Slides for Fining Tuning talk

Here are the slides for my recent talk at Ratio Christi, "Explanations for Fine Tuning":


Click on that link to find out about:

Part I: The physics of constants and units
Part II: How physicists diagnose fine-tuning
Part III: Some examples of fine tuned constants
Part IV: My own take on proposed explanations

Regrettably there was no recording, so those of you who weren't there won't get the benefit of the marathon Q&A session.  I try to put a lot of words on my slides, so hopefully most of them will be at least somewhat self-explanatory without me talking over them.  (I assumed the audience was already familiar with scientific notation...)

If you want to know more about the fine tuning of constants of Nature you could check out Luke Barnes' blog or order his book.  Or, if you are thirsting for a few more details about the "renormalization group flow" you could start with John Baez's explanation.

Posted in Talks | 71 Comments

Ratio Christi talk on Fine Tuning

Some of you may recall that last February I gave a talk on Science and the Resurrection to Ratio Christi, an apologetics club that meets at Rutgers University in New Brunswick.

Well, this Monday (the 26th) I'm giving a talk on "Explanations for Fine Tuning":

Were the laws of physics selected to produce life? This talk will
describe several examples of fundamental physics parameters which seem to be "fine-tuned", i.e. taking on special values that permit life to exist. We can use techniques from modern particle physics, such as the "renormalization group flow", to help decide which claims of fine-tuning are real, and which are only apparent. Some examples, such as the Cosmological Constant Problem, seem very unlikely to have any normal scientific explanation. I will argue that the only plausible solutions involve God or a multiverse.

Any of you who are in the area are welcome to attend.  This one is at 9 pm at the College Ave Student Center, room 411C.  For more details, see their Facebook page.  Please note that the location and time are different from my previous talk.

Posted in Talks | 19 Comments

Saints and Miracles

A reader kashyap asks:

Excuse me for a completely off-topic question, but this is of current interest to me.  I read in the paper that sainthood was bestowed upon Mother Theresa. One of the requirement is performance of two miracles.  I understand as a devout Christian, you believe that resurrection (a miracle) was so important that God made exception to the laws of nature to make it possible.  I do not have any problem in people believing in their faith. But my problem would be that if you require exceptions (miracles) for every sainthood, there would be too many exceptions to the laws of nature.  What is your opinion on this? If you have talked about such things before, please just give a reference.  Thanks.

The canonization of saints is a Roman Catholic thing, whereas Protestants like myself do not recognize the authority of the Pope, nor do we pray to saints.  Therefore I am not responsible for defending their canonization process, even though (in this case) it couldn't have happened to a nicer person...  ;-)

What is common ground, accepted by both groups, is that God calls all Christians to be saints, people who are holy just like he is holy, and fills us with his Holy Spirit in order to accomplish this.  Obviously, the results are more effective in some people's lives than in others, depending on our response to his grace.

Catholics* believe that people who are especially holy go directly to Heaven when they die (whereas they say that most Christians need to spend time in "Purgatory" being cleansed from their sins, before they can enter Heaven).  They believe that these people have an especially powerful ability to intercede with God, and that Christians on earth can petition saints in heaven to pray for their needs.  They also believe that the Pope has the power to infallibly* declare that certain deceased people are, in this sense, "saints"; although in modern times he normally only does this on the recommendation of a committee that investigates the person for evidence of "heroic virtue" and (yes) a minimum number of miracles.  (However, it is a common journalistic mistake, misrepresenting Catholic doctrine, to say that "sainthood was bestowed" on the person; in their theology it is God who makes somebody a saint; the church merely recognizes the fact afterwards, in some subset of cases.  On Nov 1st there is an "All Saints Day" holiday to commemorate all the saints who served in positions of obscurity, without earthly recognition.)  They also believe that the good works of the saints build up a "treasury of merit" which can be dispensed by the Pope to any Catholic who performs certain actions called "indulgences", in order to reduce or eliminate their time in Purgatory.

* at least, many Catholic theologians believe it is infallible

* The term catholic means "universal".  I generally use their preferred term out of politeness, although obviously I believe that Protestants are also full members of the "holy catholic church" founded by Jesus.

Whereas Protestants generally reject most of the things I mentioned in the previous paragraph.  We believe that the sacrifice of Christ already provides full forgiveness for all sins without needing to add any extra "merit" from saints on Earth or in Heaven.  And that, while there is nothing wrong with thanking God for the accomplishments of Christians of past ages, or of asking people on earth to pray for us, the practice of asking deceased people for favors is spiritually dangerous because of the temptation to idolatry, and the danger of treating saints (especially St. Mary) as though they were polytheistic deities having power of their own.  (Of course Catholics deny that this is what they are doing, but I don't think there are enough "safety measures" in place to prevent it from happening sometimes.)  Because of this danger, and because the practice is not commanded or authorized by the Bible, we avoid it.  We also do not believe that Purgatory has sufficient warrant in Scripture to be accepted as a doctrine; instead we teach that everyone who is saved goes directly to be with Jesus when they die.

It is the practice of the New Testament to refer to groups of Christian believers as "saints".  He wants us all to be holy, because he is Holy.  This is the justification for this blog's highly unique canonization policy.  To me holiness is a more important thing than miraculous signs, and there may be exceptionally holy people who never do any miracles at all.  The more important "miracle" is the work of transformation that God wants to do in people's hearts, in order to fill them with love, because he is Love.

Now none of this actually answers your question about the prevalence of signs and wonders.  I personally believe that God does a fairly large number of miracles even in modern times (associated with the ministries of many kinds of Christians, including Catholics and Protestants).  The most scholarly compilation of modern day Christian miracles I know of is in this 2 volume tome, by St. Craig Keener.  Despite the subtitle, the book is really mostly about modern times.  Since you are a Hindu I should also mention that non-Christian miracles are outside the scope of his work.  (I plan to blog about Keener's book eventually, but I haven't gotten around to it.)

Is this "too many exceptions"?  Well, too many for what purpose?  Most of these are miracles of healing, and judged from the poverty and diseases we see in many countries, one might just as easily argue that there are too few miracles in the present day, rather than too many.  Certainly there are not so many miracles that we are unable to do Science, and identify the usual course of events in Nature!

I guess the real question concerns the trade-offs God is making between consistency, mercy, and revelation, as he governs the world, but:

Such knowledge is too wonderful for me, too lofty for me to attain.  (Psalm 139:6)


I do not concern myself with great matters or things too wonderful for me.  (Psalm 131:1)

where that the last Bible verse ought to be the motto for this blog, because I violate it almost every time I submit a post!

The Bible also records many miracles besides the Resurrection, although these miracles are more like "signs" or "pointers" that help illustrate particular points about the meaning of creation and salvation.  (This viewpoint is explained in St. Lewis book on Miracles, which is in turn based on St. Athanasius' book On the Incarnation.)  For example, when Jesus miraculously multiplied the bread and fish of a child's lunch in order to feed thousands of hungry people, this miracle illustrates the fact that God is always multiplying grain and fish in Nature, and that every time we eat we can be thankful for his loving provision.  It also reminds us of the spiritual nourishment which Jesus, the Bread of Heaven, provides to those that trust him.

Whereas the Incarnation of Christ, and especially his Death and Resurrection, is the central event of the Christian faith, the event that vanquishes sin, defeats death, and brings in life everlasting.  It permanently negotiated a new relationship between God and Man, and when Christ comes back from Heaven to Earth (I am talking about the return of the same body that was crucified in the 1st century, not reincarnation as a new human) his resurrection power will cause every human being who has ever lived to come back to life again with immortal physical bodies.  But it is not enough to merely ransom the human race; the entire universe will be renewed as well, so that there will be "a new Heaven and a new Earth, the home of righteousness" (2 Pet 3:13).  And there, his saints will reign with him forever.  So the Resurrection is indeed what you might call an important miracle, one that catalyzes a whole host of other miracles.

(Since earlier I was talking about disputes between different kinds of Christians, I should probably state that everything in the previous paragraph is agreed upon by all major branches of Christianity, including Protestants, Roman Catholics, Eastern Orthodox, Coptics, and the Assyrian Church of the East.  In my view, the beliefs that all Christians share in common are more important than the doctrines that divide us.)

Anyway, you don't really say in your comment why you think it would be a problem to have "too many miracles", so I'm not sure how to respond right now.  But feel free to elaborate on your thinking in the comments section.

Posted in Theology | 25 Comments

Is God allowed to update the Torah?

On my last post, a reader going by the name JPH comments:

The resurrection is irrelevant.

God appeared to a nation and gave them 613 commandments. He said they were eternal, everlasting, binding for all generations. There is NOT ONE about worshiping God's son or the Messiah. (Exodus 4:22 says God's son is Israel.) There are horrifying threats for deviating from these commandments in Deuteronomy 28. The thirteenth chapter is devoted to prophets who can perform "signs and wonders" and advocate the worship of gods "whom your forefathers did not know." Their forefathers did not worship Jesus. Deut 13 explicitly grants the possibility of miracles in false traditions and says, "Do not hearken unto that prophet." It says nothing about surviving an execution as an exception or some big standard.

Why do Christians think the resurrection cancels/changes the Torah? According to what standard? (No, the prophets didn't say so: Most of these aren't just wrong, they're cringe-worthy. The prophets received their authority from the 5 Books of Moses. Whatever the prophets were saying, it wasn't to subtract from theses books and approach God via some unheard-of intermediary.)

Sabbatai Tzvi, too, was considered by many to be the Messiah. He performed signs and wonders. He had his own St. Paul (Nathan of Gaza) who interpreted his conversion to Islam as some humiliating atonement. He still has followers. So what? Miracles don't cancel the Torah. The only reason to think otherwise is because your Bible already has a New Testament attached.

Thanks for your comment.

I.  Matters of Interpretation

First of all, your method of interpretation, which sees very few Messianic prophecies in scripture, and assumes that if there is a literal application there cannot also be a secondary symbolic application, is simply not in line with traditional Jewish rabbinic interpretation.  Why can't some passages refer to both Israel and the Messiah, for example?

Many of these passages were traditionally interpreted as Messianic by Jewish rabbis, until it became inconvenient given the fact that Christians were continually citing them.  See here for a discussion of the Talmud's take on this:

Messiah: The Talmud on Messianic Prophecy

which includes quotations from the Talmud which state that “All the prophets prophesied only for the days of the Messiah”!  So, unlike the link you provide which keeps stating "not a prophetic prediction" over and over again, it was apparently an accepted view within Talmudic circles that (with some hyperbole) denied the existence of any non-Messianic verses in the Bible!

In any case, there are several passages which are agreed on by everyone to be Messianic, that have this "double fulfillment" aspect.  For example, the central Messianic text is Nathan's prophecy to David, in which he predicts that David's dynasty will last forever, is found in 2 Sam. 17 and 1 Chron. 17.  It is clear that this prophesy has aspects which were fulfilled in the next generation (when Solomon built the Temple) but it also has aspects which speak about David's continuing dynasty, which are ultimately fulfilled by the fact that the Messiah himself will personally reign forever.

Similarly, when the prophet Isaiah talks about Israel returning from captivity under Babylon, he keeps talking about it in terms which suggest that it will usher in the Messianic Era in which there will be peace forever and God will never have wrath towards Israel again.  (A particularly fine example of this is in chapter 54.)  Now we all know that these events did not happen at the same time, but there is a certain allegorical similarity about them which justifies talking about them at the same time.

So, if some Scriptures clearly have both an immediate application to the present day, and also a distant future fulfillment, then there may be double meanings in other Scriptures as well.  (Although in what follows, I will try to confine myself to the plain meaning of the Hebrew Scriptures as much as possible, not because I am conceding the absence of double meanings, but in order to keep the argumentation as clear as possible.)

Now that is not to say that the particular unknown missionary tract that your link is refuting gets everything right.  But, 353 one-liners followed by another 353 one-liners doesn't really seem like the most productive way to engage.  It's a mile wide but only an inch deep. The real debate here is about methods of interpretation--and also the fact that, when the historical evidence is strong enough that God supports something, sometimes one should admit that one's interpretation of Scripture might be wrong!  Also, at least sometimes the Hebrew text is ambiguous (or there are variant manuscripts), so you need to check multiple translations before rejecting the idea that a given meaning could be part of the original text.

So I think the author would have been better off engaging in some work of serious Christian scholarship, rather than some random tract he got in the mail.  (The post you link to doesn't even state the author and publication information!  So I have no idea whose views the tract is supposed to represent.)

II.  Can the Commandments Change?

Secondly, I do get that there are passages in the Torah which may seem, at first sight, to state that the laws of the Torah are eternal and immutable.  (Although the precise translation of these words in the Hebrew can be tricky, as discussed here.)

But when you dig deeper into the Tanakh, I think you will be able to see that there is also significant conflicting evidence, which indicates that parts of the Torah are provisional, if you keep your mind open to the possibility.  For example, the Torah itself explicitly says that:

A prophet will HaShem thy G-d raise up unto thee, from the midst of thee, of thy brethren, like unto me; unto him ye shall hearken; according to all that thou didst desire of HaShem thy G-d in Horeb in the day of the assembly, saying: 'Let me not hear again the voice of HaShem my G-d, neither let me see this great fire any more, that I die not.'  And HaShem said unto me: 'They have well said that which they have spoken.  I will raise them up a prophet from among their brethren, like unto thee; and I will put My words in his mouth, and he shall speak unto them all that I shall command him.  And it shall come to pass, that whosoever will not hearken unto My words which he shall speak in My name, I will require it of him.  (Deut. 18:15-19)

[This quotation is from the JPS 1917, a Jewish translation.  Note that in this translation HaShem ("the Name") is the standard substitute in order to avoid writing out God's Name, just as many English translations substitute LORD.]

This passage makes it pretty clear that there will be new divine instructions post-Torah; in fact it is 1 of the 613 commandments to obey these new laws!  Regardless of whether the singular term "prophet" is interpreted to refer generically to all later prophets, or specifically to the Messiah, the passage seems to indicate that there will be new commandments revealed at that time.  Note the specific statements that the prophet will be like Moses (who gave the law), it will be like the event at Mount Horeb (where the law was given), and that the people need to "hearken" to the new words, i.e. listen to them and obey them.

And indeed, sometimes the prophets in the Tanakh announce changes to the law, even ones which abrogate old provisions.  For example, Solomon modified various details of the construction of the Tabernacle when he built the Temple, and Ezekiel 40-48 changes a bunch of the rules for Temple worship, while Jeremiah 3:16 states that the Ark of the Covenant would go permanently missing, and that nobody would miss it or ever build a new one.  (For that reason, Zerubbabel's Temple had no Ark in its Holy of Holies.)  This single passage, taken all by itself, makes it clear that a key ritual of Moses' sacrificial system, the Day of Atonement, will never again be celebrated according to the precise rules of the Torah, no not even in the Messianic Age!  So clearly, some of the commandments in the Torah can be changed.

These passages already refute the interpretation of Judaism you are advocating, without any need to discuss Christianity or the New Testament.  If you think the commandments in the Torah can't be updated, then to be consistent you would also need to reject the Nevi'im and Ketuvim, like the Samaritans do.

In life, there is always change.  Even the rabbis have changed many things, extending some commandments and replacing others.  Half the commandments in the Torah became impossible after the Destruction of the Temple, so the rabbis substituted various prayers and other rituals.  The Tanakh itself shows that history is not static, and that what was appropriate for Israel at one stage in her development is inappropriate at another stage.  If the religion of Israel had already reached its perfect form immediately after they entered the Promised Land, then there would have been no need to subject Israel to any of the further developments of the next 3,500 years.  The real question is one of authority: who is in charge of deciding what should change, God or human beings?  It was human beings who were charged not to add to or subtract from the Torah; but the Lord (blessed is he) can do as he likes.  He is allowed to modify the terms of the agreement.

Speaking of modifications, Jeremiah goes on to say that God will make a New Covenant with Israel, in which the Torah will be written on their hearts instead of simply in a book:

Behold, the days come, saith HaShem, that I will make a new covenant with the house of Israel, and with the house of Judah; not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; forasmuch as they broke My covenant, although I was a lord over them, saith HaShem.  But this is the covenant that I will make with the house of Israel after those days, saith HaShem, I will put My law in their inward parts, and in their heart will I write it; and I will be their G-d, and they shall be My people; and they shall teach no more every man his neighbour, and every man his brother, saying: 'Know HaShem'; for they shall all know Me, from the least of them unto the greatest of them, saith HaShem; for I will forgive their iniquity, and their sin will I remember no more.  (Jeremiah 31:31-34)

That is an even bigger deal than a change in the rules; it portends a change in how people relate to the whole concept of rules.  It is what Moses wished, when he said “Are you jealous for my sake? I wish that all the LORD's people were prophets and that the LORD would put his Spirit on them!” (Num 11:29).  I understand that you are also jealous to protect Moses, but here Moses himself says he is looking forward to something better!  Moses wanted the Spirit to speak directly into people's hearts, giving them individual guidance about what to do, rather than following a list of rules written in a book somewhere.

(In addition to changing how Israel relates to God, this passage also seems to indicate that this New Covenant involves a more universal access to forgiveness than was previously available.  But, we need not argue here about whether this New Covenant is the same one that is described in the New Testament.  Pretend for a moment that you've never heard of Jesus, that you are a Jew reading this passage before Christianity started.  Isn't it clear that any New Covenant, just by virtue of being New, must necessarily imply some sort of changes to the old way of doing things?)

Furthermore, reason also tells us that the Law of Moses has to change with changing circumstances.  I am not just talking about how some of the commandments seem more suitable for an ancient patriarchal tribal society than to a modern civilized society, or the commandments which refer to people and objects which have not existed for thousands of years (although these facts are worth noting).  I am also talking about situations where God himself tells us why he gave the commandment, and we can see explicitly that this reason is no longer applicable.  For example, in Leviticus chapter 20 God states explicitly the reason for the kosher laws, saying that it is to keep them separate from the nations which engage in more serious wicked practices:

And ye shall not walk in the customs of the nation, which I am casting out before you; for they did all these things [e.g. incest, adultery, sacrificing their children to Moloch, etc.], and therefore I abhorred them.  But I have said unto you: 'Ye shall inherit their land, and I will give it unto you to possess it, a land flowing with milk and honey.'  I am HaShem your G-d, who have set you apart from the peoples.  Ye shall therefore separate between the clean beast and the unclean, and between the unclean fowl and the clean; and ye shall not make your souls detestable by beast, or by fowl, or by any thing wherewith the ground teemeth, which I have set apart for you to hold unclean.  And ye shall be holy unto Me; for I HaShem am holy, and have set you apart from the peoples, that ye should be Mine.  (Lev. 20:21-26)

The logical structure implied by this passage seems to be as follows:

1. The surrounding nations do objectively bad things, like killing their children and having sex with close relatives (listed previously in the chapter).
2. God wants them to be holy like he is, and not do those things.
3. So, in order to prevent them from being corrupted by these cultures, God creates a more trivial rule (don't eat certain kinds of animals labelled as unclean).
4. By obeying this rule, Israel is prevented from fully participating in the life of their pagan neighbors, and also gets some practice in the art of making distinctions between "clean" and "unclean" situations.

But suppose a time were to come when the nations stop doing all of these disgusting things.  Suppose further that God wanted the Gentiles and Jews to join together into one people with common religious rituals.  In that case, the reason for the kosher commandments would no longer apply; in fact the separation would become counterproductive.  Therefore, if this were in fact God's plan, it would stand to reason that the kosher rules would no longer apply to the new situation.

But would God in fact want to make such profound changes?  We do not have to look anywhere in the New Testament to prove that he would.  We need only look at the prophets which are accepted by Jews.  The prophet Zechariah says that there will come a time when there will be ten times as many Gentiles as Jews, who are seeking after the Lord of Israel:

Yea, many peoples and mighty nations shall come to seek HaShem of hosts in Jerusalem, and to entreat the favour of HaShem.  Thus saith HaShem of hosts: In those days it shall come to pass, that ten men shall take hold, out of all the languages of the nations, shall even take hold of the skirt of him that is a Jew, saying: We will go with you, for we have heard that G-d is with you.  (Zech. 8:22-23)

And Isaiah tells us that God will illuminate these converts and extend his salvation to them:

And now saith HaShem that formed me from the womb to be His servant, to bring Jacob back to Him, and that Israel be gathered unto Him--for I am honourable in the eyes of HaShem, and my G-d is become my strength.  Yea, He saith: "It is too light a thing that thou shouldest be My servant to raise up the tribes of Jacob, and to restore the offspring of Israel; I will also give thee for a light of the nations, that My salvation may be unto the end of the earth."  (Isaiah 49:5)

We need not stop to argue about whether the "servant" described in this passage refers to Isaiah himself, Israel, or the Messiah (or maybe all three!)  The important thing for the moment is that it clearly describes the conversion of the Gentiles to the God of Israel, in fulfillment of God's promise to Abraham that "in thee shall all the families of the earth be blessed" (Gen 12:3).

Another passage (Isaiah 66:18-21) can even be read as saying that God will accept some people from Gentile nations as priests and Levites, which would definitely require a change in the rules, although alternative interpretations of this passage are possible.  Or consider Psalm 87, in which people from all kinds of nations—those which were originally hostile to Israel—are recorded as having been born in the city of Zion.

This sort of thing is a pretty recurrent theme in the Prophets (as is the theme of Israel being rebellious for a long period of time but eventually being reconciled to God).  More examples could be multiplied to prove this point, but I don't think I need to, since I'm pretty sure it's already a standard Jewish teaching that, in the Messianic Age, the Gentiles will also enter God's kingdom.

When this happens, the divinely stated reason for the kosher laws will no longer apply, and so there is no reason for them to continue.

Some strictly observant Jews might be tempted to counter-argue as follows: it is not for human beings to pronounce judgement on the reasons for God's commandments.  God might happen to mention some of his purposes in passing, but regardless of what motivates the commandment, Israel's response should always be unquestioning and unconditional obedience.  But that argument seems to presuppose that what God likes best are ignorant slaves, who obey him without knowing the reasons why.  If Moses and Jeremiah are right that God wants people who are inspired by his Spirit to want to keep his laws, then acting based on our best understanding of God's reasons is essential.

God does not just want people to go beyond the letter of the law in order to reach its true point (although that is of course highly commendable).  Sometimes he even wants the kind of people who break the letter of the law in order to keep its true spirit, as for example when David ate the showbread that was reserved for the priests.  (If God were only interested in legalistic obedience, he would never have made David king in the first place, since his great-grandmother Ruth was a Moabitess (Ruth 4:21-22), and in the Torah the descendants of a Moabite were not allowed into the assembly of the Lord down to the 10th generation (Deut 23:3).)

Of course, since the Torah was divinely inspired, nothing in it simply gets discarded or thrown out.  The written record remains forever to serve as a moral guidepost and a record of God's dealings with humanity.  This is possible even if some commandments stop being followed according to the letter.  There is an important difference between abolishing the law, and fulfilling it.  The former is like burning up an acorn in a fire, the latter is like planting it and letting it grow into an enormous oak tree.  The two are completely different in their degree of respect for the acorn's purpose—but either way, the acorn is gone and it isn't coming back!

So I think I have adequately proven, from the Tanakh alone, that (whether or not Christianity is true) when the Messiah comes we should expect some changes to the commandments.  If you agree with that, then that's probably quite enough progress for a single day!

But there is a major issue raised by your comment which I haven't dealt with yet...

III.  Following Other Gods?

So far, I have left untouched the gigantic stumbling block of Christ's claims of divinity. Certainly I can see why this is a huge issue for you.

Now Christians claim—and I think the link you cite barely scratches the surface of what you would need to do to evaluate this claim properly—that there are hints throughout the Tanakh that:

(a) God, although he is one, also has some kind of plural aspects within his being;

(b) the Messiah, as the king who reigns forever, will be more than just an ordinary human, but plays some sort of mediatorial role, reconciling human beings to God;

(c) and that God himself is going to somehow dwell with Israel or live among them, in a more intimate way than before, in the Messianic era (despite the fact that other passages speak poignantly of being rejected by Israel).

This is a huge topic and it would take a whole additional blog post to provide all the Scriptures for each point, but these passages are there if you look for them honestly, rather than trying to fit everything into a predefined theology.

Instead, let's cut to the chase and ask whether the claim is precluded outright by the Torah?  Between Deut. 18:20-22 (which is right after the passage I quoted) and Deut. 13:2:6 (the passage you made reference to), there are 2 different tests to distinguish true from false prophets.  Somebody can be judged a false prophet if they flunk either test.

The first test is to check whether the claimant's prophetic signs come to pass.  Jesus predicted that he would rise from the dead after he was crucified, and the historical record strongly suggests that he did!  So he passes that test.

The second test (which, as you correctly say, applies even if the prophet performs a sign or wonder) is that if a prophet says "Let us go after other gods, which thou hast not known, and let us serve them", then he is still to be rejected (and executed!).

So this passage does raise a serious issue for Christianity.  But at the risk of maybe sounding a bit pedantic, I would humbly submit to you that Jesus did not tell people to turn aside and worship other gods, gods that the Israelites' forefathers had not known.  Rather he told people to worship the Father—his title for the God of Israel described in the Hebrew Scriptures—and whenever he made striking claims about himself, he never suggested that he was some additional or separate deity, apart from the Father.  (Indeed, in the Gospels Jesus states multiple times that there is only one God and that only God is worthy of worship.)  In the passages in which he claims some sort of divine sounding status, he is always claiming to be the somehow part of the same being as the Father.

In these same passages, he often asserts his radical dependency on the Father, to have no independent will or words apart from him.  To take one example, after healing a crippled man on the Sabbath day:

And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day.  But Jesus answered them, "My Father worketh hitherto, and I work".

Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.

Then answered Jesus and said unto them, "Verily, verily, I say unto you, The Son can do nothing of himself, but what he seeth the Father do: for what things soever he doeth, these also doeth the Son likewise."  (John 5:16-19)

For this reason, in Christian theology, Jesus is not considered to be a separate god the way that the Greeks considered Zeus and Hera and Athena to be separate gods.  We consider him to be the Incarnation in human flesh of the same God who made covenant with Abraham, and who asserted his unique power over Resurrection long ago when he said to Moses:

"See now that I myself am he!  There is no god besides me. I put to death and I bring to life, I have wounded and I will heal, and no one can deliver out of my hand."  (Deut 32:39)

The claim that Jesus is the meaning of the Torah, is not one that can be assessed simply by taking a giant list of claimed Messianic prophesies, and asking whether there is any way to interpret them in isolation, such that they agree (or don't agree) with similarly isolated New Testament passages.

No, it is a holistic judgement involving thinking carefully about the whole thing.  It requires meditating on what is God trying to do in the Hebrew Scriptures?  And, where is his Spirit leading you as you try to follow his commandments to love him with your whole self, and your neighbor as yourself?   And then asking whether it the same thing as what God is portrayed as doing in the New Testament.  Jesus himself says:

If I am not doing the works of My Father, then do not believe Me.  But if I am doing them, even though you do not believe Me, believe the works themselves, so that you may know and understand that the Father is in Me, and I in the Father.”  (John 10:37)

In any case, one cannot avoid the conclusion that, false prophet or true, so far it is Jesus whom God has used as his primary vehicle for spreading the message of the Hebrew Scriptures among the Gentiles, just as the prophets said would happen.  I didn't come to Christianity by conversion from Judaism (although my best friend did); I'm a Gentile.  If it weren't for Jesus, I wouldn't even be arguing with you about the Torah!  I guess I'd be off in some forest somewhere, sacrificing to a pagan god.

Of course I am aware that there have been plenty of false Messianic claimants (although giving up on the claim in order to convert to Islam does seem like a pretty convincing refutation).  False Messiahs are a dime-a-dozen.  What I can't imagine though, is how there could be a Real Messiah that is better than Jesus, who showed us how the path of love is strong enough to conquer even the grave.  To me it is obvious that Jesus is deeply good, and that his healing grace and power are in continuity with the best that can be found in Hebrew Scripture.

[Update 8/30/16:  In the 5th to last paragraph of section II, I edited "best guess" to "best understanding", for reasons described in the comments section.]

Posted in Theological Method | 32 Comments

Just how certain can we be?

I.  The Setup

On my post Black Swans, I received the following question from St. "naclhv", who is also a physicist... and a Christian... and a blogger who has discussed Bayesian arguments that the Resurrection of Jesus is highly probable!  So that's a fair amount of commonality... and yet there are also some differences, as we shall see!  I had said:

First of all, I should say you should be VERY SUSPICIOUS of any person who starts their argument by making concessions that huge to the other side. Factors of 10^{297} are ridiculous numbers that should never be thrown around in almost any real life situations, and if he concedes something that ridiculous to his opponent, he ought to be guaranteed to lose, plain and simple.  He's like a stage magician who makes a big show of how he's blindfolded and his hands are tied behind his back and so on.  You can be very sure there's a trick somewhere, and that all that patter is there to distract you from the way he actually does the trick.

(The other guy, St. Calum Miller, is also making a fallacy, when he quotes a likelihood factor of 10^{43} for the Resurrection; this number incorrectly assumes that the evidence from each apostle's testimony counts independently.  The odds of a group conspiracy to lie are certainly bigger than 10^{-43}, which is an astronomically tiny number.  No real historical event is ever that certain.  That being said, he's right that the evidence for the Resurrection is extremely strong, as far as historical evidence goes!  It's just that nothing in life is really that certain.)

naclhv responded:

Hey Aron,

Long time lurker here. I love your site and the work you do. I would have stayed lurking longer, but I decided to comment because I happen to be writing my own argument for the resurrection over on my blog (

Specifically, I'm also getting likelihood ratios around 10^{43} from my own calculations, and I thought they were quite reasonable - very conservative, even. So I thought that I'd run that value by you again, as someone whose opinion I highly value.

[some parallels to physics and history which I will quote in a later section...]

So, I'd love to get your feedback on this way of thinking about probabilities. It forms an important part of my argument for the resurrection, and I'm always looking to refine my ways of thinking.

Thanks in advance for your reply, and thanks again for the work you do here!

You're welcome!

So I read his blog series, which turns out to be quite long, and still continuing.  (This response will also be quite long.)  I find it hard to read long blog series without an outline of where I'm supposed to be in the argument, so I've broken it into some major sections so you can decide for yourself how much you want to read.  Fortunately much of what I want to talk about is in the first four posts:

1. The Main Argument
1 2 3 4

2 Considering possible objections
6 7 8 9 10 11 12

3. more examples for calibrating based on testimony
14 15 16

4. comparison to other claimed resurrection events
18 19 20 21 22
23 + more to come

As requested, I will now provide some friendly fire, against my own side of the argument.  But there's plenty of good stuff in there which I won't be addressing.

II.  Is an individual testimony worth 8 orders of magnitude?

First though, a commendation.  One of the major strengths of this series is that, instead of simply guessing how much evidence a single "seemingly earnest, sincere, personal testimony" is worth, he actually tries to explicitly estimate it using a variety of real-life examples (some of them are thought experiments, while others are taken from his own life, or the news, or gambling situations, and other such situations).

(If you want to decide for yourself how you'd evaluate these decisions, without being tainted by his own suggestions, you should read his first post before proceeding.)

The second post is an interlude in which, for no particularly good reason, he spots the skeptic an enormously tiny prior probability for the Resurrection, namely 22 orders of magnitude: 10^{-22}.  This is, of course, just showmanship—the exact same thing I chewed out Dr. Robert Cavin for at the very top of this post, albeit more modestly—because the goal is to show that the evidence for the Resurrection is powerful enough to overcome even this handicap.  Well I don't think it is, as we shall see below.  If tomorrow I learned a new fact that was 10^{22} more likely to occur if Christianity were false, then if it were true, I'm pretty sure I would deconvert.  I think it's not possible for controversial historical judgements to be that powerful... I intend to explain why below.

In the 3rd post he writes:

Let's use my personal answers, given below, as an example for how to do these calculations. These are my gut answers to the questions, before doing an actual probability calculations. Remember, these are the events that I'm willing to give even odds (50/50 chance) on, based solely on an earnest, personal testimony. It does not mean that I'm willing to believe 100%, and it does not mean that I'd stop looking for more evidence. It only points to how much I'm willing to adjust my beliefs based on someone saying "yes, I know it's unlikely, but it really happened".

For the shared birthday question, I would easily believe that my friend shared a birthday with me. I would also not have any real problem believing that our mothers also shared birthdays. At three people - myself, mother, and father - I would start becoming skeptical, but would probably give my friend the benefit of doubt. Starting with four shared birthdays in the family, I would start leaning more heavily towards skepticism.

On winning the lottery, I would not really doubt that my friend won the lottery. I would start doubting if he says that he won two consecutive lotteries.

On getting a royal flush, I think I could almost believe that my friend got two such hands in a very lucky night at the table. I feel like three would be entering the realm of the fantastical, and I would doubt my friend at around this number.

On pocket aces, I would be willing to believe that my friend had up to four or five pocket aces in a lucky night of Hold'em.

On the multiple births, I would not have any real problems believing that someone was a part of quadruplets. A claim to be in a quintuplet would start to cause a little bit of doubt to me, and a claim of sextuplets would need additional evidence.

On being struck by lightning, I actually had someone around me claim that this had recently happened to her. I had no problem believing it. Even if she had claimed two such accidents I don't think I would have really doubted her. If she had claimed three, I would start to be skeptical.

Now, calculating the numerical probability values for all these things is pretty straightforward:

[He goes on to calculate and gets numbers approximately equal to 10^{-8}]

(In the fourth post, he calculates the testimony of the disciples as being worth a whopping 54 orders of magnitude, but I will hold off on criticizing this number until later.)

There is room to criticize some of the specific examples here.  Maybe I'm just cynical, but I don't think I would believe an acquaintance who claimed to have gotten two royal flushes in the same sitting of poker!

And I also don't think he's right to say that, if someone were to lie on LinkedIn about having a Ph.D. from Harvard, "there is not much concrete negative consequences for lying, while the incentive of getting a job or a business contact can be quite appealing".  There's little point in lying on LinkedIn unless you plan to sustain the lie for your next employer.  But doing that is very high risk, since it's an easily checked fact, and getting caught would result in you getting fired and maybe blacklisted.

But this is quibbling around the edges with the exact numbers.  I think there's a really important point here, namely that sometimes human testimony can really be surprisingly powerful in its effects.

To make my own example, if somebody on a college campus told me, in a nonjocular way, that they'd just seen a building that was on fire, I would think they were probably telling me the truth, even if I was indoors and couldn't check to see if there was smoke.  Even if they looked drunk or disreputable, so long as I had no specific reason to think they were lying, I would certainly entertain the possibility that they were telling the truth.  But, the odds that any given building is on fire at any moment is very small.  If we suppose that a campus has at most one visible building fire (on average) every few years, and that the fire lasts for an hour before being contained, that's a prior odds of at least 1:25,000, brought up to around parity by a not-particularly reliable seeming source.  One could bump the prior odds still lower by adding on some extra details (e.g. somebody jumped out of a window into one of those nets that looks like a trampoline), so long as the extras didn't seem too implausible to be believed.  So I agree that testimony can do a lot!

But I don't think I would interpret this fact in exactly the same way naclhv does.  Suppose it were really true that, in general, "seemingly earnest, sincere, personal testimony" is false only 1 in 10^{8} times.  We can check this by asking how many times in my life have I been lied to?

Now except for pathological liars, people seldom lie about inconsequential facts that they have no emotional stake in; they may lie about trivial matters that make them look bad, but not when you simply ask them the time of day.  Let's instead ask how often people lie about matters of emotional significance.  Things that meet this threshold probably don't come up more than about 10 times a day.  Multiply by about 300 days in a year, and 30 years of life, that's probably about 100,000 situations in my life when somebody has been tempted to lie to me.  If the odds of them lying to me were really 10^{-8}, then that means I might expect to live to be a thousand times my age before somebody would lie to me once. 

Maybe that's is a little unfair because naclhv does specify that the testimony must be "seemingly earnest, sincere, personal testimony", whereas a lot of lies are insincere, easily detectable, or the person backs down immediately when confronted, etc.  But even that sort of really serious lie, surely has happened several times to any of us!  (And there are fewer opportunities for people to make them, too.)  So I think the point stands that the general honesty of human beings ain't 10^{-8}, or anywhere close to it.

So this raises an apparent conflict with the examples naclhv provides, some of which seem fairly reasonable.  I think the resolution of this paradox requires noticing another important principle, which can be illustrated as follows:

Suppose someone tells you that their license plate number is 4ZIW623.  Discounting the possibilities of a vanity plate, them not owning any vehicles etc. the prior odds of this are 10^{-4} \times 26^{-3} = 5.7 \times 10^{-9}.  But more likely than not, they are telling the truth.  Why?  It is emphatically NOT because the odds of them lying about their license plate number are that low.  Instead, it is for this reason: even if they chose to lie, they would have no particular reason to pick that particular plate.  If they randomly make up a license plate, the odds of getting that specific one are also 5.7 \times 10^{-9}, so those two large factors cancel out.  You're just left with your gut feeling about how likely a lie was (say 1 in 100).  That's why you should be more suspicious if they say their plate was (e.g.) 6DVL666.  The odds of getting that plate by chance are the same (assuming your DMV doesn't throw it out for looking devilish), but the odds of somebody thinking it's funny to lie about having that plate are substantially larger because it's not randomly selected; it's special.

This has a number of implications for evaluating human honesty.

One is that weird things happen all the time, and we tend to talk about them because they are more interesting then all the non-weird things that happen to us.  So if somebody says they got a royal flush in poker, that's the particular weird thing that happened to them.  If it hadn't happened, and instead they'd had an affair with a Soviet spy, they'd talk about that instead.  1-in-a-million things happen to a lot more often than 1-in-a-million people, because every day we do a thousand different things where an interesting thing might happen.

So, supposing it's really true that a typical piece of testimony is worth 8 orders of magnitude, I'm guessing about 6 of those orders of magnitude are due to the license plate effect, while only about 2 of them are due to people being reluctant to lie.  At least 1% of the things you hear are lies, but the 99% that is true is nonrandomly selected from the most interesting things that have happened to a person, so even the stories whose prior odds are 1 in 10^{-8} are still true most of the time.  But you shouldn't believe that even a plausible ordinary fact some schmoe tells you is 99.999999% likely to be true, as you would if you naively slapped 8 orders of magnitude on a 1:1 odds proposition.

This means, that if somebody claims to have gotten two royal flushes in one sitting, that's a lot more improbable than what you'd expect from simply squaring one royal flush.  Because getting one royal flush is just one of a gazillion different noteworthy things that might happen to a person, but getting two in one day is relevantly special, like the numbers matching on a license plate.  A liar can add on an extra royal flush with barely more trouble than it took to lie the first one, but a truth-teller had to be just that lucky.

In other words, if I'm right about the 8 = 6 + 2 split, you can only discount that 6 once.  Any additional improbability of the same sort, is on your own head.

So, a sufficiently implausible story is indeed more likely to be a lie than the truth.  But, the implausibility has to arise from some inherently improbable aspect of the story, which would be more likely to be invented by a liar than it is to really happen.  Merely adding additional details, more information ("and it turned out he was really named Aleksey Smirnov and was dropping off the secrets to a man who drove up in a green car..."), lowers the prior probability, but it doesn't matter to whether you should believe them because of the license plate effect.  (Of course the details do matter if they seem to involve corroborating or suspicious aspects, but the mere presence of lots of detail isn't the crucial thing.)  So this is a magical aspect of testimony, that it can cancel out any amount of low prior probability so long as it's merely due to there being large amount of detail, instead of something intrinsically unlikely happening.

(Of course, with a sufficiently large amount of detail, the odds are good that the person would make at least one mistake of perception recall.  But I am talking about evaluating the odds that the testimony is substantially true, not the odds that it is absolutely inerrant.  Minor mistakes and discrepancies are not to the point here.)

III.  What happens when we stack up multiple testimonies?

This also shows the wisdom of the biblical rule that a person should only be found guilty of a crime on the testimony of at least 2 witnesses.  (Still more or less true in Scots law, although the rule has been adapted to modernity by saying that the witnesses need not be human beings, one of them could be a DNA test or something.)  1 witness can just make up whatever details, but if 2 witnesses agree on the same highly specific thing (the more specific, the better), the probability of all those details being false is infinitesimal unless the witnesses aren't independent.  (For example, if there was a conspiracy to perjure themselves).

Informally, it might seem like this means that 2 witnesses can be more than twice as good as one witness.  That's not really the way the math works though.  What's really happening technically from a Bayesian point of view, is that most of the first witness testimony was used up fighting against the low prior probability of the specific claim (see the "prosecutors fallacy"), leaving the second witness testimony free to provide lots of extra gravy on top!

But what if we keep on stacking on more and more witnesses?  Does each one of them produce an additional new factor of 10^{8}?  No, no, no!  First of all, as I argued in the previous section, I think 10^{8} is already too high for evaluating a single witness.  The odds of getting a liar are at least 1 in 100, for the reasons I said above.  Secondly, conspiracies between multiple people do happen.  (As well as other forms of nonindependence, for example someone being influenced by another person's recollection.)

Suppose that, to the best of our ability to tell, based on the factual details of situation, it looks like the witnesses are all more-or-less independent.  Can we then multiply out all the numbers to get a tiny probability of them lying?  (Say, 10^{-54}, as naclhv claims for the various disciples mentioned in 1 Cor 15.)

Absolutely not.  Because it is always possible you are wrong about the factual details of the situation, and the witnesses are not in fact independent.  How would we go about evaluating the probability of this?  Well, to do proper Bayesian reasoning, you have to think about all the possible scenarios, and assign each one of them a prior probability.  You aren't supposed to assign anything a 0 probability, unless it really is absolutely impossible, nor are you supposed to make it really really tiny without good reason.  So, the probability that the witnesses are not independent should always be assigned some not-gigantically-tiny probability.

Now, consider 2 rival scenarios, one in which N witnesses are e.g. independent and lying, and the other where there is a gigantic conspiracy to lie.  Is it not clear, that, as N gets bigger and bigger, the probability of the second scenario will always exceed the probability of the first?  The plausibility of the independence scenario falls off exponentially with the number of witnesses.  While the plausibility of the conspiracy always remains at a reasonably small (but not too small) tiny value.  Since larger conspiracies are harder to hold together than smaller ones, a big conspiracy is going to be somewhat—perhaps even rather—less likely than a small one, but at least it doesn't fall off at a steep exponential slope, as a function of N.

One can generalize this argument further.  Any time you've successfully argued that some hypothesis which uses independence has a likelihood of 10^{-54}, this pretty much guarantees that any hypothesis which does not assume independence is going to do better.  Unless you think the argument for their independence is itself a 54-orders of magnitude slam dunk, but that just pushes the question back to how one could be so sure of that question.

It's absolutely fine, as a rhetorical technique, to try to show that a viewpoint is implausible by showing that all of the most obvious ways for it to be true would involve the conjunction of several improbable events occurring.  But if one actually multiplies out the numbers, one should not take the final answer too seriously—because the most likely way for you to be wrong, is always going to be that you were in error to multiply out those large numbers in the first place, due to some breakdown of your model (including, but not limited to, failures of independence).

IV.  Why we should not be fantastically certain about almost anything

Here are a couple highly relevant blog posts on the subject, by an expert in reasoning I highly respect, who blogs by the pseudonyms Scott Alexander / Yvain (unfortunately not yet a Christian).  The first is about not taking arguments completely seriously when they lead to hugely confident predictions:

Confidence Levels Inside and Outside an Argument

The second one is about a super-Artificial-Intelligence (AI) taking over the world in the near future.  I don't take this hypothesis anywhere near as seriously as the community of Less Wrong rationalists does, but I have to agree with him that it's way more likely to matter than 10^{-67}.  But you can take this as a general parable about a broader issue:

On Overconfidence

So, when you are evaluating the odds of e.g. the disciples claiming to have seen Jesus risen from the dead, the scenario to worry about is always going to be the one where the disciples are not independent, possibly for some reason that didn't fully make it into the historical record.  So when naclhv says that:

Incidentally, if you thought that I forgot to adjust my calculations for the fact that the testimonies are not independent, this is why - the three named witnesses in my argument ARE largely independent; they come from very different backgrounds and met the risen Christ under different circumstances. Especially in Paul's case, if anything you'd expect his testimony to be anti-correlated with Peter's. For the other witnesses where dependency is expected, I explicitly called it out and severely discounted the Bayes' factor values in the calculation.

for the reasons stated above it's hard to imagine that any three witnesses could ever be "largely independent" for purposes of multiplying many tiny probabilities.  Because the "error" due to them maybe not being independent is always going to swamp the situation where they are.

They may still be "largely independent" in the sense that postulating a common conspiracy requires making some improbable background assumption.  But, in that case you only pay the price of that background assumption (assuming that is more probable than multiplying out all the numbers on the assumption of independence).

V.  A similar issue with the McGrews

naclhv isn't the only smart person to make this mistake.  In an otherwise very fine article on the evidence for the Resurrection, Sts. Tim and Lydia McGrew claim a Bayes factor of around 10^{44} for the Resurrection, coming largely from the assumption that the testimony of the Twelve Disciples should be independent of each other (together with smaller additional boosts from the women, St. James, & St. Paul).

They then consider the possibility that the disciples were not independent, explaining that:

But when probabilistic independence of testimonial evidence fails, it need not fail in the way sketched above.  Probabilistic relevance can be either positive or negative... [some math follows]

This general statement about probability theory is correct.  But it is not really relevant, once you start claiming that something is really, really implausible.  Suppose that you aren't sure whether the failure of independence is going to be in a positive positive or negative.  In fact it depends on your background assumptions (And in a good Bayesian calculation, you should never really allow yourself to be 100% certain of anything.)

Suppose, just for the sake of argument, we granted to them a 99% chance to Scenario X, where the disciples' testimony would be negatively correlated (or else independent), and only a 1% chance to Scenario Y, where it is positively correlated.  Well, X gets killed by a huge factor of (according to them) > 10^{44}, while the latter gets beaten down by a much smaller factor (since the disciples testimony is now positively correlated).  So Y is always going to win!  (Even if the final result for Y is damped by the 1% factor, that's nothing compared to 10^{-44}!)

They go on to articulate a particular reason to believe that some of the disciples' testimonies might be negatively correlated instead of positively correlated:

If A dies (especially in some unpleasant way) for his testimony to the risen Christ and B hears about it – and there is no serious doubt that the apostles knew when one of their number was put to death – does this make B more likely to stand firm until death in his own testimony? It seems to us that the opposite is true, that knowing of such a death is plausibly and under ordinary circumstances negatively relevant to B’s willingness to remain steadfast. B may well be frightened by the fate of A and drop his claims. In this case, treating A’s and B’s deaths for their testimony – their “martyrdoms” in the original sense of the term “martyr” as “witness” – as probabilistically independent actually understates the case for R.

This correctly identifies a possible mechanism, by which, given certain background assumptions, one disciple's false testimony might make another's (continued) false testimony less likely.

Personally I don't think that this is a more important effect than the sort of obvious social fact that people tend to imitate their friends' behaviors even when those behaviors are self-destructive.  (Consider how gang members react to the death of a gang leader.)

But it doesn't really matter much whether the failure of independence is more likely to be positive or negative.  So long as somebody can articulate any scenario in which the disciple's testimony was positively correlated, that is the scenario to worry about.  (So long as it doesn't also involve implausibilities worth many orders of magnitude, but it's hard to get there without multiplying a bunch of small numbers, and the whole point of these scenarios is that they try to avoid these things...)

Hence, the McGrews analysis provides an overestimate of how likely the Resurrection is.  That doesn't mean there aren't some strong historical arguments in their paper.  But the mathematical statements are hyperbolic and need to be discounted.

VI.  Are alternatives already factored in?

In a later post, naclhv fights against the possibility of alternative analyses here.  After mentioning some specific whacko conspiracy / delusion theories of the usual sort that people bring out to explain the Resurrection—and quite correctly saying that they not are well supported by any of the data that we actually have—he goes on thus:

First, note how weak this argument is, even if we were to grant it everything that it asked for. Remember, the odds for the resurrection are currently at 1e32, so the odds against it are therefore at 1e-32. Now, we'll allow for each independent objection to count as having the full weight of these odds. Never mind that many of these objections contradict one another and therefore reduce the probabilities of the other objections (increasing the probability for 'insanity' decreases the probability for 'conspiracy', because a conspiracy is less likely to succeed with insane people in it). We'll just ignore that. Never mind also that these complex speculations are naturally less likely because of their complexity. We'll also ignore that as well. So, if we can think of a hundred such objections, each of which carries the full weight of the 1e-32 odds for 'no resurrection', the final odds for the resurrection would drop all the way down to... 1e30

Let me first extract a correct and important point from this paragraph.  One doesn't really get out of mileage from simply coming up with large number of fantastically improbable anti-Resurrection scenarios.  For example, the Swoon Theory, the Identical Twin Theory, the Hallucinatory Drugs Theory etc.  For if it is true that each theory contains some individually highly unlikely coincidence (even a 1-in-a-million event) then simply coming up with a hundred or so different theories doesn't get you out of the hole.

But, the skeptic does get some mileage out of suggesting scenarios in which independence of the disciples breaks down, for the reasons explained in the previous section.  naclhv goes on to argue:

But more importantly, this kind of objection is simply, fundamentally wrong: it would not fly in any other investigation into a personal testimony, because it completely ignores the rules about how we evaluate evidence in a Bayesian framework.

Imagine, for instance, that your friend claims to have been struck by lightning. You've taken stock of this claim and have decided to assign it a Bayes' factor of 1e8. But then you say, "well, you may be just a little crazy. And you might have had a nightmare about a thunderstorm last night. Then you might have gone to a hypnotist and who had you recall your dream, which you're now confusing with reality. Or maybe it was the hypnotist who planted the suggestion in your mind first and that caused your nightmare. Really, it might have been any of these things - and isn't it more likely that at least one of these possibilities is true, rather than for you to have been actually struck by lightning?"

Should you or your friend then discount the previously assigned Bayes' factor in light of these new possibilities? Absolutely not. The thing to note here is that the Bayes' factor ALREADY includes all of the ways that this claim may be wrong. It is the numerical estimation of the weight of evidence for a human testimony, and as such already inherently includes the possibility that the evidence may be misleading.

Having established its value, it is simply incorrect to further modify it with no evidence, based on enumerating possibilities that were already included in its evaluation. Your friend's proper reply to your wild speculation would be to say, "what makes you think that I had visited a hypnotist or had a nightmare? Of course, anyone might be wrong about anything in any number of ways - but don't you already know how much you trust me? How does a list of ways that I might be wrong, with no evidence behind any of it, make you trust me less?"

That is quite true and correct for evaluating a single witness, if we have already calibrated the probability of error using everyday examples, as naclhv has attempted to do.

But it does not apply to hypothesis in which independence of multiple eyewitnesses breaks down, because the effects of those scenarios have not already been taken into account.

VII.  On tiny probabilities in physics

You mention that numbers like 10^{43} or 10^{297} are ridiculously large and should not be taken seriously, especially in historical settings. I would, in general, agree with you - but there are exceptions to this rule in some kinds of math, and probabilities is one area where such numbers are not uncommon. Here's how I'm thinking about this:

Let me give some examples from probabilities inherent in everyday objects. The probability of shuffling a deck of cards to a specific order is about 10^{68}. The probability of recreating a game of chess through random play is about 10^{120}.

Even in physics, 10^{43} would be a ridiculously large number if we were talking about something like time (is that in seconds or years? It doesn't matter - it's basically "forever"). But in the branch of physics that deals with probabilities - that is, in statistical mechanics, 10^{43} is nothing.

For example, the standard molar entropy of water vapor is 188.8 J/K/mol. So the number of microstates for a mole of water vapor at standard conditions is e^{(188.8/k_{boltzmann})} - that is, about 10^{(10^{25})}. Lest anyone think that this is so large only because we're talking about one mole of something, even if we take the moleth root of this number we still get about 10^{10} - so, even just five molecules of water vapor will have something like 10^{50} microstates.

The trouble with these examples is that they are all conditional statements of the form:

  • If model M is correct (where independence holds) the probability of event E is tiny.

where the model M is a truly random shuffle, or the statistical mechanics of water, or whatever.  But that does not mean that the probability of an actual shuffle to result in a given configuration is that low.  The cards might be being "shuffled" by a card sharp like Scarne!

Similarly if all the air molecules go to one corner of the room, that would mean there's some natural (or supernatural) effect we didn't take into account.  It would not mean that a 10^{-(10^{25})} event just happened.

In other words, the model M could always be false.

Also, you mentioned that probability values like 98% are actually not at all extreme. I also think that as well. But the five sigma probability of about 10^{-6} is also not all that extreme - it corresponds to something that we're barely certain enough to publish on, at the cutting edge of science.

That's what we do in particle physics, anyway.  But in the soft sciences, they publish at 2 sigma which is why you can't trust anything you read in science news about people.  :-)

However, the 5 sigma rule = 3.5 \times 10^{-6} doesn't actually mean that the odds of being wrong are less than one in a million.  The reason why particle physicists adopted that rule is that, when they used 3 or 4 sigma, they kept getting false alarms!  There seems to have been a recent example of this at the LHC.  This makes it clear that it's an overreaction to guard against biases that weren't taken into account.

One possible source of bias is the Look Elsewhere Effect, where there are a large number of possible theories that you could have checked for, and you just notice the thing that happens to look anomalous.  In Bayesian terms, this is closely related to the fact that theories which predict specific new particles and forces have low prior probabilities.  Finally, there's good old systematic error, the bane of experimentalists everywhere.

So really the 5 sigma rule is just a kludge, which exists precisely because things are never quite as sure as they appear to be, so you need to up the standards a little.

Several independent verification at the 10^{-6} level would easily bring the overall probability to something like 10^{-43}, and any well-established scientific laws would easily break 10^{-100}, by a large margin.

Assuming complete independence, yes.  But systematic error is not independent, nor is failure to properly consider alternative explanations, nor group-think bias, nor grand scientific conspiracies to mislead the public, nor malicious spirits playing jokes on us, etc.

So, even in history, I can easily imagine a statement like "The Roman Empire existed" having an odds of 10^{300} for being true. Basically, my rule of thumb is that probabilities or odds are not "too large" unless their logs are "too large". This makes sense, given the multiplicative nature of probability.

Same as above.

VIII.  Back to Jesus and the Resurrection

So where does this leave probability arguments for the Resurrection?  I made my own attempt to do a probability calculation in these posts:

Let us Calculate
Christianity is True

For the moment let's ignore the philosophical stuff about the argument from evil and fine-tuning, which maybe could also used to be ramped down a bit, and let's discuss the historical stuff.

Well, I still think that all of the basic component arguments here are good.  Well, it's still true that there's good reasons to believe each of the following is true:

a) Jesus was a very special person, apart from the unusual circumstances after his death

b) a few days later his tomb was empty

c) many of his disciples claimed to have seen him alive, including both women (the first eyewitnesses), the full group of 11 remaining apostles, St. James the brother of Jesus, and others.  [Consider "as read" the standard arguments about the testimony of women not being highly regarded among 1st century Jews, and at least some key witnesses being martyred for their faith.]

d) that some highly unusual vision/phenomenon—according to Acts it was noticeable to others and caused him temporary blindness, but even if we consider this to be an exaggeration, it seems likely to have been at least an epileptic fit of some kind—caused St. Paul, an enemy of Christianity, to convert and become a zealous missionary (and eventually get executed himself).

I originally said that (a), taken by itself, roughly cancels out a factor which is basically the Look Elsewhere Effect (discussed in section VII).

I also said that (b,c), taken by themselves, amounts to about 8 orders of magnitude (from many witnesses) and I'm prepared to stand by that given the weirdness of the situation.  Bear in mind that since tens of billions of people have died in historical times, a mere 10^{-8}-level coincidence following somebody's death should still have happened at least a hundred times in history.  For the kinds of skeptical reasons I stated above, it would be hard to get this much above 10^{11} by itself since then we run out of the ability to check how many potential parallels there are.

Finally, (d) taken by itself, is at least a 1-in-a-million event and I stand by that.  I'm pretty sure there are not 40,000 non-Christians alive today who have had similarly dramatic conversion visions leading them to become zealous for a religion they previously disliked.  (It would be circular to count the Christians here, since if we're right God still does dramatic things to convert some people.)  Maybe we need to shave off a factor of 10, because of the existence of multiple possible persecutors in early Christianity whose conversions would have been equally dramatic (e.g. Caiaphas).

Now, under some fairly reasonable background assumptions, if we trust the New Testament texts even a little bit, some of these assumptions seem at least partially independent of the others.  (For example, even very skeptical scholars agree we have at least some information about Jesus' teachings prior to his death.  And that Paul was originally a persecutor of Christians, and therefore not likely to be sympathetic, we have from his undisputed letters, as a testimony against his own current interests.)

But, clearly the right approach for a skeptical attack, the only one that has a hope of success (other than an almost complete skepticism towards the texts which I really don't think is justified), will be to attack the independence of these events.  And there are some ways of doing this that probably do shave off several orders of magnitude.  I just don't feel like they are strong enough to explain all of the data.

For example, it probably IS true that if an unimportant rabbi seemingly rose from the dead due to a coincidence, that people would make up a bunch of stories about him and maybe put some words in his mouth.  But I don't think such an invented composite would end up being plausibly the most insightful and challenging moral thinker the world has ever known.  (And I don't think this is that subjective of a criterion.  The vast majority of people wouldn't pass the "laugh test" for that position.)  Nor would I expect multiple early detailed texts along the lines of the Gospels.

Going in the other direction, if a charismatic religious leader made grandiose claims about his own identity, I quite agree that it makes it more likely for his followers to report grand miracles after his death.  But I wouldn't expect it to involve quite so many coincidences as we find in the New Testament, I wouldn't expect such a large base of eyewitnesses, and I wouldn't expect the whole thing to be so well documented so early.  (Whereas legends that develop over centuries, that can happen to anybody.)

Finally, crankish people converting to a false religion is commonplace, but it's more surprising when one of your biggest persecutors has a vision of Jesus and goes blind until someone comes to baptize him, and it's also a bit surprising when he then goes around doing miracles, all of this described in a text (Acts) which to all appearances looks like a careful historiography, in parts styled very like a personal memoir by a close companion.   (Of course St. Paul's conversion is also mentioned in his own letters, I mean the ones that even anti-Christian theologians think were really written by him.)  You can, of course, say he was a sincere fanatic who (overcome by guilt for his persecution) confabulated multiple miracles, but that still leaves him more or less separate from the others.  To really undercut the independence from (b, c) you have to say he was a plant, or that he was a fraud who made up most of the other disciples' testimonies, but any of these tactics is an uphill battle for various reasons.

So, if you disbelieve the New Testament accounts of the Resurrection you can and should deny the independence of these pieces of evidence.  It's just, you have to pay a price for doing so.  I still think the most parsimonious explanation is that a large group of people deliberately and intentionally conspired to make up the whole thing.  It's more likely than the other naturalistic explanations, it's just not all that likely.

But because naclhv invited me to critique his argument, I'm going to be merciless and observe that he oversteps again when he says this:

Let me reiterate and clarify that, because it's important. There is an utter lack of evidence for disbelieving the resurrection: literally every single record we have from the people who were actually connected to the event to any reasonable degree ALL portray the resurrection as something that actually happened.

If you believe in the resurrection, you have the unanimous support of all the people who were actually close to the event and would know for certain. If you disbelieve the resurrection, literally every piece of evidence - every single testimony of every single person who ever testified about the actual event - is against you.

He has forgotten an important class of witnesses against the Resurrection, namely the guards at the tomb.  St. Matthew's Gospel tells us quite frankly that:

While the women were on their way, some of the guards went into the city and reported to the chief priests everything that had happened.  When the chief priests had met with the elders and devised a plan, they gave the soldiers a large sum of money, telling them, “You are to say, ‘His disciples came during the night and stole him away while we were asleep.’ If this report gets to the governor, we will satisfy him and keep you out of trouble.”   So the soldiers took the money and did as they were instructed. And this story has been widely circulated among the Jews to this very day.

Of course we owe this account to a Christian, but it is hard to imagine anyone would write these words unless either (1) the guards really did report that somebody had stolen the body, or at least (2) some of the Jews claimed that the guards had said this.  Now people do not usually make up, entirely out of whole cloth, arguments against their own position to respond to.  Maybe they unfairly caricature them as strawmen, but usually they are responding to real people.  So it seems historically very probable that there was in fact some kind of anti-Resurrection testimony to this effect.

It is a separate question whether this anti-Resurrection testimony, as we have it, is at all plausible.  It does nicely undercut the independence of (b) and (c) by postulating that the nefarious disciples conspired to produce both effects, even if their motivations at this stage would be obscure.  But, we can expect that the guards would have been severely punished for sleeping on duty, especially if all of them slept at once.  (This would be true for a Jewish guard, but even more true for a Roman one where the punishment would be execution.  Since Pilate's words were "you have a guard": it is unclear whether he was providing a guard or observing they already had one.)  And, if there was in fact a heavy stone and a seal, it would have been quite challenging to move it without wakening anyone.  And, if the guards were really asleep, how could they possibly know who had stolen the body?

Their testimony may even ultimately favor Christianity, since it's existence helps confirm that there was a guard, which makes the empty tomb a lot more impressive.  But, it is false to say that no one was claiming the Resurrection hadn't happened.  The guard—and apparently the Jewish leaders that allegedly bribed them—were putting forth a different story.  But for some reason, even the skeptics have preferred to tell other tales.

So where does this leave us?  I'm reluctant to slap a number on this now, because earlier I concluded that, if you're really sure something is true, inevitably the best possible skeptical hypothesis is always going to be the thing you didn't think of, something that undermines all of your assumptions.  This means, the more and more sure we get, the harder it is to even calculate just how sure we should be.  But, we should not be too sure.

Leaving aside truly awful skeptical scenarios, like we're all in brains in the Matrix being toyed with, surely we can be pretty darn sure that e.g. Julius Caesar was assassinated.  As I have argued before, the evidence for Christ's Resurrection is almost as strong.  But, very tentatively, it seems reasonable to maybe put a cap on how sure we can be of any particular historical event, maybe 99.99% tops for the final answer, to something we've carefully investigated that seems to require an unlikely "conspiracy" to explain away.  Unless it's something really basic like "The Roman Empire existed", where we should be able to go a bit further.  (Part of me feels a bit dirty assigning some historical conspiracy theories a probability of more than 1 in a million, and maybe that's correct, I'm really not sure where the threshold should be.)

This is just a kludge, until somebody figures out a way of assigning a number to "failures of independence in ways that you haven't even thought of yet".  But, this is good enough for now.  It seems to me one can still be highly confident, on the basis of historical data, that Jesus rose from the dead.  Just not quite as confident as naclhv and the McGrews claim you can be.

(Of course, a complete analysis would have to include all the rest of the evidence from philosophy, experience, etc.  aside from the immediate historical data for the Resurrection.)

IX.  Epilogue

Some people might wonder why I'm spending time criticizing an argument for my own religion, saying that it is too strong.  Most people spend their time arguing against things they don't believe in.

Well, I'm not most people.  I'm hoping to do something a little more unusual, which is trying to follow the truth wherever it leads.  Superficially, it is rhetorically effective to play up the strengths of one's own argument, and the weaknesses of the other side.  Unfortunately, this can lead to a tendency towards dishonesty, ignoring the flaws on one's chosen side.

So I have a different evil plan, which is to evaluate arguments in a fair and unbiased way the way a rational person would.  You see, if I can successfully pretend to be doing that, then people on the other side will say to themselves,

"Here's this reasonable looking person, who doesn't seem biased, crazy, or stupid, and he knows about science, and yet he still thinks it's historically plausible that some dude was God's Son, and came back to life again.  Maybe there's something too it, and I should take another look."

So, there are advantages to pretending to be reasonable.  But I find that the easiest way to pretend to be reasonable, is to actually be reasonable.  And—joking aside—my first priority is to the Truth.  If Christianity is right, Jesus is the Truth, so loving Truth and loving Jesus works out to the same thing in the ultimate analysis.  But, if that weren't the case, I would want to know it, rather than living out my life based on a lie.

Other Christians might say, well what about the certainty which comes through the testimony of the Holy Spirit?  Who cares about probability theory and this historical jibber-jabber?  I kind of doubt whether anyone like that has read this far, but if you have, here's my response:  Obviously I'm not going to tell the Spirit not to bear witness to the truth in people's hearts.  And while much of the time he leaves us to our own devices, sometimes it does seems like he's bearing witness to my heart.  But, although I've had some fairly dramatic spiritual experiences, none of them are so strongly powerful that there's absolutely no chance I could be wrong about their cause.   Which is not unexpected, given that "we live by faith, not by sight" (2 Cor 5:7).

So, they also can't make me perfectly certain as a Bayesian reasoner.  But Bayes' Theorem isn't how people actually think internally.  It's just a somewhat useful model of what a hypothetical Spock-like rational entity would do.

When it comes to emotional certainty, I honestly don't think there's that big of a difference between, a calculation that says you should be 99.5% sure, and one that says you should be 99.999999999999999999% sure.  The heart doesn't really resolve that kind of difference.  Whether or not you trust in Jesus isn't really a matter of having an enormous probability, although you shouldn't do it if you don't think it's true.  It's a matter of making a decision to trust.

Once you've decided to trust, additional percentage points maybe help you sleep at night but I don't think they are all that spiritually valuable one way or another.  Emotional certainty can be spiritually valuable, if it's built up by trusting God in difficult circumstances.  As we all know, it doesn't come automatically from simply being intellectually persuaded.  That's where faith comes in.

To use a classic sermon illustration: what shows you have faith that a plane will arrive at its destination safely?  The answer is if you're willing to get on it.  One person may be trembling in fear, another may be cocksure, but whether or not you get on the plane is a yes/no question, not a continuous probability value judgement.  Maybe the first person gets on and the second doesn't.  So, you can even be a Christian even if you only think it only has a 70% chance of being true, as long as you are willing to get on the plane.  Those who do get on board usually become more sure, while those who don't often become less sure.  Which of these effects is primarily due to bias, I guess depends on who is right!

So, there are credences (i.e. probability assignments), there is the feeling of emotional confidence, and then there is trust, and none of these are exactly the same as each other, even though sometimes they are related.  What we are entitled to is just enough to get by on: "Give us this day our daily bread..."

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