“In the beginning, God created the heavens and the earth.” While the world definitely had a beginning, there’s a question of whether we can prove this by reason alone (i.e., by philosophical arguments).

Defenders of the Kalaam cosmological argument often use an argument like this one, which is found in William Lane Craig’s book Reasonable Faith:

1) An actually infinite number of things cannot exist.

2) A beginningless series of events in time entails an actually infinite number of things.

3) Therefore, a beginningless series of events in time cannot exist.

I have a problem with the first premise, but that’s a topic for another time. Here I’d like to look at Craig’s second premise.

Is it true that a beginningless series of events entails an actually infinite number of things?

At first glance, the answer would seem to be yes, but the reality is more complex.

The Nature of Time

The answer depends on your view of time. Here we need to consider two major theories of time, which are known as eternalism and presentism.

Eternalism holds that all of time exists. The past, the present, and the future are all real from the ultimate perspective—that is, from the eternal perspective outside of time. We may only experience history one bit at a time, but from the “eternal now” that God dwells in, all moments of time are equally real.

Presentism (as we will be using the term) holds that, from the ultimate perspective, the only time that exists is right now—the present. The past used to be real, but it is no longer. And the future will exist, but it does not yet. Since neither the past nor the future are real, they do not exist in any sense of the word. If you asked God—from his ultimate perspective—“What is real in the created order?” he would answer, “Only the present.”

The Eternalist Option

Supposing that eternalism is true, Craig’s second premise would be true. From the eternal perspective outside of time, God would see an infinite series of past events laid out before him.

Or, if you wish to avoid the question of how God’s knowledge works then, as the Creator, God would be causing that infinite series of past events to exist.

They would all be equally real—equally actual—from his perspective, and—since they have no beginning—they would be infinite. Being both actual and infinite, the events of a beginningless history would represent an actual infinity. Thus, the second premise would be true.

But for a classical Christian theist, there would be a problem, because Christianity teaches that God will give people endless life. While human beings may come into existence at the moment of their conception, they will never pass out of existence.

Therefore, humans have an endless future. And that future also will be equally real to God.

From his eternal perspective outside of time, God sees and creates all the moments of our endless future. They are both real—actual—from his perspective, and they are infinite in number. Being both actual and infinite, the moments of our future also would be an actual infinity.

From the viewpoint of a classical Christian theist, eternalism implies the existence of an actual infinity of future moments, giving such theists reason to challenge Craig’s first premise (that an actual infinity can’t exist).

However, this post is only examining his second premise, so let’s consider the other option we need to look at.

The Presentist Option

If only the present exists, is it true that a beginningless series of events in time entails an actually infinite number of things?

No. At least not an actual infinity of real things.

The reason is that, on the presentist view, only one moment of time exists. No past moments exist, and no future moments exist.

It doesn’t matter how many events took place in the past, because those events are no longer real. As soon as a new moment arrived, all the events taking place in the previous moment evaporated and are no longer actual.

Therefore, it doesn’t matter how many past events there have been—it could be a finite number or an infinite number—because they have all ceased to be actual. The only actual events are those occurring in the present.

So, if presentism is true, the second premise of Craig’s argument is false if applied to concrete, real things like events. A beginningless series of events in time does not entail an actually infinite number of such things because those things are no longer actual.

For a collection of things to be actually infinite, they all have to be actual from some perspective. On eternalism, that can happen, because all the moments of time are actual from the eternal perspective outside of time.

But it can’t happen on presentism, because this view holds that, from the ultimate perspective, only one moment is real, and one is a finite number. This view entails that no actual infinity of moments in time exists, because only one moment of time is actual.

This is why Aristotle could believe that the world did have an infinite history. Even though he thought an actually infinite number of things couldn’t exist at the same time, history didn’t present that problem, because one moment passed out of existence when another came into it, so the total number of moments was always finite.

The Counting Argument

In the Blackwell Companion to Natural Theology, Craig and coauthor James Sinclair respond to this issue with two lines of thought.

The first is based on counting, and their reasoning (omitting examples for brevity) goes like this:

[W]e may take it as a datum that the presentist can accurately count things that have existed but no longer exist. . . .

The nonexistence of such things or events is no hindrance to their being enumerated. . . .

So in a beginningless series of past events of equal duration, the number of past events must be infinite, for it is larger than any natural number. . . .

[I]f we consider all the events in an infinite temporal regress of events, they constitute an actual infinite.

It’s true that a presentist can count things that have existed but no longer exist (e.g., the number of days that have elapsed so far this year)—and their nonexistence doesn’t prevent this counting (just look at a calendar!).

The problem comes in the third statement, because it can be understood in more than one way.

In terms of what is real on the presentist view, the number of past events is not infinite, because no past events exist. That’s a key point of presentism.

If you want to talk about an infinite number of past events, you have to shift from speaking of events that do exist to those that have existed, and those aren’t the same thing.

Yes, on presentism, we could speak of an infinite collection of events that were real but aren’t anymore. And that’s the point: They aren’t real.

This points to a second way of reading the statement when Craig and Sinclair speak of “the number of past events.”

If we are talking about the number of events, then we’re no longer talking about the events themselves. Instead, we’re talking about a number, which raises a question.

What Are Numbers?

Mathematicians and philosophers have a variety of views about what numbers are. Some classify them as “abstract objects” that exist independent of the mind. Others think of them as mental constructs of some kind. There are many variations on these views.

Whatever the case may be, Craig doesn’t see infinite numbers themselves being a problem.

In his talks and writings, he has frequently said that he doesn’t have a problem with the mathematics of infinity—that modern mathematical concepts dealing with the infinite are fine and useful as concepts. Thus, the infinite set of natural numbers (0, 1, 2, 3 . . . ) is a useful concept.

Craig doesn’t reject the idea that the set of natural numbers is actually infinite. It’s just not the kind of actual infinity that causes a problem for him because numbers aren’t concrete objects in the real world.

So, actual infinities of the numerical order are fine, in which case it’s fine if the number of past events is actually infinite. It’s an actual infinity of events themselves that he says can’t be part of the real world.

And on presentism, they’re not. Past events would have to be understood in some other way. They might be abstract objects, like many mathematicians hold numbers to be. Or they might be purely mental concepts at this point, as others regard numbers.

Whatever is the case, on presentism they do not exist in the real world. And so, whatever kind of infinity a beginningless universe would involve, it doesn’t violate the principle that—while actual infinities may exist in an abstract way, as in mathematics—they don’t exist in the real world.

Back to the Future

There is another way of illustrating the problem with the argument from counting, and it involves considering the number of future events.

If the universe can’t have a beginningless past because an infinite set of non-real past events can’t exist, then we also can’t have an endless future, because that entails an infinite set of non-real future events.

The argument simply involves shifting from events that used to be real to those that will be real.

If God gives people endless life, then the number of days that we will experience in the future is infinite. As the hymn says about heaven,

When we’ve been there ten thousand years,

Bright shining as the sun,

We’ve no less days to sing God’s praise,

Than when we first begun.

As Craig and Sinclair acknowledge:

It might rightly be pointed out that on presentism there are no future events and so no series of future events. Therefore, the number of future events is simply zero. . . . [O]n presentism, the past is as unreal as the future and, therefore, the number of past events could, with equal justification, be said to be zero. It might be said that at least there have been past events, and so they can be numbered. But by the same token there will be future events, so why can they not be numbered? Accordingly, one might be tempted to say that in an endless future there will be an actually infinite number of events, just as in a beginningless past there have been an actually infinite number of events.

So, why should an infinite number of future events be considered more permissible for a presentist than an infinite number of past ones?

Possible vs. Actual Infinity

Craig and Sinclair’s response involves the difference between an actual infinity (where an unlimited number of elements exist simultaneously) and a potential infinity (where an unlimited number of elements don’t exist simultaneously). They write:

[T]here never will be an actually infinite number of [future] events since it is impossible to count to infinity. The only sense in which there will be an infinite number of events is that the series of events will go toward infinity as a limit. But that is the concept of a potential infinite, not an actual infinite. Here the objectivity of temporal becoming makes itself felt. For as a result of the arrow of time, the series of events later than any arbitrarily selected past event is properly to be regarded as potentially infinite, that is to say, finite but indefinitely increasing toward infinity as a limit.

This reasoning is mistaken. It is false to say that “the series of events later than any arbitrarily selected past event is . . . finite but indefinitely increasing toward infinity as a limit.”

No. If you arbitrarily select any event in time and consider the sequence of later events, they do not “indefinitely increase toward infinity.” They are always infinite.

Consider January 1, 1900. On the Christian view, how many days of endless life will there be after that? An infinite number.

Consider January 1, 2000. How many days are to come? Again, an infinite number.

Consider January 1, 2100. How many days follow? Still an infinite number.

As the hymn says, “We’ve no less days to sing God’s praise than when we first begun!”

What Craig and Sinclair are thinking of is the fact that, if you pick a date and go any arbitrary distance into the future, your destination will still be a finite number of days from your starting point.

Thus, the number of days that has elapsed between the start and finish of your journey grows toward infinity but never gets there, making this span of days a potential rather than actual infinity.

But it does not follow—and is simply wrong—that the complete set of future days is only potentially infinite. To show this, just give each day a number: Today is 0, tomorrow is 1, the next day is 2, and so on. We can thus map the set of future days onto the set of natural numbers, which is actually rather than potentially infinite.

Take any day you like, and on the Christian view the quantity of days that will be after it is identical to the quantity of natural numbers.

The quantity of days that will be—like the quantity of natural numbers—does not grow. This quantity just is.

Unless you say—contrary to the teaching of the Christian faith—that the number of future days is finite and God won’t give us endless life, then there is an actual infinity of future days.

And if a presentist wants to affirm an actual infinity of currently-not-real days that will be, he must allow the possibility of an actual infinity of currently-not-real days that have been.

Conclusion

In summary, Craig’s second premise was:

2) A beginningless series of events in time entails an actually infinite number of things.

Whether this is true will depend on one’s view of time and the status of non-real things.

On eternalism, a beginningless series of events in time would involve an actually infinite number of things, for all these moments exist from God’s perspective outside of time. But so would the actually infinite number of future days that God promises us, giving the eternalist reason to reject the idea that an actual infinity cannot exist in the real world.

On presentism, a beginningless series of events in time would not involve an actual infinity of events existing in the real world, because presentism holds that the past does not exist.

Such a series of events might result in an actual infinity of (past) non-existent days, but so would the actual infinity of (future) non-existent days. And if a Christian allows one set of non-existent days, the other must be allowed as well.

The fact that the past days are countable is irrelevant, because so are the future days.

And it is simply false to say that the days that will be are only potentially infinite. They’re not. Right now, the number of days that will be is actually infinite, the same way the set of natural numbers is actually infinite.

Based on what we’ve seen here, presentism does not exclude an infinite past any more than it does an infinite future.

In recent years, one of the most popular arguments for the existence of God has been the Kalaam cosmological argument.

Ultimately, I think this argument is successful, but many of the ways it has been employed are unsuccessful.

It is an argument that needs to be used carefully—with the proper qualifiers.

Stating the Argument

We can state the Kalaam argument like this:

1) Everything that has a beginning has a cause.

2) The universe has a beginning.

3) Therefore, the universe has a cause (which would be God).

Is this argument valid? Is it sound?

Valid arguments are ones that use a correct logical form—regardless of whether their premises are true. The Kalaam argument falls into this category, which is not disputed by its critics.

If a valid argument has true premises, then its conclusion also will be true. Valid arguments that have true premises are called sound arguments, and I agree that the argument’s premises are true:

1) It is true that whatever has a beginning has a cause.

2) And it is true that the universe has a beginning (approximately 13.8 billion years ago, according to Big Bang cosmology).

Since the Kalaam argument is valid and has true premises, it is a sound argument.

Using the Argument Apologetically

The Kalaam argument is sound from the perspective of logic, but how useful is it from the perspective of apologetics? There are many arguments that are sound, but sometimes they are not very useful in practice.

For example, in their famous book Principia Mathematica, Bertrand Russell and Alfred North Whitehead spend the first 360 pages of the book covering basic principles that build up to them rigorously proving that 1 + 1 = 2.

While their book is of interest to mathematicians, and their proof extremely well thought-out, it is so complex that it is not of practical use for a popular audience. For ordinary people, there are much simpler ways to prove that 1 + 1 = 2. (If needed, just put one apple on a table, put another one next to it, and count the apples both individually and together.)

Complexity is not the only thing that can limit an argument’s usefulness. Another is the willingness of people to grant the truth of its premises. Here is where some of the limitations of the Kalaam argument appear. While it is very simple to state and understand, defending the premises is more involved.

The First Premise

The first premise—that everything that has a beginning has a cause—is intuitive and is accepted by most people.

Some object to this premise on philosophical grounds or on scientific ones, such as by pointing to the randomness of quantum physics.

Both the philosophical and the scientific arguments can get technical quickly, but a skilled apologist—at least one who is actually familiar with quantum mechanics (!)—would still be able to navigate such objections without getting too far over the heads of a popular audience.

This—plus the fact that a popular audience’s sympathies will be with the first premise—mean that the argument retains its usefulness with a general audience.

The Second Premise

The second premise—that the universe had a beginning—is also widely accepted today, due in large part to Big Bang cosmology. A popular audience will thus be generally sympathetic to the second premise.

That’s apologetically useful, but we need to look more closely at how the second premise can be supported when challenged.

Since “The Bible says the universe has a beginning” will not be convincing to those who are not already believers, there are two approaches to doing this—the scientific and the philosophical.

The Scientific Approach

For an apologist, the approach here is straight forward: For a popular level audience, simply present a popular-level account of the evidence that has led cosmologists to conclude that the Big Bang occurred.

On this front, the principal danger for the apologist is overselling the evidence in one of several ways.

First, many apologists do not keep up with developments in cosmology, and they may be relying on an outdated account of the Big Bang.

For example, about 40 years ago, it was common to hear cosmologists speak of the Big Bang as an event that involved a singularity—where all matter was compressed into a point of infinite density and when space and time suddenly sprang into existence.

That view is no longer standard in cosmology, and today no apologist should be speaking as if this is what the science shows. Apologists need to be familiar with the current state of cosmological thought (as well as common misunderstandings of the Big Bang) and avoid misrepresenting current cosmological views.

Thus, they should not say that the Big Bang is proof that the universe had an absolute beginning. While the Big Bang is consistent with an absolute beginning, cosmologists have not been able to rule out options like there being a prior universe.

One way apologists have dealt with this concern is to point to the Borde-Guth-Vilenkin (BGV) theorem, which seeks to show that—on certain assumptions—even if there were one or more prior universes, there can’t be an unlimited number of them.

It’s fair to point to this theorem, but it would be a mistake for an apologist to present it as final proof, because the theorem depends on certain assumptions (e.g., that the universe has—on average—been expanding throughout its history) that cannot be taken for granted.

Further, apologists should be aware that authors of the theorem—Alan Guth and Alexander Vilenkin—do not agree that it shows the universe had to have a beginning. Guth apparently believes that the universe does not have a beginning, and Vilenkin states that all the theorem shows is that the expansion of the universe had to have a beginning, not the universe itself.

It thus would misrepresent the BGV theorem as showing that the scientific community has concluded that the universe had to have a beginning, even if it were before the Big Bang. (It also would be apologetically dangerous and foolish to do so, as the facts I’ve just mentioned could be thrown in the apologist’s face, discrediting him before his audience.)

Most fundamentally, the findings of science are always provisional, and the history of science contains innumerable cases where scientific opinion as reversed as new evidence has been found.

Consequently, apologists should never sell Big Bang cosmology—or any other aspect of science—as final “proof.”

This does not mean that apologists can’t appeal to scientific evidence. When the findings of science point in the direction aspects of the Faith, it is entirely fair to point that out. They just must not be oversold.

The Philosophical Approach

Prior to the mid-20^th century, Big Bang cosmology had not been developed, and the scientific approach to defending the Kalaam argument’s second premise was not available.

Consequently, earlier discussions relied on philosophical arguments to try to show that the universe must have a beginning.

Such arguments remain a major part of the discussion today, and new philosophical ways of defending the second premise have been proposed.

Authors have different opinions about how well these work, but in studying them, I find myself agreeing with St. Thomas Aquinas that they do not. Thus far, I have not discovered any philosophical argument—ancient or modern—that I thought proved its case.

This is not to say that they don’t have superficial appeal. They do; otherwise, people wouldn’t propose them.

But when one thinks them through carefully, they all contain hidden flaws that keep them from succeeding—some of which are being discussed in this series.

I thus do not rely on philosophical arguments in my own presentation of the Kalaam argument.

Conclusion

The Kalaam cosmological argument is a valid and sound argument. It does prove that the universe has a cause, which can meaningfully be called God.

As a result, it can be used by apologists, and its simplicity makes it particularly attractive.

I use it myself, such as in my short, popular-level book The Words of Eternal Life.

However, the argument needs to be presented carefully. The scientific evidence we currently have is consistent with and suggestive of the world having a beginning in the finite past, though this evidence must not be oversold.

The philosophical arguments for the universe having a beginning are much more problematic. I do not believe that the ones developed to date work, and so I do not use them.

I thus advise other apologists to think carefully before doing so and to rigorously test these arguments: Seek out counterarguments, carefully consider them, and see if you can show why the arguments don’t work.

It is not enough that we find an argument convenient or initially plausible. We owe it to the truth, and honesty in doing apologetics compels us not to use arguments just because we want them to be true.

God created the universe a finite time ago, but there’s a question of whether we can prove this by reason alone.

Defenders of the Kalaam cosmological argument often claim that the universe cannot have an infinite history because “traversing an infinite” is impossible.

In his book Reasonable Faith (pp. 120-124), William Lane Craig puts the argument this way

1. The series of events in time is a collection formed by adding one member after another

2. A collection formed by adding one member after another cannot be actually infinite

3. Therefore, the series of events in time cannot be actually infinite.

The second premise of this argument is the one that deals with “traversing an infinite.” Craig writes:

Sometimes this problem is described as the impossibility of traversing the infinite.

Still a third way of describing it is saying that you can’t form infinity “by successive addition.”

Whatever expression you prefer, each of these expressions refer to the intuition people commonly have about infinity—that “you can’t get there from here.”

Where Is “Here”?

If you can’t get to infinity from here, where is “here”?

However you want to phrase the problem—getting there from here, traversing an infinite, or successive addition, this is a question that needs to be answered.

Let’s take another look at the second premise:

2. A collection formed by adding one member after another cannot be actually infinite

What does it mean to “form” a collection by adding one member after another?

Perhaps the most natural way to take this would be to form such a collection from nothing. That is, you start with zero elements in the collection (or maybe one element) and then successively add one new member after another.

And it’s quite true that, if you form a collection this way, you will never arrive at an infinite number of members. No matter how many elements you add to the collection, one at a time, the collection will always have a finite number of elements.

This can be seen through a simple counting exercise. If you start with 0 and then keep adding +1, you’ll get the standard number line:

0, 1, 2, 3, 4, 5, 6, 7 . . .

But no matter how many times you add +1, the resulting number will always be finite—just one unit larger than the previous finite number.

However, there is a problem . . .

The First-and-Last Fallacy

As I’ve discussed elsewhere, any string of natural numbers that has both a first and a last element is—by definition—finite.

Any time you specify a first natural number and a last natural number, the space between them is limited.

It thus would be fallacious reasoning to envision an infinite timeline with both first and last elements.

Yet it is very easy to let the idea of an infinite past having a beginning somewhere “infinitely far back” unintentionally sneak back into discussions of the Kalaam argument.

It can easily happen without people being aware of it, and often our language is to blame:

• The natural sense of the word “traverse” suggests going from one point to another, suggesting both a beginning point and an end point.
• So does the idea of “forming” an infinite collection. If we imagine forming a collection, we naturally envision starting with nothing (a collection with no members) and then adding things to it.
• And if we think of getting to infinity “from here,” we naturally think of a starting point in the finite realm (“here”) and an end point (“infinity”).

Without at all meaning to, it’s thus very easy to fall into the trap of subconsciously supposing both a starting point and an ending point in a supposedly infinite history.

This happens often enough that I’ve called it the First-and-Last Fallacy.

Taking No Beginning Seriously

In Reasonable Faith, Craig denies that this is how his argument should be understood. He writes:

Mackie and Sobel object that this sort of argument illicitly presupposes an infinitely distant starting point in the past and then pronounces it impossible to travel from that point to today. But if the past is infinite, they say, then there would be no starting point whatever, not even an infinitely distant one. Nevertheless, from any given point in the past, there is only a finite distance to the present, which is easily “traversed.” But in fact no proponent of the kalam argument of whom I am aware has assumed that there was an infinitely distant starting point in the past. The fact that there is no beginning at all, not even an infinitely distant one, seems only to make the problem worse, not better (boldface added).

Craig thus wishes us to understand his argument not as forming an infinite collection of past historical moments from an infinitely distant starting point—i.e., from a beginning.

It’s good that he is clear on this, because otherwise his second premise would commit the First-and-Last Fallacy.

But does this really make things worse rather than better?

It would seem not.

Formed from What?

If we are not to envision a collection being “formed” from nothing by successive addition, then it must obviously be formed from something. Namely, it must be formed from another, already existing collection.

For example, suppose I have a complete run of my favorite comic book, The Legion of Super-Heroes. Let’s say that, as of the current month, it consists of issue #1 to issue #236.

Then, next month, issue #237 comes out, so I purchase it and add it to my collection. I now have a new, larger collection that was “formed” by adding one new member to my previous collection.

Now let’s apply that to the situation of an infinite history. Suppose that the current moment—“now”—is the last element of an infinite collection of previous moments (with no beginning moment).

How was this collection formed?

Obviously, it was formed from a previous collection that included all of the past moments except the current one.

Let’s give these things some names:

• Let P be the collection of all the past moments
• Let 1 represent the current moment
• And let E represent the collection of all the moments that have ever existed

With those terms in place, it’s clear that:

P + 1 = E

We thus can form one collection (E) from another collection (P) by adding a member to it.

But Can It Be Infinite?

Now we come to Craig’s second premise, which said that you can’t form an actually infinite collection by adding one member after another.

If you imagine forming the collection from nothing—and thus commit the First-and-Last Fallacy—then this is true.

But it’s not true if you avoid the fallacy and imagine forming an actually infinite collection from a previous collection by adding to it.

The previous collection just needs to be actually infinite as well. If P is an actually infinite collection and you add 1 to it, E will be actually infinite as well.

And this is what we find in the case of an infinite past. Let us envision an infinite past as the set of all negative numbers, ending in the present, “0” moment:

. . . -7, -6, -5, -4, -3, -2, -1, 0.

The set of all the numbers below 0 is infinite, but so is the set of all numbers below -1, all the numbers below -2, and so on. Each of these collections is actually infinite, and so we can form a new, actually infinite set by taking one of them and adding a new member to it.

Understood this way, Craig’s second premise is simply false. You can form an actually infinite collection by adding new members to an actually infinite collection—which is what we would have in the case of a universe with an infinite past, one that really does not have a starting point.

Conclusion

What we make of Craig’s argument will depend on how we take its second premise.

Taken in what may be the most natural way (forming an infinite collection from nothing—or from any finite amount—by successive addition), will result in the argument committing the First-and-Last Fallacy.

But if we take it in the less obvious way (forming an infinite collection by adding to an already infinite collection), then the second premise is simply false.

There may be other grounds—other arguments—by which one might try to show that the universe cannot have an infinite past.

But the argument from “successive addition,” “traversing an infinite,” or “getting there from here” does not work.

Depending on how you interpret it, the argument either commits a fallacy or uses a false premise.

Sometimes defenders of the Kalaam cosmological argument defend its second premise (i.e., that the world couldn’t have an infinite past) by proposing a paradox involving counting.

The line of reasoning goes something like this:

A. Suppose that the universe has an infinite history (the kind of history you’d need to do an infinite countdown).

B. Suppose that a person has been counting down the infinite set of negative numbers (. . . -3, -2, -1) for all eternity, and they finish today, so today’s number is 0. It took them an infinite amount of time to reach 0 in the present.

C. Now suppose that we go back in time to yesterday. How much time was there before yesterday? Also an infinite amount of time! Given that, they could have counted down the infinite set of negative numbers so that they reached 0 yesterday instead of today!

D. So, we have a paradox: If the person had been counting down the negative numbers for all eternity, they could have finished today—or yesterday—or on any other day in the past, since there was always an infinite number of days before that.

E. There needs to be a sufficient reason why they stop on the day they did.

The Kalaam defender then challenges the Kalaam skeptic to name the sufficient reason, and if he’s not convinced by the answer, he rejects Step A of the argument—the idea that the universe has an infinite history—since there doesn’t seem to be anything wrong with Steps B, C, D, or E.

What’s problematic about this line of reasoning?

Arbitrary Labels

To see what the answer is, we need to think about the arbitrariness of the labels involved in the countdown.

In Part B, the Kalaam defender chose to use the set of negative numbers, but he could have chosen something else.

For example, he could have chosen the digits of the irrational number pi (3.14159 . . . ) in reverse order (. . . 9, 5, 1, 4, 1, 3), in which case today’s number would be 3.

Or he could have used the Golden Ratio and chosen the digits of the irrational number phi (1.61803 . . . ) and reversed them, in which case today’s number would be 1.

Or he could have picked anything else, such as an infinitely long string of random numbers—or random words—or random symbols.

Any string will do for an infinite count of the past—as long as it’s an infinitely long string.

The point we learn from this is that the labels we apply to particular days are arbitrary. It depends entirely on what labels we choose. We can pick any labels we want and use them for any set of days we want.

Forward Counts

To underscore this point, let’s consider counts that go forward in time rather than backwards.

For example, we could choose the set of natural numbers (0, 1, 2, 3 . . . ), assigning 0 to today, 1 to tomorrow, 2 to the day after that, and so on.

Or we could use the digits of pi, in which case today would be 3, tomorrow 1, the day after that 4, etc.

Or the digits of phi, so today would be 1, tomorrow 6, the day after that 1, etc.

Or we could use something else—such as an infinite string of random numbers, words, or symbols.

We can pick whatever labels for a set of days, beginning with today, that we want!

A Count-Up Paradox

Now consider the following line of reasoning:

A*. Suppose that the universe has an infinite future (the kind of future you’d need to do an infinite count going forwards).

B*. Suppose that a person starts counting the infinite set of natural numbers (0, 1, 2, 3 . . . ) today, so that today’s number is 0, tomorrow’s is 1, the next day is 2, etc.

C*. Now suppose that we go forward in time to tomorrow. How much time is there left in the future of the universe? Also an infinite amount of time! Given that, the person could start their count of the infinite set of whole numbers so that they begin with 0 tomorrow instead of today!

D*. So, we have a paradox: If the person counts the set of whole numbers for all eternity, they could have started today—or tomorrow—or on any other day in the future, since there will always be an infinite number of days after that.

E*. There needs to be a sufficient reason why they start on the day they do.

If we’re challenged to name the sufficient reason why the person starts counting on the day they do, what will our answer be?

Mine would be, “Because that’s how you set up the thought experiment! You made this determination in Step B*. You could have chosen to start the count on any day you wanted (today, tomorrow, yesterday—or any other day), and you chose the set of numbers that would be used to label these days. Your choices are the sufficient reason for why the count starts and why it labels the days the way it does.”

Turn About Is Fair Play

And this is the answer to the original line of reasoning we presented. The same logic is present in A-E that is present in A*-E*, so the answer is the same.

The reason that the original countdown stopped today, which was labelled 0, is because those were the choices made in Step B. The person setting up the thought experiment chose that the countdown stop today, and he chose that it would stop with 0.

Once again, it is the choices that the person made that determine when the count stops and what it stops on.

There is only a “paradox” here if you lose sight of the fact that these choices were made and demand a sufficient reason over and above them.

To say—in the first case—“I know I made these choices in Step B, but I want a reason over and above that to explain why the countdown doesn’t stop on another day” is the same as saying—in the second case—“I know I made these choices in Step B*, but I want a reason over and above that to explain why the count doesn’t start on another day.”

No such reasons are needed. The choices made in Step B are sufficient to explain why the countdown works the way it does, just as the choices made in Step B* are sufficient to explain why the count-up works the way it does.

So, like a lot of paradoxes, the “countdown paradox” has a perfectly obvious solution once you think about it.

God as the Decider

Now let’s apply this to the question of whether God could have created the universe with an infinite past. In this case, we’re doing a thought experiment where God is the one making the choices.

A**. Suppose that God creates a universe with an infinite past (the kind you need for an infinite countdown).

B**. Suppose that–within this timeline–God creates a person (or angel, or computer, or whatever) that counts down the negative numbers so that he finishes today, and today’s number is 0.

Why didn’t the person stop counting on some other day or with some other number? Because that’s not what God chose. He chose to have it happen this way, with the person counting the number -2 two days ago, the number -1 one day ago, and the number 0 today.

Could he have have done it differently? Absolutely! God could have made different choices!

In fact–to go beyond what we’ve stated thus far–God may have created other people doing just that.

C**. Suppose that God also created a second person who has been counting for all eternity such that he ended yesterday with the number 0.

D**. Suppose that God further created a third person who has been counting for all eternity such that he ended two days ago with the number 0.

These are also possible, and we can modify our thought experiment such that God creates any number of people we like, finishing an infinite count on any day we like, with any number (or word or symbol) we like.

In each case, it is God’s choice that is the sufficient reason why the person finished when he did and with what he did.

The situation is parallel to the following:

A***. Suppose that God creates a universe with an infinite future (the kind you need to do an infinite count going forward).

B***. Suppose that–within this timeline–God creates a person who starts an infinite count today, beginning with the number 0.

As before, we can include any number of counters we want:

C***. Suppose that God also creates a second person who begins counting tomorrow, starting with the number 0.

D***. Suppose that God further creates a third person who begins counting the day after tomorrow, starting with the number 0.

As before, we can modify our thought experiment to include any number of counters we want, they can start on any day we want, and they can start with whatever number (or word or symbol) that we want.

Yet in these scenarios, it is God’s choices that determine who is created, when they start counting, and how the count works. These choices are the only reasons we need to explain what is happening.

If there is no unsolvable paradox preventing the scenarios described in A***-D***, then there is no unsolvable paradox preventing the scenarios described in A**-D**–or in any of the previous scenarios we’ve covered.

There just is no problem with the idea of a person doing an infinite countdown ending today–any more than there is with the idea of a person beginning an infinite countdown today.

Do they?

Before we began, I want to lay my cards on the table and say that I’m a fan of Sabine Hossenfelder. She’s smart, well qualified, and a research fellow at the Frankfurt Institute for Advanced Studies.

I appreciate her commitment to explaining physics in comprehensible terms and her willingness to challenge ideas that are fashionable in the physics community but that are not well supported by evidence.

She also doesn’t reject religious claims out of hand—as many do. Instead, she typically concludes that they are beyond what science can tell us, one way or the other.

A Finely Tuned Universe?

In her recent video, she notes that many people argue that the laws of physics that govern our universe seem finely tuned to allow life to exist. Even slight changes in the constants they involve would prevent life from ever arising.

An example she cites is that if the cosmological constant (i.e., the energy density of space) were too large, galaxies would never form.

Similarly, if the electromagnetic force was too strong, nuclear fusion would not light up stars.

Given all the values we can imagine these constants having, it seems unlikely that the laws that govern our universe would be finely tuned to allow life to exist just by random chance, so the question is how to explain this.

God or the Multiverse?

One proposed explanation is that the universe isn’t finely tuned by chance. It’s finely tuned by design.

Some entity with immense, universe-spanning power (i.e., God) designed the universe to be this way, and in religious circles, this type of argument is known as a “design argument” for God’s existence.

Another proposed explanation is that our universe is finely tuned for life by chance. But since it would be improbable to get a finely tuned universe with a single throw of the dice, it’s inferred that there must be other throws of the dice.

In other words, our universe is just one of countless universes that contain other laws and constants, and we just happen to be living in a universe where the things happen to come up right for life to exist.

(After all, we wouldn’t be here if they didn’t.)

Such a collection of universes is known as a multiverse.

God and the Multiverse?

From a religious perspective, the multiverse hypothesis can look like an attempt to get around the obvious implication of the universe’s apparent design—i.e., that it has a Designer.

However, that doesn’t mean that the multiverse doesn’t exist. If he chose, God could create a vast array of universes, each of which have different laws, and not all of them may contain life. (After all, most of our own universe does not contain life!)

Similarly, from the perspective of someone who believes in the multiverse, multiple universes wouldn’t rule out the existence of God, because you could still need a God to explain why the multiverse exists at all.

The God hypothesis and the multiverse hypothesis thus are not incompatible.

Both Are Possibilities

Dr. Hossenfelder acknowledges that both God and the multiverse could be real, but she says—correctly—that this would not add to our knowledge of how our universe works.

If God exists, that doesn’t tell us what the laws of our universe are. We still have to discover those by observation.

And if the multiverse exists, that also doesn’t tell us about the laws of our universe. Observation is still necessary to figure them out.

Circular Reasoning?

Her claim is that the fine-tuning arguments for both God and the multiverse don’t work—and, specifically, that they involve circular reasoning.

She fleshes out this claim along the following lines:

1. To infer God, the multiverse, or anything else as the cause for why our universe seems finely tuned, you need evidence that our universe’s combination of constants is unlikely.
2. However, the only evidence we have is what we have measured, and—precisely because the constants are constant—we always see them having the same values.
3. Therefore, we have no evidence that the combination we see is unlikely.
4. So, advocates of these views must assume what they need to prove—that the combination is unlikely—and that’s circular reasoning.

The Pen Objection

Dr. Hossenfelder seeks to head off an objection to her argument by pointing to a parallel case: Suppose you saw an ink pen standing upright on a table, balanced on its point.

It seems very unlikely that a pen would be balanced in this way, and so you’d suspect there was a reason why the pen was standing like this—perhaps a special mechanism of some sort.

But, she says, the reason that we can rationally suspect this is because we have experience with pens and know how hard it is to balance them this way.

Therefore, it would not be circular reasoning to propose an explanation for the oddly balanced pen.

However, the only experience we have with the constants of nature is the set we see. We thus can’t estimate how likely or unlikely they are to occur, because we don’t have evidence about the probability of this combination of constants.

What Do You Mean by “Evidence”?

The problem with Dr. Hossenfelder’s argument is the way she uses the term “evidence.”

In the video, she seems to assume that “evidence” must mean empirical evidence—that is, evidence derived from observation using the physical senses (and their technological extensions, like radio telescopes and electron microscopes).

This is the kind of evidence used in the natural sciences, and so you also could call it “scientific evidence.”

However, this is not the only kind of evidence there is.

Fields like logic, mathematics, and ethics depend on principles—sometimes called axioms—that cannot be proved by observation.

The evidence we have for them comes in the form of intuitions, because they seem either self-evidently true or self-evidently probable to us.

Since each of these fields is part of or closely connected with philosophy, we might refer to this intuitive evidence as “philosophical evidence.”

Whatever you want to call it, it’s evidence that we depend on—certainly in every field that involves logic, mathematics, and ethics.

Science involves all three, and so, while the scientific enterprise depends on observational evidence, it also depends on intuitive, philosophical evidence.

Do We Lack Observational Evidence?

It’s true that we can’t observe other universes, and so we lack observational evidence of the laws and constants that might be at play in them.

But does this mean that we lack any observational evidence that constants could have different values?

Confining ourselves strictly to our own universe—the only one we can observe—we see that not all constants have the same value. For example:

• The strong coupling constant is about 1
• The fine-structure constant is about 1/137
• The top quark mass is about 1/10^17
• The bottom quark mass is about 3/10^19
• The electron mass is about 4/10^23

Clearly, we see things that we regard as constants with different values, even in our own universe. The constants I’ve just listed span 23 orders of magnitude!

Why do all these dimensionless constants have different values?

That’s a natural question to ask!

And so, one could argue that we do have observational evidence that constants can have different values—not from universe to universe but from constant to constant—and that leaves many people asking why.

Variable Constants

Further, we even have evidence that some of these constants may vary over time.

In particular, we have evidence that the fine-structure constant—which deals with the strength of the electromagnetic interactions—may have varied slightly over time within our universe.

Dr. Hossenfelder says in her video that this “has nothing to do with the fine-tuning arguments,” but this seems false.

If we have evidence that some things scientists initially took as constants aren’t constant after all, then it further raises the question of why they have the values they do.

The Evidence of Intuition

I’m not at all convinced that we don’t have observational evidence that invites us to ask why the constants we see in our universe have the values they do.

However, even if I were to waive this point, we still have one other line of evidence: direct intuition.

People who study the constants can imagine them having different values. We can, for example, imagine the electron mass being twice—or half—what its measured value is.

That makes it rational to ask why a constant has the value it does. As theoretical physicist and Nobel laureate Richard Feynman famously said about the fine-structure constant:

It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)

Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed His pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out – without putting it in secretly!

In Search of Explanations

Finding out the explanations for things is a key part of the scientific enterprise. The same is true of the philosophical enterprise.

We have a powerful (philosophical) intuition that things we encounter have explanations, and thus we seek them.

In philosophy, this intuition is sometimes framed as the Principle of Sufficient Reason, and while precisely how to formulate the principle is controversial, some kind of sufficient-reason quest is behind the scientific enterprise.

It would not do at all—and it would not be scientific at all—to encounter phenomena like stars shining, plants growing, and objects falling and say, “Those are just brute facts that don’t have explanations.”

Our intuition tells us that they need explanations, and it is the task of science to find them—to the extent it can—based on observation of how they work.

When we discern that many of these phenomena can be explained in terms of a set of underlying laws and constants, it’s then natural to ask what the explanation for these is—particularly when we notice that if these things were even slightly different, we wouldn’t be here.

The Limits of Science

Ultimately, Dr. Hossenfelder doesn’t deny that explanations for these things exist. She specifically says:

But this does not mean god or the multiverse do not exist. It just means that evidence cannot tell us whether they do or do not exist. It means, god and the multiverse are not scientific ideas.

The problem with this is how she’s using the word “evidence.” She’s taking it to mean empirical/observational/scientific evidence.

And it’s true that, at least in any conventional sense, you can’t do a laboratory experiment that shows that God exists—or a laboratory experiment that shows the multiverse exists.

Consequently, both ideas are beyond what can be proved scientifically.

But that doesn’t mean you can’t argue for them on other grounds. You can, in fact, argue for them based on your intuitions about what needs to be true in order to explain the constants as we see them.

This makes God and the multiverse subjects of philosophical argumentation rather than scientific demonstration.

Not Circular Reasoning

And that means that the charge of circular reasoning is false.

It would be circular reasoning to simply assume that it’s improbable the values of the constants we see in our universe should have the values they do.

But it’s not circular reasoning to say, “I have a strong intuition that this calls for an explanation” and then reason your way to what you think best explains it—even if that explanation lies beyond what’s scientifically measurable.

In other words, just because you’re doing something beyond science, it doesn’t mean that you’re simply begging the question.

The Return of the Pen

Let’s apply this insight to the ink pen example that Dr. Hossenfelder brought up.

Even if I’d never before seen a pen–or any similar object–it would make sense, when I first encountered one, for me to ask why it is the way it is.

Just like scientists and philosophers ask this for anything else they encounter.

I don’t need to know how likely or unlikely it is that an ink pen would be balanced on its point. The fact I can conceive of it being otherwise makes the question of why it’s standing rational.

Just asking the question is not begging the question.

And neither is having an intuition that it’s unlikely to be standing on its point (or in any other position) without an explanation.

Tying up Loose Ends

To keep things simple, I haven’t responded to everything Dr. Hossenfelder says in her video, since I wanted to keep things focused on her main argument.

However, I would like to circle back to the God hypothesis and the multiverse hypothesis as explanations for the apparent fine-tuning of our universe.

Personally, I like the idea of there being multiple universes—not for scientific or philosophical reasons, but just because I think it would be cool.

I’d also be fine with them having different laws and constants governing them. That would only add to the coolness.

But—speaking philosophically—there would still need to be a reason why the whole collection of them exist and why the laws that govern them vary from one to another.

Elsewhere, I’ve written about this as a “cosmic slot machine”:

If there is a multiverse with every possible combination of natural laws in the universes it contains . . . what is driving the change of laws in each universe? If there is a cosmic slot machine, whose innards cause the constants to come up different in each universe, why is that the case?

To explain the existence of such a cosmic slot machine, we’d need to appeal to something beyond the multiverse itself.

And so, whether or not there is a multiverse, I favor the God hypothesis.

Atheist scholar Bart Ehrman is a smart guy, but he sometimes handles his sources in the most frustrating and misleading manner.

For example, in his 2012 book Did Jesus Exist?: The Historical Argument for Jesus of Nazareth (where he is on the right side for once), he writes:

Several significant studies of literacy have appeared in recent years showing just how low literacy rates were in antiquity.
 
The most frequently cited study is by Columbia professor William Harris in a book titled Ancient Literacy (footnote 6).
 
By thoroughly examining all the surviving evidence, Harris draws the compelling though surprising conclusion that in the very best of times in the ancient world, only about 10 percent of the population could read at all and possibly copy out writing on a page.
 
Far fewer than this, of course, could compose a sentence, let alone a story, let alone an entire book.
 
And who were the people in this 10 percent?
 
They were the upper-class elite who had the time, money, and leisure to afford an education.
 
This is not an apt description of Jesus’s disciples. They were not upper-crust aristocrats.
 
In Roman Palestine the situation was even bleaker.
 
The most thorough examination of literacy in Palestine is by a professor of Jewish studies at the University of London, Catherine Hezser, who shows that in the days of Jesus probably only 3 percent of Jews in Palestine were literate (footnote 7).
 
Once again, these would be the people who could read and maybe write their names and copy words. Far fewer could compose sentences, paragraphs, chapters, and books.
 
And once again, these would have been the urban elites (Did Jesus Exist?: The Historical Argument for Jesus of Nazareth, 47-48).

The issue here is not the level of literacy in the ancient world or in Roman Palestine—it was, from the evidence we have, startlingly low.

The issue is the claim he makes about  Catherine Hezser.

It’s true that she published a very thorough examination of literacy in Palestine (i.e., her book Jewish Literacy in Roman Palestine).

But did she “[show] that in the days of Jesus probably only 3 percent of Jews in Palestine were literate,” where literacy is defined as the very limited ability to “read and maybe write their names and copy words”?

It would be nice to look up what Hezser said on the matter, but when you look at Ehrman’s footnote, all you find is this:

7. Catherine Hezser, Jewish Literacy in Roman Palestine (Tübingen: Mohr Siebeck, 2001).

No page number. No chapter number. Just a gesture at the whole book.

Okay, well, if you look in Hezser’s book, there is a chapter called “Degrees and Distribution of Literacy,” which is also the very last chapter in the book.

That’s exactly the kind of chapter that would present her final conclusions regarding the degree of literacy among Jews in Roman Palestine.

And, indeed, when we turn to the beginning of that chapter, we find Hezser writing:

Although the exact literacy rate amongst ancient Jews cannot be determined, Meir Bar-Ilan’s suggestion that the Jewish literacy rate must have been lower than the literacy rate amongst Romans in the first centuries C.E. seems very plausible.
 
Whether the average literacy rate amongst Palestinian Jews was only 3 percent, as Bar-Ilan has reckoned,(footnote 1) or slightly higher, must ultimately remain open.
 
The question naturally depends on what one understands by “literacy.” If “literacy is determined as the ability to read documents, letters and “simple” literary texts in at least one language and to write more than one’s signature itself, it is quite reasonable to assume that the Jewish literacy rate was well below the 10-15 percent (of the entire population, including women) which Harris has estimated for Roman society in imperial times.(footnote 2)
 
If by “literacy” we mean the ability to read a few words and sentences and to write one’s own signature only, Jews probably came closer to the Roman average rate.
 
Whereas exact numbers can neither be verified nor falsified and are therefore of little historical value, for the following reasons the average Jewish literacy rate (of whatever degree) must be considered to have been lower than the average Roman rate (Jewish Literacy in Roman Palestine, 496).

Gah!

You see the multiple ways Ehrman has misrepresented Hezser:

• Whereas Ehrman said she “shows that in the days of Jesus probably only 3 percent of Jews in Palestine were literate,” but what she actually says is that “the exact literacy rate amongst ancient Jews cannot be determined,” that the question “must ultimately remain open,” and that “exact numbers can neither be verified nor falsified and are therefore of little historical value”!
• Ehrman presents the 3 percent figure as representing Hezser’s own findings (she “shows” it as a result of her study), but she indicates that the figure isn’t hers and that she got the figure from Meir Bar-Ilan.
• Her own conclusion is that the figure might be 3 percent “or slightly higher” but is unknowable.
• Finally, whereas Ehrman said the 3 percent figure represented only limited literacy—the ability to read and write your name and maybe copy words—Hezser indicates that the 3 percent represented a broader form of literacy, with “the ability to read documents, letters and ‘simple’ literary texts.”
• By contrast, Hezser says that if only low-level literacy is meant (“the ability to read a few words and sentences and to write one’s own signature only”) then—contra Ehrman—the number was higher and “Jews probably came closer to the Roman average rate” of 10-15 percent!

So Ehrman has completely botched this source and misrepresented what Hezser said.

Why?

Presumably because at some point in the past he encountered the 3 percent reference in her book and it stuck in his mind. That’s about all he remembered, though.

When it came time to write his own book, he didn’t look up the reference in Hezser (thus explaining the absence of a page number) and mentally reconstructed what he thought she had said.

If he was being more careful, Ehrman would have looked up what Hezser wrote and either represented her accurately and/or (even better) looked up Bar-Ilan’s paper and gone directly to the source of the estimate.

I don’t want to be too hard on Ehrman, because anybody can botch a source (and everybody does from time to time—and precisely because of fuzzy memories), but this is not the only time I’ve found Ehrman misrepresenting verifiable facts—something we may look at further in future posts.

By the way, Hezser does give a specific citation to Bar-Ilan’s estimate of ancient Jewish literacy.

His paper is online here if you care to read it.

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In the meantime, what do you think?
 
 
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What year was Jesus born? The answer may surprise you.

You might think that Jesus was born in the Year Zero–between 1 B.C. and A.D. 1. You often hear that Jesus was born around 6-7 B.C. The evidence from the Bible and the Church Fathers, however, support a different year.

Here’s what the evidence says . . .

Not in Year Zero

There is a good reason why Jesus wasn’t born in Year Zero: there wasn’t one. The sequence of years before Christ ends at 1 B.C. and the A.D. series picks up the very next year with A.D. 1. This is a bit surprising to us, since we’re used to working with number lines that have a zero on them, but zero wasn’t a concept on the intellectual scene when our way of reckoning years was developed.

If it helps, you can think about it this way: suppose you have a child and you want to date events relative to that child’s birth. The first year before the child was born would be 1 B.C. (Before the Child), and the first year after his birth (that is, the year ending with his first birthday) would be the first year of the child. If the child happens to be the Lord, that would be the first year of the Lord, which in Latin is Anno Domini, from which we get A.D. Thus there is no Year Zero between 1 B.C. and A.D. 1.

(By the way, please note that the “A.D.” goes before the number. “A.D. 2013″ = “The Year of the Lord 2013,” which is an intelligible phrase. If you write “2013 A.D.” that would be “2013 the Year of the Lord,” which is gibberish.)

So what year was Jesus born?

1 B.C.?

The guy who developed the way we reckon years was a 6th-century monk named Dionysius Exiguus (“Dennis the Short”). He apparently thought Christ was born in 1 B.C. (actually, it’s a bit more complex than that, but we’ll keep this simple).

Today most think this date is a little too late and that the evidence supports a date a few years earlier.

6-7 B.C.?

For a little more than a century, the idea has been popular that Jesus was born in 6-7 B.C. The reasoning goes like this: Jesus was born late in the reign of Herod the Great, who died in 4 B.C. Furthermore, the wise men saw the star rise in the east two years before they came to visit Jerusalem, where they met Herod. Back up two years from 4 B.C. and you get 6 B.C. Back up another year in case Herod didn’t die immediately after they visited, and you get 7 B.C.

So: 6 or 7 B.C.

The problem, as we saw in a previous post, is that the arguments that Herod died in 4 B.C. are exceptionally weak.

3-4 B.C.?

Let’s take the same logic as above and plug in the more likely date of Herod’s death.

As we saw in a previous post, the evidence points to him dying in 1 B.C. So . . . back up two years from that and you get 3 B.C. Back up another year for cushion and you get 4 B.C.

Thus: 3-4 B.C.

That’s not an unreasonable estimate, but there are two issues with it:

1. It’s got a couple of problematic assumptions.
2. Other evidence, including other evidence from the Bible, suggests it’s a little too early.

The problematic assumptions are that the star was first visible in the east at the moment of Jesus’ birth and that it was visible for a full two years prior to the magi’s arrival.

The first of these assumptions is problematic (among other reasons) because its appearance could be connected with another point in Jesus’ life, such as his conception. If that were the case, you’d need to shave nine months off to find the point of his birth. It’s also problematic because Matthew doesn’t say that the star appeared two years earlier. What he says is that Herod killed all the baby boys in Bethlehem that were two years old and under, in accord with the time he learned from the magi. That means that there is some approximating going on here.

Herod would certainly want to make sure the child was dead, and he would err on the side of . . . well, the side of caution from his perspective. That is, he would to some degree over-estimate how old the child might be in order to be sure of wiping him out. Thus all the boys two and under were killed. That means Jesus was at most two years old, but he was likely younger than that.

What may well have happened is Herod may have been told that the star appeared a year ago and he decided to kill all the boys a year on either side of this to make sure of getting the right one.

And then there’s the fact that the ancients often counted parts of a year as a full year in their reckoning, so “two years” might mean “one year plus part of a second year.”

All this suggests that two years was the maximum amount of time earlier that Jesus was born, and likely it was less than that.

Thus . . .

2-3 B.C.?

This date would be indicated if we start with Herod’s death in 1 B.C. and then, taking into account the factors named above, backed up only one year, suggesting 2 B.C. Then, if we back up another year to allow for the fact Herod didn’t die immediately, that would suggest 3 B.C. So, sometime between 2-3 B.C. would be reasonable, based on what we read in Matthew.

Do we have other evidence suggesting this date?

We do, both inside and outside the Bible.

The Gospel of Luke

Although Luke offers some helpful clues about the timing of Jesus’ birth, we don’t know enough to make full use of them. The date of the enrollment ordered by Augustus is notoriously controversial, for example, and too complex to go into here. However, later indications he gives in his gospel are quite interesting.

He records, for example, that John the Baptist began his ministry in “the fifteenth year of Tiberius Caesar” (3:1). Tiberius became emperor after Augustus died in August of A.D. 14. Roman historians (e.g., Tacitus, Suetonius), however, tended to skip part years and begin counting an emperor’s reign with the first January 1 after they took office. On that reckoning, the fifteenth year of Tiberius Caesar would correspond to what we call A.D. 29. (Remember, the 15th year is the time between the completion of the 14th year and the completion of the 15th year, the same way a child’s first year is the time between his birth and his first birthday.)

Jesus’ ministry starts somewhat after John’s, but it doesn’t appear to be very long. Perhaps only a few weeks or months. If so, Jesus’ ministry also likely started in A.D. 29.

That’s important, because Luke gives us a second clue: He says Jesus was “about thirty years of age” when he began his ministry (Lk 3:23). So, if you take A.D. 29 and back up thirty years, when does that land you? You might think in 1 B.C., but remember that there’s no Year Zero, so it would actually be 2 B.C. or the end of 3 B.C. if Luke was counting Tiberius’s reign from when he became emperor rather than from the next January 1.

Thus: 2-3 B.C. is a reasonable estimate.

That’s still only an estimate, though, because Jesus could have been a little less or a little more than thirty.

(For purposes of comparison, note that when Luke describes the age of Jairus’s daughter, he says she was “about twelve” (Lk 8:42). So Luke doesn’t seem to go in for rounding things to the nearest 5 years; he tries to be more precise than that. When Luke says Jesus was “about thirty,” he’s probably not envisioning anything between 25 and 35 but a range narrower than that.)

To confirm our estimate, it would be nice if we had an exact naming of the year Jesus was born, and in fact we do . . .

The Fathers Know Best

There is a startling consensus among early Christian sources about the year of Jesus’ birth.

Here is a table adapted from Jack Finegan’s excellent Handbook of Biblical Chronology (p. 291) giving the dates proposed by different sources:

 
As you can see, except for a few outliers (including our influential friend, Dionysius Exiguus), there is strong support for Jesus being born in either 3 or 2 B.C.

Note that some of the sources in this table are quite ancient. Irenaeus of Lyon, Clement of Alexandria, Tertullian, Julius Africanus, and Hippolytus of Rome all wrote in the late 100s or early 200s.

We thus have strong indication–from a careful reading of Matthew, from Luke, and from the Church Fathers–that Jesus was born in 3 or 2 B.C.
 
 
 
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Originally posted at JimmyAkin.com. Used with permission.

The Gospel of Matthew tells us that Jesus Christ was born in the final years of the tyrant known as Herod the Great. He tells us that when Jesus was born, Herod panicked and had all the baby boys in Bethlehem killed. Fortunately, the Jesus' family escaped to Egypt and remained there until Herod was dead.

They didn't have to stay long, though. Here's when Herod the Great actually died . . .
 

Setting Aside a Common Mistake

 
For just over a hundred years, the question of when Herod the Great died has been dominated by a proposal by the German scholar Emil Schurer. He suggested that Herod died in 4 B.C., and this view took off in scholarly circles. But in recent decades, it's been challenged and, as we saw in a previous post, the arguments for this position are exceptionally weak.

So when did Herod actually die?
 

The Length of Herod's Reign

 
Here is how the Jewish historian Josephus describes the timing of Herod's death:

"So Herod, having survived the slaughter of his son [Antipater] five days, died, having reigned thirty-four years, since he had caused Antigonus to be slain, and obtained his kingdom; but thirty-seven years since he had been made king by the Romans."  [War of the Jews, 1:33:8 (665); cf. Antiquities of the Jews 17:8:1 (191)]

In this place, Josephus dates Herod's death by three events:

1. Five days after the execution of his son Antipater.
2. Thirty-four years after he "obtained his kingdom" (i.e., conquered Jerusalem and had its Hasmonean king, Antigonus, killed).
3. Thirty-seven years after "he had been made king by the Romans."

The death of Antipater isn't a particularly helpful clue, but the two ways of reckoning the length of his reign are.

First, though, we need to answer one question . . .
 

How Is Josephus Counting Years?

 
Kings don't tend to come into office on New Year's Day, and so they often serve a partial year before the next calendar year begins (regardless of which calendar is used). They also don't die on the last day of the year, typically, so they also serve a partial year at the end of their reigns. This creates complications for historians, because ancient authors sometimes count these additional part-years (especially the one at the beginning of the reign) as a full year. Or they ignore the calendar year and treat the time that a king came into office as a kind of birthday and reckon his reign in years from that point.

What scheme was Josephus using?

Advocates of the idea that Herod died in 4 B.C. argue that he was named king in 40 B.C. To square that with a 37-year reign ending in 4. B.C., they must count the part year at the beginning of his reign and the part year at the end of it as years. That's the only way the math will work out.

The problem is that this is not how Josephus would have reckoned the years. Biblical chronology scholar Andrew E. Steinmann comments:

"[T]here is no evidence for this [inclusive way of reckoning the partial years]--and every other reign in this period, including those of the Jewish high priests, are reckoned non-inclusively by Josephus." (From Abraham to Paul, 223)

In other words, Josephus does not count the partial first year when dating reigns in this period.

Knowing that, what would we make of Josephus's two ways of dating Herod's reign?
 

Herod Appointed King

 
As we saw in the previous post, Josephus gave an impossible date (one that did not exist) for Herod's appointment as king. He said it was in the 184th Olympiad, which ended in midyear 40 B.C. and that it was in the consulship of Calvinus and Pollio, which began in late 40 and extended into 39. Those can't both be right, but one of them could be.

Which one? The evidence points to 39 B.C., because we have another source on this: the Roman historians Appian and Dio Cassius. Appian wrote a history of the Roman civil wars in which he discusses the appointment of Herod in the midst of other events. By comparing this set of events to how they are dated in Dio Cassius's Roman History, it can be shown that the events in question--including the appointment of Herod--took place in 39 B.C.

Given how Josephus dates reigns in this period, he would not have counted Herod's partial first year in 39 B.C. but would have started his count with 38 B.C.

Count 37 years forward from that and you have 1 B.C.
 

Herod Conquers Jerusalem

 
As we saw in the previous post, Josephus gives contradictory dating information for Herod's conquest of Jerusalem. Some of the dating information he provides points to 37 B.C. and some points to 36 B.C. Josephus said Herod died 34 years after the event.

Bearing in mind that Josephus wasn't counting partial first years, that would put Herod's death either in 2 B.C. (if he conquered Jerusalem in 37) or in 1 B.C. (if he conquered the city in 36).

There are various ways to try to resolve which, but some are rather complex.

At least one, however, is quite straightforward . . .
 

Herod's Lunar Eclipse

 
We saw in the previous post that Josephus said Herod died between a lunar eclipse and Passover. While there was a partial lunar eclipsed before Passover in 4 B.C. there was a total lunar eclipse before Passover in 1 B.C. Further, the lunar eclipse in 1 B.C. better fits the situation Josephus describes (see the previous post for details).

Since 4 B.C. is outside the range indicated above, and since the 1 B.C. lunar eclipse fits the situation better, that lets us decide between 2 B.C. and 1 B.C. in favor of the latter. There was no lunar eclipse in 2 B.C., pointing us toward 1 B.C.
 

Final Answer?

 
Putting together the pieces above, we have:

• Reason to think Herod died in 1 B.C. based on the amount of time he served after being appointed king by the Romans.
• Reason to think Herod died in either 2 or 1 B.C. based on the amount of time he served after conquering Jerusalem.
• Reason to think Herod died in 1 B.C. because of the lunar eclipse that occurred before Passover.

More specifically, he would have died between January 10, 1 B.C. (the date of the lunar eclipse) and April 11, 1 B.C. (the date of Passover).

Most likely, it was closer to the latter date, since Josephus records a bunch of things Herod did after the eclipse and before his death, some of which required significant travel time.

There is also one more reason that we should reject the death of Herod in 4 B.C. in favor of a 1 B.C. date . . .
 

We Know When Jesus Was Born

 
We don't have to restrict our knowledge of when Herod died to the sources and events mentioned above. We can also date his death relative to the birth of Christ. For some reason, moderns seem to think that the dating of Herod's death should govern when Jesus was born, but the logic works both ways: if we know when Jesus was born, that tells us something about when Herod died.

And we, in fact, have quite good information about the year in which Jesus was born.

It was after 4 B.C., ruling out that date.

So . . . what year was Jesus born?

Stay tuned for my post tomorrow on Christmas Day. . . 
 
 
 
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Originally posted at National Catholic Register. Used with permission.

St. Luke begins the second chapter of his Gospel with a chronological note about when Jesus was born, writing:

"In those days a decree went out from Caesar Augustus that all the world should be enrolled. This was the first enrollment, when Quirinius was governor of Syria." (Luke 2:1-2)

This passage has been subject to a lot of criticism, because Luke has already linked the birth of Jesus to reign of Herod the Great (Luke 1:5), and Quirinius did not become governor of Syria until years afterwards.

What Happened When?

Precisely when Herod’s reign ended is a matter of dispute. Historically, the most common view—which is also in accordance with the Church Fathers—is that Herod died in 1 B.C.

Just over a hundred years ago, however, a German scholar named Emil Schürer argued that Herod died in 4 B.C., and this became the most popular view in the 20^th century. More recent scholarship, however, has supported the idea that Schürer was wrong and that the traditional date of 1 B.C. is correct.

After Herod’s death, his kingdom was divided, and his son Archelaus became the ruler of Judaea (Matt. 2:22). Archelaus, however, was a terrible ruler, and in A.D. 6 he was removed from office by the Romans and banished to what is now France. In his place, a Roman prefect was appointed to govern the province, which is why Pontius Pilate—rather than one of the descendants of Herod the Great—was ruling Judaea at the time of Jesus’ adult ministry.

According to the Jewish historian Josephus, Quirinius (aka Cyrenius) was sent to govern Syria after the banishment of Archelaus. He also took a tax census of Judaea at this time and made an accounting of Archelaus’s finances (Josephus, Jewish Antiquities 18:1:1).

The Sequence

From the above, the overall sequence of events is clear:

1. Herod the Great dies (1 B.C. or 4 B.C.)
2. Archelaus becomes his successor in Judaea
3. Archelaus is deposed
4. Quirinius does his census (A.D. 6)

Given that sequence, if Luke identified Jesus’ birth with a census conducted in A.D. 6 then we would have an implicit contradiction with Luke 1, which links Jesus’ birth to the reign of Herod the Great, and an even clearer contradiction with Matthew 2, which is explicit about the fact that Jesus was born during the reign of Herod the Great.

Finding a Solution

Scholars have proposed a number of solutions to this. There isn’t space to review them all here, but I’d like to look at one of them. In his book Who Was Jesus? the former Anglican bishop N. T Wright states:

"The question of Quirinius and his census is an old chestnut, requiring a good knowledge of Greek. It depends on the meaning of the word protos, which usually means ‘first’.
 
Thus most translations of Luke 2:2 read ‘this was the first [protos] census, when Quirinius was governor of Syria’, or something like that.
 
But in the Greek of the time, as the standard major Greek lexicons point out, the word protos came sometimes to be used to mean ‘before’, when followed (as this is) by the genitive case." (p. 89)

The genitive case is a grammatical feature in Greek. It is often used to indicate possession (as in “Jesus’ disciples”) or origin (as in “Jesus of Nazareth”). Wright, however, is pointing to a special use of the genitive when it follows the word protos and protos ends up meaning “before.” He writes:

"A good example is in John 1:15, where John the Baptist says of Jesus ‘he was before me’, with the Greek being again protos followed by the genitive of ‘me’."

In a footnote, Wright continues:

"The phrase is repeated in John 1:30; compare also 15:18, where Jesus says ‘the world hated me before [it hated] you’, where again the Greek is protos with the genitive.
 
Other references, in biblical and non-biblical literature of the period, may be found in the Greek Lexicon of Liddell and Scott (Oxford: OUP, 1940), p. 1535, and the Greek-English Lexicon of the New Testament of W . Bauer, revised and edited by Arndt, Gingrich and Danker (Chicago: University of Chicago Press), pp. 725f. 19.
 
This solution has been advanced by various scholars, including, interestingly, William Temple in his Readings in St John’s Gospel (London: Macmillan, 1945), p. 17; cf. most recently John Nolland, Luke 1–9: 20 (Dallas: Word Books, 1989), pp. 101f."

Wright’s Solution

Wright then explains how this can relate to the enrollment of Quirinius:

"I suggest, therefore, that actually the most natural reading of the verse is: 'This census took place before the time when Quirinius was governor of Syria.'"

He also notes:

"This solves an otherwise odd problem: why should Luke say that Quirinius’ census was the first? Which later ones was he thinking of?
 
This reading, of course, does not resolve all the difficulties. We don’t know, from other sources, of a census earlier than Quirinius’. But there are a great many things that we don’t know in ancient history.
 
There are huge gaps in our records all over the place. Only those who imagine that one can study history by looking up back copies of the London Times or the Washington Post in a convenient library can make the mistake of arguing from silence in matters relating to the first century.
 
My guess is that Luke knew a tradition in which Jesus was born during some sort of census, and that Luke knew as well as we do that it couldn’t have been the one conducted under Quirinius, because by then Jesus was about ten years old. That is why he wrote that the census was the one before that conducted by Quirinius."

An Objection

An objection that some have raised about this solution is why, on this theory, Luke would bother mentioning Quirinius’s census.
 
Think about it for a moment: It can sound a little strange to say, “This census took place before the time when Quirinius was governor of Syria.”

Why would Luke do that?

There are at least three reasons . . .

Avoiding Confusion

The census of Quirinius was famous enough that Luke’s audience would have heard of it—otherwise he wouldn’t have bothered mentioning it.
 
Given that it was well known, Luke would have wanted to avoid people confusing it with the enrollment during which Jesus was born.
 
He would especially want to avoid confusion in light of what he had established about King Herod...

Herod’s Death

Previously, in Luke 1:5, the Evangelist established that John the Baptist was conceived by his mother Elizabeth during the reign of Herod the Great.

Then, in 1:26 and 36, he established that Gabriel announced the conception of Jesus “in the sixth month” (i.e., what we would call the fifth month) of Elizabeth’s pregnancy. This means that Jesus would have been conceived much too early to have been born during Quirinius’s census.

Since Luke has already established this, it gives him a reason—when he records the fact that Jesus was born in connection with an enrollment—that it was not the famous census of Quirinius. It was an earlier one, in keeping with the timeframe Luke has already established.

But there is another reason why Luke would want to point this out...

In the Fifteenth Year of Tiberius Caesar

Luke 2 begins with a time cue that connects the birth of Jesus to the reign of Augustus Caesar. Luke 3 begins with an even more elaborate time cue linking the beginning of Jesus’ adult ministry to the reign of Augustus’s successor, Tiberius.

Luke writes:

"In the fifteenth year of the reign of Tiberius Caesar, Pontius Pilate being governor of Judea, and Herod being tetrarch of Galilee, and his brother Philip tetrarch of the region of Ituraea and Trachonitis, and Lysanias tetrarch of Abilene, in the high-priesthood of Annas and Caiaphas, the word of God came to John the son of Zechariah in the wilderness." (Luke 3:1-2)

The fifteenth year of Tiberius Caesar is what we would call A.D. 28/29.

After John’s ministry begins, Jesus quickly comes and is baptized, thus beginning his own ministry. When that happens, Luke informs us:

"Jesus, when he began his ministry, was about thirty years of age." (Luke 3:23)

If you back up 30 years from A.D. 28/29 (remembering that there is no “year 0” so you skip from A.D. 1 directly to 1 B.C.), you land in 2/3 B.C., which is the year that the early Church Fathers overwhelmingly assign Jesus’ birth to.

People back then knew when Tiberius reigned, and they could do the math as well as we. In fact, since they were used to dating years in terms of the emperor’s reign, they would realize even more quickly than we the year in which Luke 3 indicates Jesus was born.

Thus, on Wright’s theory, Luke would have an additional motive to make sure there was no confusion about Jesus being born during the famous census of Quirinius.

Think about it from Luke’s point of view: After years of gathering his research, he’s now drafting his Gospel, and, when he reaches Luke 2, he includes a time cue for the birth of Jesus during an enrollment ordered by Augustus. He already knows, however, that he is planning on beginning Luke 3 with a time due identifying the beginning of John the Baptist’s ministry and that he’s going to give Jesus’ approximate age at the time of his own ministry’s commencement.

Since the later time cues he’s planning to give point to a date earlier than the famous census of Quirinius, Luke would want to head off any potential confusion by stressing that this happened before that census, in keeping with the implications of Luke 3.
 
 
 
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Originally posted at Catholic Answers. Used with permission.
 
 
(Image credit: Wikipedia)

You know how people often say that Jesus was born in 4 B.C., 6 B.C., 7 B.C., or a time earlier still? The calculations that lead to these dates are all based on a proposal that was made just over a hundred years ago.

But now scholars are challenging this proposal, because it looks like it's wrong. And it's been distorting our understanding of when Jesus was born for over a hundred years.

Here's the story. . . .

When Herod Died

 
The Gospel of Matthew records that Jesus was born during the reign of Herod the Great. Luke doesn't say it explicitly, but he does indicate that the birth of John the Baptist was foretold during Herod's reign. If Jesus was born during the reign of Herod the Great then he must have been born before Herod died. (He wasn't a zombie king.)

Here's where the problematic proposal comes in: In the late 1800s, a German scholar named Emil Schurer proposed that Herod died earlier than previously thought.

Specifically, he claimed that Herod died in 4 B.C. This view caught on among scholars, and so now it's common for people to date the birth of Jesus no later than 4 B.C.

If a scholar takes seriously the account of the slaughter of the holy innocents then, since Herod killed all the baby boys two years old and under, that would push Jesus' birth up to two years earlier, landing us in 6 B.C.

And it could have happened even before that.

So that's why people often date Jesus' birth in this way, even though it is not when the Church Fathers indicated Jesus was born.

Why 4 B.C.?

 
Why do advocates of the Schurer view hold that Herod died in 4 B.C.? Here are several reasons:

1. Based on statements in the Jewish historian Josephus, Herod was first appointed king in 40 B.C. and then reigned for 36 years (so, he died in 4 B.C.).
2. Again based on Josephus, after Herod was appointed king, he conquered Jerusalem in 37 B.C. and reigned for 33 years (again, dying in 4 B.C.).
3. Again based on Josephus, Herod died between a lunar eclipse and Passover. In 4 B.C., there was a partial lunar eclipse 29 days before Passover.
4. We have various lines of evidence suggesting that Herod's sons took office in 4 B.C.

Sounds like a solid case, right?

Not exactly. It's shot through with problems.

Let's take a brief look at each of the four arguments . . .

1. When Herod Was Appointed King

 
Since the B.C./A.D. system of dates hadn't been invented yet, Josephus used ancient methods of dating that we no longer use.

One method was dating events in terms of which Olympiad they took place in. An Olympiad was a four-year period based on when the Olympic Games took place. (Yes, the ancients were huge sports fans.) Each Olympiad began in midyear and ran for four years.

Josephus says that Herod was appointed king during the 184th Olympiad, which ran from July 1, 44 B.C. to June 30, 40 B.C.

He also says that he was appointed during the consulship of Calvinus and Pollio. Consuls were Roman officials who reigned during specific years, and it was common to date events by the consuls who were in office at the time.

Calvinus and Pollio began their consulship after October 2, 40 B.C. That's in the 185th Olympiad.

See the problem?

The 184th Olympiad ended before Calvinus and Pollio were consuls. Josephus has given us an impossible date. He must be wrong on this one.

2. When Herod Conquered Jerusalem

 
Josephus says that Herod conquered Jerusalem in the 185th Olympiad during the consulship of Marcus Agrippa and Caninius Gallus. That does point to 37 B.C.

But Josephus also says that Herod conquered Jerusalem exactly 27 years--to the day--after it fell to the Roman general Pompey. But Pompey conquered Jersualem in 63 B.C., and 27 years later would be 36 B.C., not 37 B.C.

Furthermore, he says that the government of the Hasmoneans (who ruled Jerusalem prior to Herod conquering the city) for 126 years. According to 1 Maccabees and Josephus himself, they began ruling in 162 B.C., which would put the date of Herod's conquest in 36 B.C. (162 -126 =36).

So Josephus, again, gives contradictory information about when Herod conquered Jerusalem, indicating in some places that it was in 37 and in others that it was 36.

3. When the Lunar Eclipse Was

 
There was, indeed, a partial lunar eclipse in 4 B.C., which took place 29 days before Passover.

However, this was not the only lunar eclipse in the period. There was another lunar eclipse in 1 B.C., which was 89 days before Passover.

Now here's the thing:

1) Since there is more than one eclipse in this period, you can't cite the 4 B.C. eclipse as evidence supporting a 4 B.C. date in particular. You have to consider other eclipses in the right time frame and see which best fits the evidence.

2) The lunar eclipse in 4 B.C. was only partial, but the lunar eclipse in 1 B.C. was full. Josephus doesn't say it was a partial lunar eclipse. He says it was a lunar eclipse, and a full eclipse fits that description better.

3) The 4 B.C. span of 29 days between the eclipse and Passover is too short. Josephus doesn't just say that Herod died between the eclipse and Passover. He also names a bunch of things Herod did during that period, including trips that required travel time.

As contemporary biblical chronologer Andrew E. Steinmann points out:

"[A]ll of the events that happened between these two [the lunar eclipse and Passover] would have taken a minimum of 41 days had each one of them taken place as quickly as possible. A more reasonable estimate is between 60 and 90 days" (From Abraham to Paul, 231)

Thus, again, the 1 B.C. lunar eclipse--89 days before Passover--better fits what Josephus describes.

4. When Herod's Sons Began to Reign

 
It is true that we have multiple lines of evidence indicating that Herod's sons began to reign in 4 B.C.

That's doesn't mean Herod died then.

It was very common for aging rulers to take their successors as co-rulers during the latter part of their reign. This both took some of the pressure off the aging ruler and helped ensure a smooth succession when he died by lessening the chance of a power struggle after his death (people were already used to the new ruler, who was already in office).

That means that when you have ask whether a particular ruler's assumption of office was as co-ruler or as sole ruler. It could have been either one, so this argument does not prove that Herod died in 4 B.C.

Furthermore, we have evidence that Herod did start giving his sons governing authority before his death.

I'm trying to keep this post as short as possible though, so . . .

The Case for 4 B.C. Is Exceptionally Weak

 
All four of the main arguments proposed are problematic:

1. The first argument names an impossible date (one that did not exist) for the beginning of Herod's reign.
2. Josephus contradicts himself about when Herod conquered Jerusalem.
3. There is another lunar eclipse that fits what Josephus says even better.
4. We have evidence that Herod began giving his sons rulership roles before he died.

And there is much more that could be said (as there always is with biblical chronology). My favorite resources on this question are Jack Finegan's outstanding Handbook of Biblical Chronology (2nd ed.) and Andrew Steinmann's informative From Abraham to Paul. Both of those are hard to get and/or expensive, though.

Fortunately, if you'd like to tear into the evidence in mind-numbing depth, you can also read this paper by Steinmann for free.

This still leaves us with the big questions: When did Herod the Great actually die? And when was Jesus Christ born?

Stay tuned for my next post on Wednesday....
 
 
 
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Originally posted at National Catholic Register. Used with permission.