Biblical inerrancy

A puzzling phenomenon is the existence of Biblical inerrantists. It seems to me to be impossible to have both (1) carefully read the Bible and (2) come to the conclusion that it’s inerrant. Bart Ehrman talks about a possible explanation for this phenomenon in the order in which people read the Gospels: if you read the Gospels all the way through, one at a time, rather than reading them simultaneously, side by side, then it’s much easier for you to fail to notice all of the discrepancies. And boy are there discrepancies!

Virtually no story that appears in multiple Gospels is identical in the different tellings. That’s not hyperbole; literally from the story of Jesus’s birth all the way to his crucifixion and resurrection, there are unambiguous contradictions to be found the entire way. I don’t think that these contradictions make it rationally impossible to be a Christian, but they certainly do make it rationally impossible to be a Christian of an inerrantist tradition. And for more liberal Christians, they face a serious challenge of how they justify placing such enormous stock in the wording of a text that is known to be error-ridden.

There are just too many examples of blatant contradictions to go through them all. It’s a remarkable fact that many Christians that have read these stories throughout their lives are completely unaware that they disagree with one another! What I want to do here is just to pick one of the most well-known stories, the empty tomb. As I go through the story as each Gospel tells it, if at any moment you feel skeptical of what I’m saying, just go look at the verses being cited for yourself! The source of all the following quotes is the New International Version (NIV).

I’ve copied the entire “empty tomb” story as it’s told in each of the Gospels and highlighted the differences.

Now, let’s test your reading comprehension! In the story of the empty tomb, how many women come to the tomb, one, two, or three? Depends on who you read! According to Mark, it was three (the two Marys and Salome). According to Matthew, it’s two (the two Marys). According to John it’s just Mary Magdalene. And according to Luke it’s some unspecified number more than 1.

How many entities do they encounter at the tomb, and are they ordinary men or angels? According to Mark, they see one young man already inside the tomb. Luke says that after they enter, two men suddenly appear beside them. Matthew describes a violent earthquake preceding the arrival of an angel from heaven, while still outside the tomb. And John describes two angels inside the tomb (seen by Mary from the outside of the tomb). What’s more, in John and Matthew the woman/women see and talks to Jesus at the tomb! You have to agree that this is a pretty noteworthy thing for Mark and Luke to leave out.

Ok, how about the stone in front of the entrance? When the women/woman arrive(s), is the stone already rolled away from the tomb (as in Mark, Luke, and John), or is it moved later (as in Matthew)?

When the one/two men/angels speak to the woman/women, do they say that Jesus will meet the disciples in Galilee? In Mark and Matthew, yes. But in Luke and John there’s no mention of this! And in fact, in Luke the disciples don’t go to Galilee to meet Jesus at all! Jesus appears to disciples in Jerusalem and tells them to stay there, which they do until the end of the gospel (Luke 24:51-53). He ascends right outside of Jerusalem (1:9,12)

When the woman/women leave the tomb, do they describe what they saw to the disciples or not? According to Luke, Matthew, and John, yes. But not according to Mark; in Mark, the women flee and in their fear “say nothing to anyone”!

Did Peter ever visit the tomb? Not in Matthew or Mark, but in Luke and John he does. Is he by himself or with another disciple? Matthew says he’s by himself, John describes another disciple with him.

So much for the empty tomb! This level of contradiction is not special to this story. Think about Jesus’s death. When did he die? This is one of the most blatant contradictions in the Bible, because both John and Mark take great pains to explicitly lay out their chronology. According to Mark, Jesus and his disciples have their last supper on the evening of the Passover (Mark 14:12-17), and the following morning he is taken to be crucified (Mark 15:1). In John there is no last supper! John explicitly states in John 19:14 that Jesus is taken away from crufixion on “the day of Preparation of the Passover”, that is, the day before Passover!

This business about the last supper is actually pretty interesting; in John there is no last supper, but the author still manages to fit in some of the dinner table discussion early in the narrative. In Matthew, Mark, and Luke, it is during the last supper that Jesus says that the bread is his body (Mark 14:22, Matthew 26:26, Luke 22:19) and the wine his blood (Mark 14:24, Matthew 26:28, Luke 22:20). In John, these things are said some 12 chapters before his arrest and crucifixion (John 6:32-58). The context is ENTIRELY different within John; there, it comes up after the miracle where he multiplies the loaves of bread and fish. His disciples talk to him about this miracle, and he responds with the famous line “I am the bread of life”. This upsets some of the Jews around him, and starts an argument about how Jesus can BE the bread, in response to which Jesus doubles down and says “I am the living bread that came down from heaven” and “Very truly I tell you, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you.” Thus the origin of this doctrine. Given the importance that Catholics place on the wording here, it should be disturbing to them that there’s such dramatic disagreement between the Gospels on the context in which he said it!

Let’s now quickly run through some more Biblical contradictions. Who was the father of Joseph, Jesus’s father? According to Matthew 1:15, “Jacob begat Joseph, the husband of Mary”, whereas according to Luke 3:23, Joseph is said to be “the son of Heli”. The genealogies presented in Matthew and Luke are virtually in complete disagreement starting two generations up from Jesus. Apologists will often argue that one of the two is presenting the maternal lineage rather than the paternal line, but this is far from obvious when you look at the wording, which is specifically about Joseph’s father not Mary’s (plus the fact that in both genealogies, the entire rest of the list follows only the paternal line.)

In Mark 5:21-24, Jairus comes to Jesus before his daughter dies and asks him to heal her (“My little daughter is dying. Please come and put your hands on her so that she will be healed and live”), but in Matthew 9:18-20 the daughter has already died by the time Jairus comes to Jesus (“My daughter has just died. But come and put your hand on her, and she will live”).

In Mark 15:37-39, the curtain that separates the holy of holies from the rest of the temple rips in two after Jesus dies. And in Luke 23:45-46, it rips before.

In Matthew 2:1-23, Joseph Mary and Jesus flee to Egypt (250 miles away) after Jesus’s birth, where they stay until King Herod dies, after which they resettle in Nazareth. But in Luke 2:1-40, Joseph and the fam do their rites of purification in Bethlehem after birth and return to Nazareth directly, 41 days after Jesus’s birth.

Also in Luke 2, it is described that Joseph and Mary travel to Galilee for a census declared by decree by Caesar Augustus to be “taken of the entire Roman world.” The problem with this is that we have good historical records of Caesar Augustus, and no such census took place!

One final one: in Mark 2:25-26, Jesus references an Old Testament passage about David eating unlawfully eating consecrated bread “in the days of Abiathar the high priest.” There’s a big problem with this: Jesus made a mistake! In the Old Testament passage, Abiathar wasn’t the high priest! The high priest was Ahimelech, whose son Abiathar would much later become high priest (1 Sam 21.1-7). So Christians have a choice to make between either Jesus not knowing his Old Testament or Mark not being an inerrant recording of Jesus’s sayings.


All these contradictions are begging for an explanation. Is one or more of the authors lying? Not necessarily. Lying implies intention, and it’s worth keeping in mind the timeline of the Bible. Jesus is purported to have lived from 0 to 30 AD. Scholars unanimously agree that the earliest of the Gospels is Mark, and that it was originally written around 70 AD. Next were Matthew and Luke, both around 80-85 AD, and finally came John, around 90-95 AD. That’s a gap of 40 to 65 years from the events that are described! What’s more, the authors of Mark, Matthew, and John were almost certainly not the actual historical Mark, Matthew, and John (for a bunch of reasons I won’t get into now, most obviously that these texts were written in Greek by highly educated individuals and all three of these individuals were uneducated and would not have known Greek). And of course, Luke wasn’t a disciple and never met Jesus personally.

So the first texts that are written are from non-eyewitnesses recording an oral tradition that had started forty to sixty-five years before! In a forty-year game of telephone, nobody needs to have lied in order for the original story to become warped beyond recognition. Anybody that doubts that stories can become so dramatically altered over time need only think about the many Trump supporters that to this day insist that Trump’s inauguration had more attendees than Obama’s, despite LITERAL TIME LAPSE FOOTAGE of the entire thing and photographs all throughout. In one poll, Trump and Clinton voters that were handed these two photos, one from Obama’s inauguration and the other from Trump’s:

And guess what? 15% of Trump voters said that the left photo has more people! Suffice it to say, in the presence of emotionally charged topics like religion and politics, human brains start to act funny. Put this in context: this is an event from four years ago that we have video records of. And it’s somehow supposed to be unimaginable that 40 years of word-of-mouth transmission by religious believers made any significant changes to the original stories?

It’s even worse than this. These first texts are not what our modern Gospels are based off of, simply because we don’t have any copies of these first texts! The first copies of the texts that we possess come over A HUNDRED YEARS LATER, meaning that we have more than a hundred years of scribes making copies of copies of copies of the original texts. We know for a fact that these scribes were not perfect copyists, from the thousands of copies of the Gospels we possess, which abound in mistakes as small as spelling errors to as large as entire missing stories or new stories that had never appeared before. I’m sure that you know the story of the adulteress who Jesus defends, saying “he that is without sin among you, let him first cast a stone at her.” Did you know that this story appears in none of our earliest copies of the Gospels? Scholars unanimously agree that this story was added by scribes hundreds of years after the original writing, both because it literally doesn’t appear in copies earlier than that and also because the writing style is different from the rest of John.

So it seems to me like there really is no mystery here once you learn about the actual history of the texts. There are contradictions in the Bible because the Bible is an extremely imperfect copy of a copy of a copy of a … copy of a text written by non-eyewitnesses that heard stories told by people who had heard stories told by… people who had heard stories told by eyewitnesses to the events.

Formal Semantics 1: Historical Prelude and Compositionality

English is really complicated. For a long time, logicians looking at natural languages believed that there could be no formal system detailing their grammar and semantics. They resigned themselves to extremely simple idealized fragments of English, like propositional logic (formalizing “and”, “not”, and “or”) and first-order logic (formalizing “every”, “some”, and “is”).

The slogan of the time was “ordinary language has no logic” (Bertrand Russell and Peter Strawson). Chomsky famously argued that the languages invented by logicians were too artificial and entirely unlike natural languages, and that therefore the methods of logicians simply couldn’t be applied to this more complex realm.

This attitude has changed over time. Perhaps the most important figure in the “logic of natural language” movement is Richard Montague, a student of the giant of logic Alfred Tarski. The first line of his paper English as a Formal Language reads “I reject the contention that an important theoretical difference exists between formal and natural languages”, and he follows this up by more or less single-handedly invented formal semantics, now a thriving field. Hilariously, Montague apparently saw this work as child’s play, writing:

I (…) sat down one day and proceeded to do something that I previously regarded, and continue to regard, as both rather easy and not very important — that is, to analyze ordinary language.

(This had to hit hard for linguists of his time.)

Alright, enough prologue. In the next few posts I want to describe a naive first pass at formalizing a fairly substantial fragment of English, modeled off of Montague semantics. The key concept throughout will be the notion of compositionality, which I’ll briefly describe now.


Compositionality is all about how to construct the meaning of phrases from their smaller components. Take a sentence like “The cat sat on the mat.” The meaning of this sentence clearly has something to do with the meanings of “the cat” and “sat on the mat”. Similarly, the meaning of “sat on the mat” must have something to do with the meanings of “sat”, “on”, “the”, and “mat”.

The compositionality thesis says that this is all that determines the meaning of “the cat sat on the mat.” In other words, the meaning of any phrase is a function of the meanings of the individual words within it. These meanings are composed together in some way to form the meaning of the sentence as a whole.

The natural question that arises now is, what is the nature of this composition? Take a very simple example: “Epstein died.” According to compositionality, the meaning of “Epstein died” depends only on the meanings of “Epstein” and “died”. That seems pretty reasonable. What about: “Epstein died suspiciously”? How do we compose the meanings of the individual words when there are three?

One proposal is to compose all three simultaneously. That’s possible, but a simpler framework would have us build up the meanings of our sentences iteratively, composing two units of meaning at a time until we’ve generated the entire sentence’s meaning.

Let me now introduce some notation that allows us to say this compactly. If X is some word, phrase, or sentence, we’ll denote the meaning of X as ⟦X⟧. Then the principle of binary compositionality is just that there’s some function F such that ⟦X Y⟧ = F(⟦X⟧, ⟦Y⟧).

There’s two major questions that arise at this point.

First, in which order should we compose our units of meaning? Should we combine “Epstein” with “died” first, and then combine that with “suspiciously”? Or should it be “Epstein” and “suspiciously” first, then that with “died”? Or should we combine “Epstein” with the combination of “suspiciously” and “died”?

One might suggest here that the order actually doesn’t matter; no matter what order we combine the meanings in, we should still get the same meaning. The problem with this is that “The Clintons killed Epstein” has a different meaning than “Epstein killed the Clintons.” If order of composition didn’t matter, then we’d expect these to mean the same thing.

Second, how exactly does composing two meanings work? Is there a single rule for composition, or are there multiple different rules that apply in different contexts? It would be most elegant if we could find a single universal rule for generating meanings of complicated phrases from simple ones, but maybe that’s overambitious.

For instance, you might model the meaning of “died” as a set of objects, namely all those objects that died at some moment in the past, and the meaning of “Epstein” as one particular object in the universe. Then we might have our composition rule be the following: ⟦Epstein died⟧ will be a truth value, and it will be True if and only if the object denoted by “Epstein” is within the set of objects denoted by “died”. So in this framework, ⟦X Y⟧ = True if and only if ⟦X⟧ ∈ ⟦Y⟧.

This works nicely for “Epstein died”. But what about “Epstein died suspiciously”? Now we have two compositions to do, and the order of composition will matter. The problem is that no matter how we compose things, it seems not to work. Suppose that we combine “died” and “suspiciously” first, then combine “Epstein” with that. Using our model, ⟦died suspiciously⟧ will be True if and only if ⟦died⟧ ∈ ⟦suspiciously⟧, which is already a little bit weird. But even worse, ⟦Epstein died suspiciously⟧ will be True if and only if ⟦Epstein⟧ ∈ ⟦died suspiciously⟧. But what would it mean for the object denoted by “Epstein” to be an element of a truth value? It looks like in this framework, most three-word sentences end up becoming vacuously false.

Anyway, the last two paragraphs only show us that one particular attempt to formalize composition fails to be universal. It doesn’t show that it’s impossible in general. In fact, we’ll end up doing pretty well with a small set of composition rules centered around function application. The idea can be very simply phrased as: ⟦X Y⟧ = ⟦X⟧(⟦Y⟧). And in particular, the meaning of “Epstein died suspiciously” will be ⟦suspiciously⟧(⟦died⟧)(⟦Epstein⟧). And that’s enough warm-up! Next we’ll explore this idea further and dive into our Montague-style system.

Two more short and sweet proofs of propositional compactness

Proof 1 (countable language)

Let S be a countable set of sentences in a propositional language with atomic sentences p0, p1, p2, ….  Assume that S is finitely satisfiable. We want to build a truth assignment V that satisfies S.

We’ll assign truth values to the atomic sentences one at a time. Vn will be the partial truth assignment after assigning the first n truth values. If W agrees with Vn on its domain, then call W an extension of Vn.

We’ll now prove by induction that for each n, every finite subset of S is satisfied by some extension of Vn.

First of all, V0 is just the empty set, and every function is an extension of the empty set. So the hypothesis follows trivially from the finite satisfiability of S. 

Now, assume that every finite subset of S is satisfied by some extension of Vn. We’ll show that the same holds of Vn+1.

Suppose not. Then both of the following must be true:
(1) Some finite subset S0 of S is not satisfied by any extension of Vn ⋃ {(pn, T)}
(2) Some finite subset S1 of S is not satisfied by any extension of Vn ⋃ {(pn, F)}

S0 ⋃ S1 is not satisfied by any extension of Vn ⋃ {(pn, T)}, or any extension of Vn ⋃ {(pn, F)}. So it’s not satisfied by any extension of Vn, contradicting the inductive hypothesis since S0 ⋃ S1 is a finite set. This proves that every finite subset of S is satisfied by some extension of Vn, for each n.

Define V = U {Vn : n ∈ ω}. We now show that V satisfies S. Consider any sentence φ ∈ S. φ contains a finite number of atomic sentences, so there’s some n large enough that Vn assigns truth values to all sentence letters in φ.  {φ} is a finite subset of S, so some extension of Vn satisfies it. Every extension of Vn agrees on the assignments to the atomic sentences that appear in φ.  So since some extension of Vn makes φ true, all extensions of Vn must make φ true.  In particular, V makes φ true.

Proof 2 (any language)

Suppose S is a finitely satisfiable set of sentences, and let L be the set of atomic sentences.

A partial function g: L → {T, F} is called good if each finite subset of S is satisfied by some extension of g.

The good partial functions are a poset under ⊆, and since S is finitely satisfiable, ∅ is good. Furthermore, the union of any chain of good functions is a good function. Thus every chain has an upper bound, namely its union.

By Zorn’s lemma, there’s a maximal good function g. Since g is maximal, the domain of g is all of L.

We now show that g satisfies every element of S.
… Suppose φ ∈ S.
… Since g is good, it has an extension satisfying φ.
… But g already has all of L as its domain, so g satisfies φ.

So S is satisfiable!