he hoped to expound on his unfinished book. But the wager, because it's a mathematical abstraction - because it's repeatable reasoning - has lived on, a zombie argument which purports to give a rational reason why you should believe in God. Ultimately, we need to carefully winnow through information that we get from others before incorporating it into our beliefs; there is no royal road to convincing anyone of anything, much less God. As for belief in God, many Christians think that must ultimately come not from reason, but from grace. Fortunately, God gives that gift of belief for free, if we want it. -the Centaur Pictured: Blaise Pascal.

Apologize for Christianity? Why, Never!

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lewis headshot Christianity has all sorts of weird words: Primum Mobile, Eucharist, Paraclete; there are other words which are used in weird ways, like adoration, adoption ... and apologetics. "Christian apologists" doesn't refer to people who are apologizing for Christianity: it refers to theologians trying to defend it. As I hinted at last time, in a worldview where belief in God rests on faith as a free gift of grace from God, Christian apologetics are both indispensable and unnecessary, essential and impossible. Christians are called on to spread the Gospel, with the knowledge that no rational argument can ever convince. That hasn't stopped people from trying, though. The greatest Christian apologist of the past two hundred years, full stop, is C. S. Lewis, author of not just the Narnia series but also great apologetic works like The Screwtape Letters, The Great Divorce and The Abolition of Man. And so, while Lewis's works have moved me greatly, I often find his works have holes in their hearts. The brilliant G. K. Chesterton, author of In Defense of Sanity, is even worse; his favorite trick is to turn common ideas into paradoxes to make a point - frequently at the cost of intellectual honesty. I've heard it said that Chesterton argued that all great things contain paradoxes, because at the heart of everything is the paradox of the cross: a tool of condemnation turned into salvation, death turned into life, failure, humiliation and defeat turned into success, glory and victory. And this is perfectly good Christian theology - and consistent with Godel's incompleteness theorem that we discussed earlier. Most Christian religions assert that at the heart of the faith are mysteries that cannot be fully understood, just like Godel showed that all systems of thought have ultimate limits. But it's unsatisfying for a rationalist, even a Christian one, for it means that many Christians - even as they are sincerely trying to do their best to spread the Gospel the best way that they know how - are at the same time committing to statements that are at best foolish and at worst lies. And if you are tempted to retort that it's good to be foolish in the name of the Lord, like David with his tamborine, I want to be super crystal clear that I don't mean the good, faithful kind of foolishness, but a performative, "bad faith" foolishness in which people pretend things are other than what they are. You've met the type. The street preacher with the specious comeback; the televangelist who carefully edits his stories to play his position. The new "friend" who, when they find out you are a Christian, asks "Why don't you come to my church?" with the words "instead of yours" hanging in the air. For a Catholic growing up in the south, in Greenville, South Carolina, hometown of Bob Jones University, this was particularly irksome. As a child, I was buttonholed by street preachers across the street from BJU, who'd pester me on subsequent weeks on whether I'd read the pamphlets they shoved on me. If these people find out you believe in evolution, whoo boy, the volume gets turned up to eleven. I aaalmost ended up going into evolutionary biology as my field, and I can't tell you how many bad arguments I've heard about why evolution won't work. No, not bad arguments - meaningless. But it wasn't just evolution. Many of the arguments which were forced upon me were purely theological. One argument really stuck with me - a true Chesterton style paradox, what at first appears to be a nearly meaningless argument which nevertheless captures an important truth about Christianity. Call this "argument" the Cross over the Chasm. The idea is that in the beginning, God and Man were united, but Adam's sin caused the Fall, creating a chasm that cannot be bridged. Man can try to cross the chasm with good works, but fails; God can try to cross it with grace, but grace doesn't reach either. But that's where the Cross comes in. While the arm of good works can't reach, and the arm of grace can't reach; but you can write Jesus vertically between them, and turn those two arms and the word Jesus into a cross that bridges the gap. Jesus's sacrifice on the cross bridges the gap between god and Man. Now, what's bad about this Cross over the Chasm episode? By itself, nothing, but in the moment, what happened was this: a friend found out that I was Catholic, and decided to "show" me the true role of Jesus in religion - except of course, in the mind of people like him, he doesn't have a religion, but a close personal relationship with Jesus Christ. Never mind that this "argument" doesn't actually "show" anything - at best, it's a mnemonic for a few bits of theology which are perfectly consistent with Catholic doctrine. (Many people in the Bible belt who are upset about what Catholics supposedly believe don't realize there are fewer differences than they think). But the real problem is that people who act like my friend did there are both implicitly rejecting the faith of fellow Christians - and lying about their own faith. Religion is the word we use for someone whose close personal relationship with an invisible person is a vital part of their worldview. Denying that is a lie. And denying the faith of a fellow Christian is attacking that faith. I also have a personal relationship with Jesus Christ - which, in humility, I'd never describe as close, because it's never as I'd like, a relationship I'm always trying to improve, with the help of His grace; but I do believe and I choose to follow Him. That's super hard, and we don't need to throw stumbling blocks up for other believers. For a Christian, other Christians should not be our theological enemies. And so, while I don't believe in buttonholing Christians to get them to convert to other branches of Christianity, I think it's good to ask: What was good about the Cross over the Chasm episode? Well, first off, it's a really clear mnemonic for really important theology. It's a great little story which clearly shares important truths about Christianity: humanity and God are separated, but reaching for each other in works and Grace, and Jesus - and His sacrifice - is the mediator that makes union possible. It's not at all a logical argument, but the story has stuck with me for years. Had my friend come up to me, enthused, about this new metaphor, rather than presenting it as one more argument against my faith (!) even though it didn't contradict my faith (!!) it could have acted as a bulwark, not a stumbling block. More importantly, at least my friend was trying to share the Gospel. Once a woman told a televangelist she didn't like how he was spreading the Gospel. He asked how she was spreading it. She replied that she wasn't spreading it. His response: "Well, I like how I'm doing it better than how you're not doing it." I'm acutely aware that many people don't want to be proselytized, and that's their prerogative, of course - I know from experience I don't enjoy it myself. I far prefer the Episcopal "Tea with the vicar OR DEATH!" "Oh? Well, tea please" to any amount of street preaching or personal buttonholing. But, if you are interested in the Christian faith, know that ultimately, rational argument will fail. A paradox - a mystery - lies at the center of the faith: "Christ has died, Christ is risen, Christ will come again." While I'm  comfortable with this idea, sometimes it takes a Chesterton paradox - or a sketched diagram of a cross - to break through the rational so that the free gift of grace will start working. -the Centaur Pictured: C. S. Lewis.

Ayn Rand and the Catholic Religion

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rand headshot At first glance, Jesus Christ and Ayn Rand seem as far apart as possible. Jesus founded the world's largest religion; Ayn Rand founded Objectivism, a prominent atheistic philosophy. Jesus sacrificed His life for our sins; Ayn Rand is the self-described "arch-apostle of selfishness." But one thing Objectivism and Christianity have in common is the importance of every person. To Ayn Rand, each individual human being is an independent entity whose rights are derived from their status as a rational human being - and the foundation of morals is respect for the rights of those individuals. Morals have a parallel foundation in Christianity. Each human is a rational animal - a being with intellect and will, one who can come to believe in Jesus and choose to follow them. Whether those beings choose to do that or not, the foundation of ethics is treating those individuals as an end in and of themselves. That's the meaning of the word "catholic" in "one holy, catholic and apostolic church" in the Nicene Creed and the name of the "Roman Catholic Church": catholic, meaning universal, meaning, embracing all believers, open to all. Christianity isn't for a specific group: it's for everyone. There are obvious differences between Objectivism and Christianity. Objectivism is based on the evidence of existence; Christianity is based on a foundation of faith. Objectivism rejects the idea of an agent as an explanation for existence; Christianity places the agent God as the logical ground of being. In Objectivism, the individual is sovereign; in Christianity, God is sovereign. In Objectivism, pursuing your own values is the ultimate end goal of your actions; in Christianity, pursuing your own will over God's is a sin, and is one of the biggest stumbling blocks we need to overcome. The biggest difference, of course, is their attitudes towards altruism: Objectivism rejects self-sacrifice as evil, whereas Christianity places it as its highest good, founded as it is on the greatest self-sacrifice of all, the Son of God's death on the Cross to blot out the sins of all mankind. But this last difference is less of a difference than it first appears. Objectivists are not altruistic, but they are benevolent: trying to make the world better for human beings. Christians should focus on the Kingdom of God rather than the world - but to do so, we must love our neighbors as ourselves. This Great Commandment, this fundamental respect for others as equals to ourselves, is all too easily forgotten in Christianity when we fall prey to one of Christianity's greatest sins: self-righteousness. Jesus told his disciples to shake the dust off their sandals and move on if people rejected the Gospel. Three and a half centuries after Jesus, Saint Augustine was recommending religious persecution for people who refused to convert to Christianity; eleven hundred years after, that had devolved into the Inquisition; fifteen hundred years after, it perhaps hit its nadir in the witch trials. God is more than capable of giving every human being the experiences they need to choose whether or not to believe in Him. He's got the budget for it. And while He wants us to witness to good news about Jesus to help them believe, He doesn't need us to do that - and doesn't want us to do it by force. Forcing others to conform to our beliefs is precisely the opposite of casting the dust off our sandals. Forcing others to conform to our beliefs is precisely the opposite of turning the other cheek. In those circumstances, that's when I turn to the Great Commandment - but sometimes, I need a little help. That's where the clarity of Objectivism comes in. Saying "love thy neighbor as yourself" is poetic, but open to a lot of interpretation about what that "love" really means. If we instead ask the very specific question: Am I treating the other human being in this transaction as a unit? we can get somewhere. Each person is a rational being, an independent agent, an end in and of themselves. Ethics consists of making decisions which are good for those people, not for abstract concepts or groups - which is where Augustine went wrong, by putting "pastoral" concerns over letting individuals make their own decisions. The temptation in dealing with the other - the jerk, the liar, the thief, the guy who leaves his shopping cart catty-cornered blocking off two parking spaces - is to demonize them, to see them as evil. But this is a kind of fundamental attribution error - blaming behavior on people's nature, rather than circumstances. Some people fail to put the shopping cart back because they're oblivious; others don't care; and yes, there are people who do it because they're deliberately trying to be jerks. The action is the same - whether it's an asshole trying to tick people off, or a harried mother whose baby's diaper has exploded. There is real evil in the world - but it rests in the actions, not the people. People, in and of themselves, are not evil. They may do evil - they may have committed sins - but in the end, they are people, individual human beings, worthy of respect - concrete units, not instances of abstract groups or concepts. Remembering that people are people, worthy of respect as people, is paradoxically hardest when the person's beliefs are different. You want to go after the jerk in the parking lot. But you also get outraged at the political opponent, or the person whose philosophy or religion are different. They're so wrong! Yet they're still people. And so, when the question arises, I ask myself: am I thinking of this person as a member of a class - as an asshole, or a political opponent, or a religious one - or as a concrete unit, as a rational being who has the same right to their own life that I do - and the same right to make choices? Once I accept that person as a person, my values say I should love them as myself - and love, to me, is taking on other's goals over your own. This isn't quite the self-sacrificial cartoon version of altruism that Ayn Rand criticized, as I have many other values which I will not and should not compromise. But Christian values come first. Ayn Rand helps me to remember that people are not abstract characters in my internal mental drama, but real, concrete, existing human beings - and once I remember that, Jesus Christ can help guide me to treat that person as my neighbor, and to love them as myself. -the Centaur Pictured: Ayn Rand. I had a trouble capturing her rotation, as this essay set her spinning in her grave.

You Can’t Prove Anything With the Bible

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james sketch While Christianity means following Jesus, the starting point for that journey today is the Bible - whether you're a fundamentalist who takes the Bible as literal truth, or a Catholic who views it through the lens of dogma and tradition, or a rational theist like myself who treats the Bible as primary source material. But one thing you can't do with the Bible - even if you're a fundamentalist and thinks it's literally true, or a Catholic who believes in the richness of orthodox doctrine, and especially not a rational theist - is actually prove anything with it, not without breaking the meaning of "proof". Perhaps I'm oversensitive about this point. In colloquial language, proof can just mean evidence offered to reach a conclusion: you can offer your driver's license as a proof of your identity, gather facts to prove innocence or guilt, offer those proofs as trial to help a jury reach a conclusion. But that's not the way that people used the word "proof" to argue about the Bible when I was growing up, nor is it the way that I've seen people use the word around me to argue for their beliefs. Those people use the word proof like this: "You should believe X, same as me, and I can prove it with the Bible!" The most egregious example I heard was a Catholic priest at Christmas mass give an enormous list of Catholic doctrine - mostly, political doctrines - which they then followed by the extraordinary statement that all of these things logically followed from the Resurrection of Jesus Christ. But the theology of the Catholic Church - four hundred pages of catechism in my 1983 copy, near nine hundred in the 1994 edition, thirteen hundred pages in McBrien's Catholicism, or 1500 pages in the latest edition of Denzinger - do not logically follow from the hundred thousand words of the Gospels and Acts. You can take the Gospels on faith. You can take the Bible to be mythical truth, like the Catholic Church does, or to be literal truth, like fundamentalists do. And, guided by grace, you can build a theology on it. But you cannot use it as a foundation for logical argument, for the text requires interpretation. The Bible consists of around seventy books with a wide variety of content - myths, histories, stories, songs, proverbs, parables, essays, biographies, letters, and prophecies. These texts are not written with sufficient precision for them to serve as axioms for logical argument - nor were they meant to. The reason is simple to understand: axioms for logical argument must be atomic, with meanings that are completely self-contained to serve as bases for logical deductions; but the meaning of any particular passage of the Bible must be taken in their textual, historical and religious context. This isn't an argument for relativism or for radical textual analysis, but the simple point that even the shortest sentence in the Bible, "Jesus wept," has a meaning which can only understood by reading the story in the text that surrounds it - and every act of reading is an act of creative imagination. Researchers in artificial intelligence have discovered that reading even the simplest possible stories generally requires inventing novel concepts that don't yet exist in the mind of the reader. Each reader must recreate within themselves knowledge contained in the stories, knowledge they don't yet have. And they recreate that information based on what they already do know, and so will idiosyncratically create their own unique interpretations of the concepts of the story. Perhaps this is why different Christian groups I encounter seem to read the Bible in such different ways. Now, most groups of Christians I know are convinced that there is one true way to read the Scriptures. One friend once claimed that there was "only one true interpretation" - despite coming from a tradition that claimed each Christian was responsible for their own interpretation of the Bible. And yet ... Catholics complain Protestants ignore the plain words of Scripture in which Jesus gives spiritual authority to Peter and his descendants - which is the source of the authority of the Pope over the Church - or the words that indicate that the bread and wine of the Eucharist become the literal body and blood of Jesus. Protestants complain Catholics read into the plain words of the Scripture things that are not there - interpreting the metaphorical language of the Last Supper to be literal - or read out things that are there - like ignoring the existence of Jesus's brothers and sisters to preserve the doctrine of the ever-virgin Mary. You might be able to build a theology on such a foundation. And, if guided by grace, you might even be able to build a true theology on such a foundation. And that theology itself might contain logical arguments. But those arguments rest on your interpretations of the Bible, not the Bible itself. Actual logical arguments require a funny kind of paradox in their application. Mathematics is repeatable reasoning, an act of creative imagination that builds tools which enables one person to build an argument which another person can reproduce precisely. But this repeatability comes at a terrible cost. Logical arguments need axioms which are unambiguous within the context of their formal language - even though they are not precisely defined in the real world. And the conclusions you draw from those axioms are true only within the context of that language, even if they have a broad scope of application. Points and lines in Euclidean geometry have a precise meaning in relationship to each other, but are "undefined terms" with respect to reality, only qualitatively described. This enables us to use the proofs of Euclidean geometry for a vast variety of practical applications, even though ideal "points" do not exist. And even though Euclidean geometry doesn't describe the real world at all. Space is actually curved - not a barrier for mathematical analysis, though it is more complicated - and intermixed with time; but the more precise details of the Einsteinian space-time continuum don't show up at normal human scales. But it does show a deeper truth: if an argument is rigorous enough to be logically true, that truth is restricted to the formal realm, and may not correspond to reality; if an argument is grounded in reality, its truth is contingent upon evidence which can be overturned, and cannot have the force of a formal proof. In the early days after Jesus's ascension, Peter thought he had it all worked out, following both Jesus and Jewish law. But God spoke to him in a dream, making Peter realize that the old rules weren't appropriate for new believers, leading to a decision to no longer require all of them. We build elaborate theological structures on top of our interpretations of the Bible. But insofar as they're based on the Bible, they're not proofs; and insofar as they are proofs, they're not guaranteed to apply to the Bible. We need to be humble about what we can prove, to leave room for the Spirit to work on us. -the Centaur Pictured: King James. Yeah, that King James, commissioner of the King James Bible.

Truth and Holiness

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  darwin headshot Back in the day, I had both a "Jesus fish" and a "Darwin fish" on the back of my car (as I recall, it was an Isuzu Rodeo, a nice car but nowhere near as reliable as my beloved Nissan Pathfinder or my seemingly unkillable Toyota Prius). I also had a "Cthulhu fish" fridge magnet which I had as a joke. But I wouldn't have put a Cthulhu bumper sticker on my car, because the school of fish on that bumper were not a joke (though I admit I enjoyed the smidge of irony) but instead represented a sincere advertisement of my beliefs - and while it's a fun story, Cthulhu doesn't cut that mustard. You're reading a Lenten series, so I hope it's apparent that I'm a Christian; during this series, I mentioned that once I thought of becoming an evolutionary biologist. To some Christians, these things seem hard to fit together, as many Christians are dead set on sticking to the cosmology of the Hebrews. But the stories told in Genesis are wrong, at least as cosmology, geology, biology or history. The meaning behind the misleading Catholic term "myth" for some stories in the Bible is that stories are inspired by God and teach important truths, even if they aren't precisely accurate histories. Despite some people's attempts to treat the Bible as a fax from God, our understanding of God has progressed since the books of the Bible were written by their authors, collated by early Christians, and ultimately approved by the early Catholic Church. For example, the Trinity - the notion that the one (1) God manifests in three distinct "persons", Father, Son and Holy Ghost - doesn't appear directly in the Bible; we developed that understanding over time. But it's the most important Christian doctrine. You can't understand Jesus as the Son of God without it. On the other hand, other ideas we have discarded. Even within the Bible, we see debates between sincere believers, such as the rejection of Jewish dietary rules for Gentiles in Acts of the Apostles. Doctrines like the divine right of kings and the proper treatment of slaves have been abandoned. Now, science is familiar with this process. Some scientific ideas were bad from the get-go. The Earth was never at the center of the universe, matter isn't composed of four elements, and the motion of projectiles can't be explained by an "impulse" that slowly runs out: these ideas were never right. Other ideas - like the Earth being round, matter being made of atoms, or light being made of waves or particles - started off right. Now, Earth isn't perfectly round, and atoms aren't perfectly indivisible, and tiny things are weirdly both waves and particles - but these ideas were on the right track from the beginning. There's very little that science can "prove" to be true. All science is based on observation, generalization and experiment, and new experiments could show nuances that could force us to throw out our ideas - the technical term for this is "defeasible" reasoning - likely outcomes which might be true. This is a natural outcome of the probabilistic reasoning that underlies most of our formal reasoning apparatus (and might even explain some of the inner guts of cognition as well): unless something is absolutely certain, conclusions founded on it can't be absolutely certain. The best you can hope for, as far as proofs go, is to develop theorems of broad applicability. Physicists argue from symmetries, which enable vast regions of deduction from very few premises. Computer scientists use the theory of computation, which applies to a broad category of possible universes. But, between our observations, our generalizations, our experiments, our theories, and our theorems, science has come up with a few things we can count on - the Earth is round, matter is made of atoms, and at the speed and scale experienced by humans, the Newtonian approximation to mechanics. Science doesn't have definitive truths, but it is an engine for seeking it - for expanding the regions we think are probable and discarding the ideas which contradict experiment or each other. "The sole test of any idea open to observation is experiment" is the best tool we have for reaching truth - in any area. That's why I put the Darwin fish with its cute little feet on my car: to represent the search for truth. But science is not enough. Science, by itself, is amoral: it can tell us what exists in the world, but it can't tell us what to do with it. That's where ethics, morals, religion and spirituality come in. You can go far without invoking the supernatural. Philosophers argue that you can't go from an "is" to an "ought" - to argue from what exists to what to do about it - but this isn't quite true. Ayn Rand points out ethics are judgments about what's good for human beings, so we're not free to pick any ethics we like. But as we discussed earlier, no individual human being experiences enough to make accurate ethical judgments on their own - nor are we guaranteed that our society has experienced enough to make our ethics accurate either. And if there really is an afterlife or a spiritual realm, experience won't cut it. If there is a God, then we rely on Him to inform us about the spiritual dimension of the universe which either exist in the afterlife we haven't yet reached or are part of the cosmic nature of the universe which we don't have the stature to grasp. And this information - this Revelation - is therefore special. This is the reason early Jews and Christians wrote down their experiences, and the reason the early Church collated it and preserved it. It's the reason fundamentalists treat the Bible as literally true, and the reason I treat the Bible as primary source material. Ethics come from the spiritual dimension of the universe, and are ultimately holy. What we should do is determined by what is - and who - is behind it. Choosing the right action isn't just a good idea: it's seeking holiness - it's choosing to follow God. And that's why the Jesus fish was on my bumper. I say "truth and holiness" - with the truth first - because truth must come first. I don't believe in Jesus because I think He's holy; I think He's holy because I believe the stories about him are true. And while parts of the Bible that are myth, to me the Gospels (and Acts) are my primary source about Jesus. But once you understand the truth, you need to decide what to do about it. And like the cosmology of the Bible was modified by on our current understanding, there are principles in the Bible that have needed refinement as we learn more about the world. But it's important to start there, every time. Truth, and holiness: first find out what's true, then try to do the right thing, treating the good as sacred. -the Centaur Pictured: Chuck D.

Suitcase Words and Sloppy Theology

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hofstadter headshot If you're a working scientist - if you work day-to-day in domains not well understood enough to engineer solutions from known principles, if collecting data, generating theories, formulating hypotheses, and testing them are your bread and butter - then religious arguments often seem pretty crappy. It's not that scientists can't make terrible mental gaffes, of course - they're human, like everyone else. But there's a certain mental discipline necessary for doing real science well which surpasses even the rigor expected in the philosophical and rationalist communities. We just don't know as much as we like. And while some theology, regardless of whether you buy the premises, is based on solid argument - even though he lacked modern tools of valid argumentation, Aquinas is no slouch - vast swathes of religious thinking is based on a particular kind of garbage: reasoning from analogy. Again, don't get me wrong: analogical reasoning is indispensable. Cognitive scientist Douglas Hofstadter built his career by demonstrating the power of analogy in thought. At one talk, his host said something like, "We'll join you at coffee hour after we drop Doug's books off at my office slash study." Hofstadter whirled, smiled, and said, "At your office slash study. Beautiful." Beautiful, because his host had illustrated precisely what Hofstadter had shown in his talk: that we use analogy constantly in our day to day reasoning, case in point: an office slash study is a place used for work and to store books. Everyone knew what he meant, and that's the beauty of the analogy. But just because we understand his off-the-cuff comment doesn't mean it's a meaningful foundation for a science of "office slash studies" - it was a convenience category, useful for calling something out, not for drawing firm conclusions. Unfortunately, Christian "apologetics" leans heavily on analogies. In God in the Dock, C. S. Lewis said that Islam is the greatest of the Christian heresies, and all that's best in Judaism survives in Christianity. Well, that's cute, and it may even make you think, but it's bunk if you know the histories of the religions. All too often, Christians use analogies about Jesus, their faith, and the world to argue for one point or the other - but then go beyond it to act as if those analogies were real. This is how Augustine got in the trap of arguing for forced conversions for "pastoral" reasons, forgetting about the real people being abused. One such analogy is behind the idea that "food dulls the soul." This is a relatively obscure theological point, I admit - as J. K. Rowling might say, we're pretty deep in wand lore here - but it illuminates both the positive value of this kind of reasoning and the pitfalls inherent in this kind of imprecise reasoning. "Food dulls the soul" is a concept - from Lewis or Miller, elaborated by a local priest - that if you find yourself backsliding into a sin you thought you'd conquered, check your diet over the last twenty-four hours: it's likely that you had a big, hearty - dare I say gluttonous - meal which softened you up. The general idea is that the Devil assails a poorly defended point - it's easy to accidentally overeat - before attempting deeper corruption. The proposed theological mechanism is that "food dulls the soul" - focusing you on your body, detaching you from your spiritual connection, making it easier to sin. I've observed this. The overall phenomenon is real. The explanation even has a grain of truith in it. But as stated, the explanation is garbage. True-sounding garbage: the precise phrase would be specious bullshit, statements that sound true but which are simply made up to suit the author's purpose. For the soul is the form of the body. At very the least, it's an eternal Einsteinian record of every event that ever happened to you in the mind of God, and at the most, it's an eternal, indestructible spiritual essence under the total control of the Supreme Being of the Universe. The soul is the form of the body. You can't separate it from the body. You can't be born without it, or sell it to the Devil, or cut it away with a subtle knife. If you hop in the transporter, or get transported to the grid, your soul will go with you, no matter how convoluted the episode. Commander Data would have one. And so: you can't "dull" the soul. That would be like wearing out the number five: it's not even wrong, it's incoherent. And yet, something rings quite true about this idea - to the point that I recognized the immediately. What gives, then? This is a problem well known to artificial intelligence researchers: "Soul" is a suitcase word. In The Emotion Machine, Marvin Minsky defines "suitcase words" as words with a whole cluster of meanings we carry around like a suitcase. My favorite is "consciousness," which packs in attention (I was conscious of the noise) to wakefulness (I lost consciousness) to sensation (conscious experience). When that priest discussed "food dulling the soul," he was engaged in a bit of sloppy theology to convey a subtle idea. The soul should be reserved for the theological soul - which has a precise definition to keep us out of trouble - but it's a stand-in for our intellects, our hearts, our spirits, our state of grace. The theological soul itself can't be dulled, but we humans as rational animals can get in a very animal state, where we are focused on this world to the exclusion of the next. Our rationality become reactive; our spiritual senses can get dulled; our actions are in touch with our bodies, not our spirits. Whether the Devil literally exists or not, whether we are tempted by spiritual forces of evil or whether we're simply vulnerable to engaging in locally greedy policies rather than appropriately delaying gratification to gather greater reward, we can get in a mode where we're self-satisfied. And when we do - when we overfeed our bellies, or underfeed our spirits - that's when we are vulnerable to falling into deeper problems. Like the "office slash study" where Hofstadter's books got dropped off, "food dulls the soul" is an analogy, a stand-in for a whole cluster of related ideas. Much of Christian apologetics and spiritual advice falls into this category. Specious bullshit is too unkind for this kind of analogical reasoning when it is used in its proper fashion: as a roadmap. This kind of theology is technically untrue, but may be useful, guiding us in the general direction of the good. Feynman once said "the sole test of any idea is experiment". But is it? Astronomers might disagree. Even though telescopes put on space probes are called "experiments", they aren't: they are instruments for gathering observations. Astronomy is an (almost) purely observational science. But even though it isn't strictly true as stated, Feynman's maxim is nevertheless useful - a bright, clearly visible sign that can guide us away from deadend a priori thought-mazes and towards evidence-grounded a posteriori theories which are falsifiable. The same can be said of many theological maxims. Food may not technically dull the soul, but it can get you into trouble. Islam isn't a Christian heresy and Judaism isn't contained within Christianity, but the faiths do exist in a relationship which is fruitful for Christian thinkers to seriously consider. But, while they may be useful, these maxims aren't literally true. So be careful with the theology you encounter. It may be a useful crutch for your thinking, but don't swallow it whole or try to build castles atop of it. At best it will leave a bad taste in your mouth, at worst buried in a pile of sand. That last bit isn't true either, but hopefully you get something out of what I mean. -the Centaur Pictured: Douglas Hofstadter.

Raise Your Oxen on the Sabbath Day

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raise your oxen Keeping with the Sunday theme of a day of rest, let's keep this short. Jesus once said:
And answered them, saying, Which of you shall have an ass or an ox fallen into a pit, and will not straightway pull him out on the sabbath day? [Luke 14:5]
To help me observe the Sabbath, I attend Mass, perhaps read a section of a religious book, and try to avoid shopping (or even to have groceries / packages arrive on Sunday, if I can). But sometimes errands gotta err. And Jesus points out that the Sabbath was made for us:
And he said unto them, The sabbath was made for man, and not man for the sabbath. [Mark 2:27]
And so one way to take your day of rest is to deal with the things which are like your oxen in the well - those things in a metaphorical pit which will keep getting worse unless you make them better. -the Centaur

Coveting is the Least of Your Worries

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watson headshot Coveting is distinctive among the Ten Commandments in that it is a thought crime. For those not familiar with the Ten Commandments, they're a set of guidelines from God in Exodus and Deuteronomy in the Bible. How the guidelines break into "ten" is up for debate, but the rough outline, loosely interpreted, is:
  1. God is the Lord of everything.
  2. Don't have any other Gods.
  3. Don't misuse God's name.
  4. Keep the Sabbath holy.
  5. Honor your parents.
  6. Don't murder people.
  7. Don't commit adultery.
  8. Don't steal things.
  9. Don't lie in court.
  10. Don't covet your neighbor's stuff.
The first command is a statement of God's authority; the second through the ninth are involve some kind of action - making an idol, cursing a blue streak, shopping on Sunday, dressing up like a bat, killing Bruce Wayne's parents, making off with the Lost Ark, telling Tom Cruise he can't handle the truth. But coveting is different. You don't have to physically do anything, like take your neighbor's nice new car: you just need to think about it. Jesus goes even further in Matthew 5:27-28, suggesting that if you look at a woman with lust, you've committed adultery with her in your heart. Seems harsh, but I've heard priests speculate that God's reasoning behind these challenging passages is that coveting is really bad for you. It's not just that coveting your neighbor's house, spouse or possessions is a gateway to theft or adultery, it's that it puts your brain in a bad state. Coveting is "yearning to possess something": possessions themselves are things which can possess us if we are not careful. But there's nothing wrong with wanting something per se: you can want a soda if you're thirsty, a better car if you're in the rat race, the four walls of your freedom if you're a monk. But coveting someone else's possessions - not wanting a house to keep up with the Joneses, but wanting your neighbor Jones's specific house - is the problem. Coveting the possessions of others puts us in mental conflict with the people around us, which can lead to real conflict. So even though it seems innocuous, coveting is a pitfall which is important enough that God wanted to warn us about it. But in a way, that makes coveting a very obvious pitfall. Unfortunately, coveting is just one of the ways that our human brains can go wrong with regards to our view of the people around us. One of the modern "technologies" that humans have developed for maintaining the health of our minds is cognitive behavior therapy, a collection of experimentally tested cognitive and behavioral psychology techniques, designed to improve our well-being by detecting and correcting bad thought patterns. These "cognitive distortions" can be self-destructive - thoughts like "I'm not good enough" - but they can just as easily be self-serving - "Everything would work out if they'd just listen to me." These self-serving narratives have the advantage of making us feel good about ourselves - but they don't better ourselves. When we interact with other people, a healthy mental response keeps things in perspective. Someone speaks over you in a meeting, which happened to me a lot today; but you recognize that there are simple explanations involving no bad intent (as it turns out, my internet was flaky, and my voice kept cutting out). But when cognitive distortions kick in, simple events like that can get overgeneralized ("This always happens to me"), magnified ("They didn't hear me at all"), can swamp out positives (like forgetting the good stuff) and can lead to catastrophizing ("Everything is going to hell in a handbasket"). These distortions aren't accurate, but they enhance the intensity of the events, worsening our stress levels - but, paradoxically, making it feel a relief when the events are over, giving us a bit of a dopamine hit for surviving the encounter, leading to the distortions growing stronger and stronger. Cognitive distortions can turn into internal narratives, which can turn a momentary event into a years-long obsession. On one volunteer project, our group leader took offense when the previous leader tried to boss me around. I'd barely remember this, if our group leader didn't bring it up every time we talk. Loving your neighbor as yourself is hard. But Jesus also says in Matthew 5:44 that you should love your enemies and pray for those who persecute you. Jesus clearly meant this to be directed at real enemies, people who've harmed us, but it applies with equal force to people who we just think have harmed us. Loving your enemies is really hard if those enemies exist only in your own mind, because your cognitive distortions will twist anything that they do into something that is evil - like in politics, where partisans disbelieve anything the opposition leader says, even if he's reading the time off of an atomic clock. But learning not to covet is like ... training wheels for eliminating cognitive distortions. It's good and healthy to want a sandwich if you're hungry. It's not so healthy to want someone else's sandwich. Perhaps that won't motivate you to take it. But you might think they got the better deal. Even in something as petty as who gets the best slice of the cake, we can build tiny slights up into a tower of resentments. Techniques such as "one cuts, the other chooses" may be game-theory optimal, but we are rarely in situations where these techniques can always be applied. So the solution starts with us. Don't covet your sister's slice of the cake. Don't resent your coworker's "DAYYMNN" sportscar. (No, really, it is VERY jawdroppingly nice). Don't covet your neighbor's spouse. Learn to distinguish between wanting to improve your situation, and envying the situations of others. Building the cognitive tools we need to avoid self-serving narratives is hard, because each person's mind and situation are unique. Fortunately, we can start with something easier, something both easy to detect and easy to fix, by following the tenth of the Ten Commandments: do not covet your neighbor's stuff. -the Centaur Pictured: John Watson, founder of behaviorism.