bookmark_borderDid Jesus Rise from the Dead? Part 1: The Hallucination Theory

On the issue of the alleged resurrection of Jesus, I usually argue in defense of the Apparent Death Theory.
I do this NOT because I believe that the Apparent Death Theory is true, but in order to show that, contrary to the claim of Christian apologists, the Apparent Death Theory is a viable theory, that there is a significant chance that it is true, and that it has NOT been disproven by Christian apologists.
One cannot prove that Jesus rose from the dead.  But one also cannot prove that Jesus only appeared to die on the cross, and that his being seen alive after the crucifixion was the result of his surviving his crucifixion.  Nor can one prove ANY of the skeptical/naturalistic theories to be true.
The basic problem is that the evidence we have is very sketchy and very dicey,  so it is insufficient to prove ANYTHING about the life, ministry, and death of Jesus:

  • We don’t know if Jesus actually existed.
  • We don’t know who actually wrote the Gospels.
  • The Gospels were probably written decades after the events they describe.
  • The Gospels are written in Greek by literate educated authors, but Jesus and his disciples probably spoke Aramaic, and were probably uneducated and illiterate.
  • The Gospels provide conflicting stories and details in general.
  • The Gospels provide conflicting stories and details about the crucifixion, burial, and resurrection appearances of Jesus.
  • We know very little about the traditional “authors” of the Gospels (i.e. Matthew, Mark, Luke, and John).
  • The Gospels were written by religious Christians who were trying to promote Christian beliefs.
  • The Gospels are at best historically unreliable accounts of the life and ministry of Jesus, and are possibly fictional stories about a fictional character named “Jesus”.

Because of the sketchy and dicey nature of the evidence we possess concerning Jesus, it cannot be proven that Jesus existed, and it cannot be proven that Jesus died on the cross.  However, IF we assume that Jesus existed, and IF we assume that the Gospels are not purely fictional but contain some historical information that can be gleaned by means of careful critical analysis, THEN it would be possible to show that one of the skeptical theories was probable, or that one of the skeptical theories was improbable.  It might also be possible to show that a disjunction of various skeptical theories was probable (“Either skeptical theory A or B or C is true.”), or that such a disjunction of skeptical theories was improbable.
Christian apologists attempt to “refute” skeptical theories about the alleged resurrection of Jesus on the basis of questionable historical claims and assumptions.  They interpret some particular Gospel passage in a way that supports a particular historical claim, and they assume not only that their interpretation of that passage is correct, but that the author of that passage was merely recording an historical event that the author observed first hand, or that some reliable eyewitness conveyed that observation directly to the author.  Such assumptions are gratuitous and dubious, and there are often good reasons to reject these assumptions.  As a result, every attempted “refutation” by every Christian apologist of every skeptical theory FAILS.  Or, at least every attempted “refutation” that I have read of every skeptical theory FAILS, and I have read many such attempted refutations, so I have good reason to believe that no such attempts have ever been successful.
I have focused my attention on the defense of the Apparent Death Theory, but attempts by Christian apologists to refute other skeptical theories are as weak and defective as their attempts to refute the Apparent Death Theory.  So, for this particular post (or series of posts), I will focus in on a different skeptical theory: the Hallucination Theory.
The basic idea of the Hallucination Theory is that one or more of Jesus’ followers had some sort of experience after the crucifixion of Jesus that they took to be an experience of a living Jesus.  This experience, when reported to others then became the basis for the belief among followers of Jesus that Jesus had physically risen from the dead.  The Hallucination Theory further claims that the original experience or experiences of this sort were NOT actually experiences of a risen Jesus, but were dreams or hallucinations or mistaken or misleading experiences of someone other than Jesus.

My Eyes at the Moment of the Apparitions by German artist August Natterer

I have described this theory in a fairly broad and general way here, which favors the truth of this theory.   Strictly speaking, a dream is NOT an hallucination, but a dream of Jesus being alive that is interpreted by the person who had the dream to be a real experience of an actual living Jesus is very similar to the idea of a person experiencing an hallucination of Jesus and then interpreting that to be a real experience of an actual living Jesus.  So, it makes sense to include “dreams” of Jesus under the same category as “hallucinations” of Jesus, so long as such experiences were (a) interpreted as being real experiences of an actual living Jesus, and (b) reports of such experiences became the basis for the early Christian belief that Jesus had physically risen from the dead.
Christian apologists, however, tend to interpret the Hallucination Theory more narrowly, in order to make it easier to “refute” this theory.  It is in some ways better to define a theory narrowly, because then it is easier to think about and evaluate such a theory.  We don’t have to worry about various different possibilities and variations that are encompassed by a broader interpretation of the theory.   However, if one defines the Hallucination Theory narrowly, as Christian apologists tend to do, then this opens the door to OTHER alternative skeptical theories that are similar to the narrowly defined Hallucination Theory.  
For example, if we distinguish dreams from hallucinations, and exclude dreams of Jesus from counting as potential examples of the Hallucination Theory, then a refutation of the Hallucination Theory might well FAIL as a refutation of the alternative skeptical view that dreams of Jesus after the crucifixion became the basis of the early Christian belief in the physical resurrection of Jesus.  So, narrow definitions of the Hallucination Theory might make it easier for Christian apologists to “refute” this theory, but this comes at a significant cost to their defense of the resurrection: this opens the door to MORE skeptical theories about how belief in the physical resurrection of Jesus came about.
We can see a related problem of ambiguity in Josh McDowell’s defense of the resurrection in The Resurrection Factor (1981, Here’s Life Publishers, Inc. ; hereafter: TRF).  On the one hand, McDowell defines “hallucination” in a fairly broad way:

The American Psychiatric Association’s official glossary defines a “hallucination” as “a false sensory perception in the absence of an actual external stimulus.” The Psychiatric Dictionary defines it as “an apparent perception of an external object when no such object is present.”  (TRF, p.83)

Notice that visual experiences in dreams fit these definitions.  So, based on these broad definitions of “hallucination”, visual experiences in a dream constitute hallucinations.  Based on these broad definitions given by McDowell, the Hallucination Theory would include dream experiences of Jesus (after the crucifixion) by followers of Jesus that (a) were interpreted as being real experiences of an actual living Jesus, and (b) became the basis for the early Christian belief in the physical resurrection of Jesus.
However, as McDowell begins his attempted refutation of this theory, he immediately attacks a narrower interpretation of the Hallucination Theory:

Why is the hallucination theory so weak?
[…]
…only particular kinds of people have hallucinations–usually only paranoid or schizophrenic individuals, with schizophrenics being the most susceptible.  (TRF, p.84)

This objection only works against a very narrowly defined interpretation of the Hallucination Theory.  It clearly does NOT work against the theory that dream experiences of Jesus led to belief in the physical resurrection of Jesus.  EVERYBODY has dreams.  Dreams are NOT exclusively experienced by “only paranoid or schizophrenic individuals”.  So, although McDowell begins his discussion of the Hallucination Theory with a very broad definition of what constitutes an “hallucination”, his very first objection against this theory assumes a much narrower interpretation of what constitutes an “hallucination”, and therefore his objection only applies to some versions of the Hallucination Theory but not to others.
McDowell’s defense of the resurrection FAILS, because his attempted refutation of the Hallucination Theory FAILS.  His attempted refutation of the Hallucination Theory FAILS because some of his objections DO NOT APPLY to versions of the Hallucination Theory that claim that dream experiences of Jesus were the basis for the early Christian belief in the resurrection of Jesus.
McDowell commits the fallacy of EQUIVOCATION, and the STRAW MAN fallacy here.  He initially defines the Hallucination Theory in a way that is fairly broad (and that includes dream experiences of Jesus), and then proceeds to raise objections that apply only to some particular versions of Hallucination Theory but not to others (e.g. not to versions about dream experiences of Jesus).
This is the fallacy of EQUIVOCATION because the term “Hallucination Theory” is used ambiguously by McDowell.  He attempts to refute the “Hallucination Theory” in one (narrow) sense of that term, but he claims to have refuted the “Hallucination Theory” in a different (broader) sense of the term.  This is the STAW MAN fallacy, because it is EASIER to attempt a refutation of the Hallucination Theory that is based on a narrow definition of what constitutes an “hallucination” than it is to attempt a refutation of this theory that is based on a broader definition of what constitutes an “hallucination”.
Furthermore, it is clear in the overall LOGIC of McDowell’s case that he needs to refute the Hallucination Theory that is based on his broader definition of what constitutes an “hallucination”.  McDowell categorizes some skeptical theories as being “Occupied Tomb” theories.  His complete list of “Occupied Tomb” theories includes the following five theories (see the diagram in TRF on page 83):

  1. Unknown Tomb
  2. Wrong Tomb
  3. Legend
  4. Spiritual Resurrection
  5. Hallucinations

Note that there is no Dream Theory in this list.  So, if the Hallucination Theory  is interpreted narrowly, and thus EXCLUDES dream experiences of Jesus as a possible explanation for early Christian belief in the physical resurrection of Jesus, then he has left out an important skeptical theory in this list of “Occupied Tomb” theories, and thus he has FAILED to refute all of the skeptical theories in the general category of  “Occupied Tomb” theories, and thus FAILED to refute all of the major skeptical theories.
In order for McDowell’s LOGIC to work, he must interpret the Hallucination Theory in a broad way that includes dream experiences of Jesus as an explanation for early Christian belief in the resurrection.  McDowell FAILED to present his case against the Hallucination Theory in a way that was consistent with his own broad definition of “hallucination”, and thus he FAILED to refute the Hallucination Theory, understood in this broad sense, and thus he FAILED to defend the belief that Jesus actually rose from the dead.

bookmark_borderThe Complete FAILURE of Peter Kreeft’s Case for the Resurrection – Part 1: Three Serious Problems

FIVE THEORIES ABOUT JESUS’ ALLEGED RESURRECTION

In Chapter 8 of Handbook of Christian Apologetics (hereafter: HCA), Peter Kreeft identifies Five Theories concerned about “what really happened in Jerusalem on that first Easter Sunday…” :

1. Christianity: “the resurrection really happened”
2. Hallucination: “the apostles were deceived by a hallucination”
3. Myth: “the apostles created a myth, not meaning it literally”
4. Conspiracy: “the apostles were deceivers who conspired to foist on the world the most famous and successful lie in history”
5. Swoon:  “Jesus only swooned and was resuscitated, not resurrected”

(HCA, p.182)
According to Kreeft all he needs to do is to refute the four skeptical theories that are alternatives to the Christian view:

If we can refute all other theories (2-5), we will have proved the truth of the resurrection (1).

(HCA, p.182)
 

TWO SERIOUS PROBLEMS WITH KREEFT’S CASE FOR THE RESURRECTION

There are at least two serious problems with Kreeft’s case for the resurrection of Jesus that I have previously discussed in my blog posts:

  • Kreeft FAILED to refute the Conspiracy Theory.
  • Kreeft FAILED to refute the Swoon Theory.

Kreeft raises seven objections against the Conspiracy Theory.  I wrote a series of blog posts showing various problems, errors, and weaknesses with Kreeft’s arguments against the Conspiracy Theory, and I concluded that each of those seven objections FAILS to refute the Conspiracy Theory.
Kreeft raises nine objections against the Swoon TheoryI wrote a series of blog posts showing various problems, errors, and weaknesses with Kreeft’s arguments against the Swoon Theory, and I concluded that each of those nine objections FAILS to refute the Swoon Theory.

  • Kreeft’s FAILURE to refute the Conspiracy Theory is sufficient by itself to SINK his case for the resurrection of Jesus.
  • Kreeft’s FAILURE to refute the Swoon Theory is sufficient by itself to SINK his case for the resurrection of Jesus.

Given that Kreeft has FAILED to refute at least two of the four skeptical theories in his list, his case for the resurrection is a complete FAILURE.  Kreeft has FAILED to prove that Jesus rose from the dead.
 

A THIRD SERIOUS PROBLEM WITH KREEFT’S CASE FOR THE RESURRECTION

But there is another serious problem with Kreeft’s case for the resurrection.  His list of skeptical theories is INCOMPLETE:

  • There are OTHER skeptical theories (besides the four that Kreeft lists) that Kreeft has NOT even attempted to refute.

Kreeft uses a bit of logic in order to try to make it appear that the four skeptical theories in his list cover ALL of the logical possibilities.  But if you examine that logic more closely, it becomes clear that there are MANY OTHER skeptical theories that he has neglected to mention or to consider, and this problem is sufficient by itself to SINK Kreeft’s case for the resurrection of Jesus.
 

THE INITIAL DILEMMA IN KREEFT’S ANALYSIS OF THE LOGICAL POSSIBILITIES

There is a diagram in Chapter 8 that is an important part of Kreeft’s case for the resurrection of Jesus (click on the image below for a clearer view of the diagram):

 
On the left side of the diagram, we see a dilemma between two alternatives:

Jesus died

OR

Jesus didn’t die

There are problems in Kreeft’s logic right away, problems with this initial dilemma.  These two alternatives are VAGUE and in need of clarification.  Taken literally, these alternatives are not relevant to the question about whether Jesus rose from the dead:

Jesus died eventually (at some point in the past).

OR

Jesus didn’t ever die (and is now a human being who is over 2,000 years old).

Those are NOT the two alternatives that Kreeft had in mind.
In relation to the question of whether Jesus rose from the dead, the first alternative can be stated more carefully and precisely:

Jesus died before he was removed from the cross.

OR

Jesus didn’t die before he was removed from the cross.

These alternatives are clearer and are relevant to the question of the resurrection, but this is NOT a true dilemma, because these two alternatives do NOT comprehend ALL logical possibilities.
Both of these statements ASSUME that there was a point in time in which Jesus “was removed from the cross”.  So, both of these statements make the following three assumptions:

  • Jesus was an actual historical person.
  • Jesus was crucified.
  • At some point in time after Jesus was crucified, Jesus was removed from his cross.

The so-called “dilemma” that occurs at the beginning of the chart about alternative theories does NOT encompass ALL logical possibilities.  It excludes, for example, the following three skeptical possibilities:

  • Jesus was NOT an actual historical person.
  • Jesus was an actual historical person, but Jesus was never crucified.
  • Jesus was an actual historical person who was crucified, but his body was never removed from his cross.

These are more extreme skeptical theories, compared to the four skeptical theories that Kreeft considers, but that is no excuse for failing to consider them, and for failing to attempt to refute them.  If Kreeft thinks that these theories are silly or ridiculous, then from that point of view it should be very easy to refute these theories, so Kreeft has no excuse for failing to attempt to refute these three additional skeptical theories, but Kreeft makes no attempt to refute any of those three theories.
 

A TRUE INITIAL DILEMMA FOR THE ANALYSIS OF THE LOGICAL POSSIBILITIES

In order to begin the logical breakdown with a true dilemma, we need to consider the following alternatives:

Jesus was an actual historical person.

OR

It is NOT the case that Jesus was an actual historical person.

The second alternative above reflects at least one skeptical theory, or one category of skeptical theories.  Kreeft makes no effort to disprove the skeptical theory that Jesus was a legend or fictional character.  So, if we add this skeptical theory to the four that Kreeft has identified, there are at least FIVE skeptical theories that need to be refuted in order for Kreeft’s case for the resurrection to be successful.
 

A SECOND NEW DILEMMA

The first alternative above (Jesus was an actual historical person) needs to be divided by another true dilemma:

Jesus was crucified.

OR

It is NOT the case that Jesus was crucified.

Again the second alternative here reflects at least one more skeptical theory, or one category of skeptical theories.  One example of such a theory is this:

There was a case of mistaken identity and someone who looked like Jesus was arrested and crucified by Roman soldiers because they thought this person was Jesus of Nazareth.  Some of the followers of Jesus saw this man crucified, and they too believed that the crucified man was Jesus.  Jesus had left Jerusalem about the same time that this other man who looked like Jesus was crucified, so when Jesus’ disciples heard that Jesus had been arrested, crucified, and buried, they believed that Jesus had in fact been arrested, crucified, and buried.  Later, when they met up with Jesus again, they sincerely but mistakenly inferred that Jesus must have risen from the dead.

This is a significant skeptical theory that Kreeft never mentions, and that Kreeft made no effort to disprove.  So, we now see that there are at least SIX skeptical theories that need to be refuted in order for Kreeft’s case for the resurrection to be successful. But Kreeft only attempted to refute FOUR skeptical theories, and he FAILED to refute at least TWO of those theories.
 

A THIRD DILEMMA, SIMILAR TO THE FIRST DILEMMA IN KREEFT’S ANALYSIS

The first alternative (Jesus was crucified) needs to be divided into two possibilities by another dilemma:

Jesus was dead when his body was removed from the cross.

OR

It is NOT the case that Jesus was dead when his body was removed from the cross.

This is similar to the original dilemma that Kreeft used to begin his analysis:

Jesus died

OR

Jesus didn’t die

But the 3rd Dilemma that I’m proposing in this revised analysis is clearer and is relevant to the issue of the resurrection.
The most obvious skeptical theory related to the second alternative of the 3rd dilemma (It is NOT the case that Jesus was dead when his body was removed from the cross) is, as Kreeft’s diagram indicates, the Swoon Theory.
However, other skeptical theories could also be related to the second alternative of the 3rd dilemma.  In Part 1 of my series “Defending the Swoon Theory”, I show that the Swoon Theory involves a claim or assumption about WHY the Roman soldiers allowed Jesus’ body to be removed from the cross (Jesus Appeared to be Dead):

(JAD) Jesus had swooned (or was unconscious) and he appeared to be dead, so the Roman soldiers mistakenly believed that he was already dead, and for that reason they allowed Jesus to be removed from the cross, even though Jesus was actually still alive.

But there are MANY different possible explanations for WHY the Roman soldiers might have allowed Jesus to be removed from the cross, even though he was still alive.
Here are six alternatives to (JAD), which would, if we define the Swoon Theory in terms of (JAD), mean that these possibilities represent SIX MORE skeptical theories in addition to the Swoon Theory:

  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they were bribed to do so.
  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they were threatened to make them do this.
  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they got drunk and fell asleep.
  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they were followers of Jesus and wanted to help Jesus to survive.
  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they were ordered by a superior officer to do so.
  • The Roman soldiers allowed Jesus to be removed from the cross while he was still alive because they were overpowered and killed by some anti-Roman Jewish Zealots who were angered by the crucifixion of Jesus.

So, if “the Swoon Theory” is understood as asserting (JAD), then it follows logically that there are at least SIX more alternative skeptical theories to add to our collection of SIX skeptical theories, meaning that at least TWELVE different skeptical theories would need to be refuted in order for Kreeft’s case for the resurrection to be successful.  But Kreeft has only attempted to refute FOUR skeptical theories, and he FAILED to refute at least TWO of those theories.
 

A FOURTH DILEMMA, VERY SIMILAR TO THE SECOND DILEMMA IN KREEFT’S ANALYSIS

The first alternative (Jesus was dead when his body was removed from the cross) needs to be divided into two possibilities by another dilemma.  We can use a dilemma that is basically the same as one used in Kreeft’s analysis:

Jesus rose from the dead.

OR

It is NOT the case that Jesus rose from the dead.

Kreeft identifies the first alternative with “Christianity” or the Christian theory.  But there are also skeptical theories that are associated with this first alternative:

  • The devil raised Jesus from the dead.
  • A demon raised Jesus from the dead.
  • An angel raised Jesus from the dead (on his own initiative, without God’s approval).
  • A witch or wizard used magic to raise Jesus from the dead.
  • A finite deity (like Zeus or Venus) raised Jesus from the dead.
  • A fairy raised Jesus from the dead.
  • Jesus rose from the dead by the power of a philosopher’s stone.

There are many other such skeptical theories that are possible.   Skeptics often reject belief in supernatural beings and forces, so most skeptics would not endorse such supernatural theories about the alleged resurrection of Jesus.  However, there are many people who do believe in supernatural beings or forces who are not Christians, and who might well challenge the Christian theory about Jesus’ death and alleged resurrection.  They might not call themselves “skeptics”, but they are nevertheless skeptical about the Christian theory.
Kreeft has not considered any such skeptical theories, nor has Kreeft made any attempt to refute such theories.  There are at least SEVEN such theories, and we have previously identified at least TWELVE skeptical theories, so there are at least NINETEEN skeptical theories that need to be refuted in order for Kreeft’s case for the resurrection to be successful.  But Kreeft only attempted to refute FOUR skeptical theories, and he FAILED to refute at least TWO of those theories.
 

THE FAILURE OF KREEFT’S TRILEMMA

Most of the skeptical theories that Kreeft does consider are related to the second alternative above (It is NOT the case that Jesus rose from the dead).  Kreeft divides this possibility into a “trilemma”, into three different categories, each of which corresponds to one skeptical theory:

The apostles were deceived—-> Hallucination Theory

OR

The apostles were myth-makers—-> Myth Theory

OR

The apostles were deceivers—-> Conspiracy Theory

But this is NOT a true trilemma, because this logical analysis FAILS to encompass ALL of the skeptical theories that are associated with the second alternative above (It is NOT the case that Jesus rose from the dead, and Jesus was dead when his body was removed from the cross).
For example, the stories about the alleged resurrection of Jesus could have developed AFTER “the apostles” (i.e. the inner-circle of disciples of Jesus) had all died.  The “deceivers” or “myth-makers” could have been the next generation of followers of Jesus (i.e. the disciples of the eleven disciples).  [This skeptical theory was mentioned in a comment by “Carstonio” in response to my Defending the Swoon Theory – INDEX post.]  There may be some significant problems with this theory, but it is clearly a skeptical theory that does NOT FIT under any of the above three categories.  Therefore, it is clear that those three categories FAIL to encompass ALL of the skeptical theories that are associated with the second alternative above (It is NOT the case that Jesus rose from the dead, and Jesus was dead when his body was removed from the cross).
This new skeptical theory means that there are now at least TWENTY different skeptical theories that Kreeft needs to refute in order for his case for the resurrection to be successful.  But Kreeft only attempted to refute FOUR skeptical theories, and he FAILED to refute at least TWO of those theories.
 

A FIFTH DILEMMA, BASED ON A LEMMA FROM KREEFT’S FAILED TRILEMMA

The existence of this added skeptical theory also means that we should revise and improve Kreeft’s logical analysis of possible theories.  I suggest we stick to using dilemmas, to make sure that we cover ALL possible theories.  Let’s start with the first lemma that Kreeft used in his FAILED trilemma:

the apostles were deceived

I prefer the clearer designation “the eleven disciples of Jesus” instead of unclear phrase “the apostles”, and we also need to be more specific about the deception involved here:

The eleven disciples of Jesus were deceived into believing that Jesus had risen from the dead

OR

It is NOT the case that the eleven disciples of Jesus were deceived into believing that Jesus had risen from the dead

Kreeft associates the first alternative with the Hallucination theory.  Experiencing hallucinations of Jesus would indeed be a way that the eleven disciples of Jesus could have been DECEIVED into believing that Jesus had risen from the dead.  But there are clearly OTHER WAYS that they could have been deceived into accepting this belief:

  • Vivid dreams – of seeing, and talking to, Jesus
  • Mistaken Identity – seeing a person who happened to look and act like Jesus
  • Intentionally Fooled – by an actor wearing make-up and/or disguised to look like Jesus
  • Intentionally Fooled – by a person who naturally (without make-up or disguise) looked like Jesus
  • False Memories – implanted by hypnosis or suggestion, of having seen, or spoken with, the risen Jesus
  • False Memories – implanted by the Devil, of having seen, or spoken with, the risen Jesus
  • Visions of Jesus in heaven – leading to the mistaken belief that Jesus had a new resurrected body

There are at least SEVEN other ways that the disciples could have been DECEIVED into believing that Jesus had risen from the dead, so if we add those skeptical theories to our existing pile of TWENTY skeptical theories, it follows that there are at least TWENTY-SEVEN skeptical theories that need to be refuted in order for Kreeft’s case for the resurrection to be successful.  But Kreeft only attempted to refute FOUR skeptical theories, and he FAILED to refute at least TWO of those theories.
I have not completed my revision of Peter Kreeft’s analysis of the logical possibilities concerning alternative skeptical theories about the alleged resurrection of Jesus, but so far I have identified a number of gaps and problems with Kreeft’s analysis, and I have shown that there are at least TWENTY-SEVEN alternative skeptical theories, which means that Kreeft needs to refute at least TWENTY-SEVEN skeptical theories, not just the FOUR skeptical theories that he attempted to refute in his Handbook of Christian Apologetics.
TO BE CONTINUED…
 
 
 
 

bookmark_borderReply to Dr. Erasmus – Part 2: Straw Man and Invalid Inference

In this post I will reply to an objection that was raised by Dr. Jacobus Erasmus against my reasoning in one of my skeptical posts about the resurrection of Jesus.

DR. ERASMUS COMMITS THE STRAW MAN FALLACY

The most basic problem with the objection raised by Dr. Erasmus is that he commits the all-too-common STRAW MAN fallacy.
He does NOT understand my reasoning, and as a result he mischaracterizes my reasoning, and then he criticizes the inaccurate and distorted representation of my reasoning instead of criticizing my ACTUAL reasoning.  I am being charitable in assuming that Dr. Erasmus did not intentionally mischaracterize and distort my reasoning.  However, this charitable assumption leads me to the conclusion that Dr. Erasmus has a poor understanding of probability.  He mischaracterized my reasoning because he does NOT have a good understanding of probability.
In the previous post where I began my reply to Dr. Erasmus, I have already pointed out the fundamental mistake that Dr. Erasmus made:  there is no hint that he noticed that I was making use of CONDITIONAL PROBABILITY in my calculations.  But for anyone who has a basic understanding of probability, it would have been obvious that I was making use of CONDITIONAL PROBABILITY.  So, because Dr. Erasmus lacks a good understanding of probability, he failed to notice the obvious and important fact that I was making use of CONDITIONAL PROBABILITY.  This resulted in his mischaracterizing my reasoning, and attacking a STRAW MAN, instead of pointing out a problem in my ACTUAL reasoning.
I could go into more detail in supporting my charge that Dr. Erasmus has committed a STRAW MAN fallacy against my skeptical post on the resurrection of Jesus, but I don’t see the point.  He clearly misunderstood my reasoning, so his objection does NOT address my actual reasoning.
If Dr. Erasmus wants to make a more serious effort to understand my reasoning, then I would be happy to discuss any new objections that he might offer, but his first attempt at an objection completely misses the mark, and is unworthy of any more analysis and discussion by me.

DR. ERASMUS MAKES AN INVALID INFERENCE

Not only does Dr. Erasmus take aim at a STRAW MAN by mischaracterizing my reasoning about the resurrection, he also FAILS to support his objection about that STRAW MAN.  He attacks reasoning that is NOT mine, and his attack of that other reasoning is based on an INVALID INFERENCE, and thus it FAILS.  His critique is doubly wrong.  He aimed at the wrong target and he also missed the target!
In his attempted counterexample, Dr. Erasmus needs to establish two main things about his example, in order for his example to make the objection that he wants to make:

  • The probabilities of (C1) and (C2) and (C3) are low.
  • The probability of (H2) is high.

Dr. Erasmus FAILS to establish either one of these key points.  I will skip over the problem with the first point, and focus on his FAILURE to establish the second point.  Actually,  I have already described the problem with the second point in my previous post where I began my reply.  So, I will be very brief here.
Dr. Erasmus uses Bayes’ Theorem to infer that the UNCONDITIONAL probability of (H2) is 0.9.   I agree that a probability of 0.9 is indeed “high”.  The problem is that the instance of Bayes’ Theorem that he uses only yields a CONDITIONAL PROBABILITY of (H2), not an UNCONDITIONAL probability.  The condition in this case is that (C1) and (C2) and (C3) are all true.
In other words, the probability of (H2) would be 0.9 IF we knew for certain that (C1) and (C2) and (C3) were all true.  But if we knew for certain that (C1) and (C2) and (C3) were all true, then it cannot also be the case that the probability of each of those three claims is low.
In any case, Dr. Erasmus does NOT understand Bayes’ Theorem well enough to grasp the obvious fact that it is an INVALID INFERENCE to conclude that the UNCONDITIONAL probability of (H2) is 0.9 based on a calculation using his instance of Bayes’ Theorem.  His formula implies only that the probability of (H2) would be 0.9 IF we knew for certain that (C1) and (C2) and (C3) were all true.
CONCLUSION
Dr. Erasmus does NOT have a good understanding of probability.  As a result, he distorts my reasoning about the resurrection and attacks a STRAW MAN instead of pointing to a problem in my ACTUAL reasoning, and his attempt to attack that STRAW MAN itself FAILS because it is based on an INVALID INFERENCE, an inference that he would not have made if he had a better understanding of Bayes’ Theorem.
=====================

UPDATE  on  1/7/19

=====================
I took another look at Dr. Erasmus’ instance of Bayes’ Theorem (“the odds form of Bayes’ Theorem”) and discovered that instead of CALCULATING the probability of the hypothesis H2, he simply ASSIGNED a probability to H2!!  So, it is clear that Dr. Erasmus does NOT understand Bayes’ Theorem, and he is very confused about what he was doing with the theorem.
When Dr. Erasmus introduces his instance of Bayes’ Theorem, he makes this statement:

We may now use Bayes’ Theorem to calculate the probability of H2.

His aim, of course, is to use Bayes’ Theorem to SHOW that the probability of H2 is high, even when the probabilities of (C1), (C2), and (C3) are low.  But in his example he simply fills in the probability for H2 on the right-hand side of the equation; he does NOT calculate that probability at all!  Furthermore, he is assigns H2 the probability of .6, which is NOT what most people would consider to be a high probability!  So, he shoots himself in both feet.
On the left-hand side of the equation is a single fraction with a CONDITIONAL probability in the numerator and a CONDITIONAL probability in the denominator:

P(H2 | C1 & C2 & C3) / P(~H2| C1 & C2 & C3)  

This ratio of CONDITIONAL probabilities is apparently what Dr. Erasmus is attempting to calculate, because the values that he provides or assigns as inputs are four fractions that appear to each be ratios of probabilities, which is exactly what we find on the right-hand side of his instance of Bayes’ Theorem:

[P(H2) / P(~H2)]  x  [P(C1|H2) / P(C1|~H2)]  x  [P(C2|H2) / P(C2|~H2)]  x  [P(C3|H2) / P(C3|~H2)]

Here are the values that Dr. Erasmus assigns to the probabilities on the right-hand side of the equation:

(0.6 / 0.4)  x  (0.7 / 0.5)  x  (0.8 / 0.5)  x (0.9 / 0.3)

Reading those assigned values back into the right-hand side of the equation, we see that he has assigned the following values to these probabilities:

P(H2)  =  0.6

P(~H2)  =  0.4

P(C1|H2)  =  0.7

P(C1|~H2)  =  0.5

P(C2|H2)  =  0.8

P(C2|~H2)  =  0.5

P(C3|H2)  =  0.9

P(C3|~H2)  =  0.3

When he assigned the value of 0.6 to P(H2), he was assigning a moderate probability to H2, the hypothesis that he was supposed to be using Bayes’ Theorem to SHOW that H2 has a high probability, even when (C1), (C2), and (C3) have low or moderate probabilities.
Instead of SHOWING that H2 has a high probability,  Dr. Erasmus was SHOWING that he does NOT understand probability calculations, especially probability calculations that make use of Bayes’ Theorem.
=====================

UPDATE  on  1/8/19

=====================
Given the above probability values that Dr. Erasmus assigned to the elements of the right-hand side of his instance of Bayes’ Theorem, we can calculate the probabilities of of (C1), (C2), and (C3).  When we do so, it turns out that NONE of them have a LOW probability, which means that his counterexample FAILS.
We know that the probability of (C1) is EQUAL to the SUM of the probability of (C1|H2) times the probability of (H2) and the probability of (C1|~H2) times the probability of (~H):

P(C1) = [P(C1|H2)  x P(H2)] + [P(C1|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C1):

P(C1) = (0.7 x 0.6) + (0.5 x 0.4)
P(C1) = 0.42 + 0.20
P(C1) = 0.62

We can similarly infer the probabilty of (C2) using a similar formula to that used above:

P(C2) = [P(C2|H2)  x P(H2)] + [P(C2|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C2):

P(C2) = (0.8 x 0.6) + (0.5 x 0.4)
P(C2) = 0.48 + 0.20
P(C2) = 0.68

We can also infer the probability of (C3) using a similar formula to that used above:

P(C3) = [P(C3|H2)  x P(H2)] + [P(C3|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C3):

P(C3) = (0.9 x 0.6) + (0.3 x 0.4)
P(C3) = 0.54 + 0.12
P(C3) = 0.66

Based on the probabilities that Dr. Erasmus assigns to elements on the right-hand side of his instance of Bayes’ Theorem, the probabilities of (C1), (C2) and (C3) would be as follows:

P(C1) = 0.62
P(C2) = 0.68
P(C3) = 0.66

NONE of these probabilities is a LOW probability. A low probability would have to be less than .5, but all three of these probabilities are significantly greater than .5.
So, Dr. Erasmus FAILED to assign probabilities in such a way that (C1), (C2), and (C3) have low probabilities, and thus his counterexample FAILS. The point of his counterexample was to SHOW that the probability of the hypothesis H2 could be high even if the probabilities of (C1), (C2), and (C3) were low. But his assigned probability values FAIL to provide an example where the probabilities of (C1), (C2), and (C3) are all low. In his example NONE of these statements has a low probability.

bookmark_borderReply to Dr. Erasmus – Part 1: Untrained in Probabilistic Logic?

MY UNDERSTANDING OF PROBABILITY

Dr. Jacobus Erasmus has raised an objection to one of my posts on the resurrection.
Before presenting his objection he takes a swipe at my credibility:
…Bowen’s argument is an example of what happens when a blogger who is untrained in probabilistic logic tries their hand at probability.
…Bowen does not seem to be aware of Bayes’ Theorem; it appears that he has come up with his own idea of how probabilities should be calculated.
I’m not sure what Dr. Erasmus knows about my education, because he provides NO FACTS or evidence about my education.  It is not correct to say that I am “untrained in probabilistic logic”.  I took multiple courses in logic and critical thinking as an undergraduate student of philosophy, and I took multiple courses in logic and was a teaching assistant for multiple courses in logic and critical thinking as a graduate student of philosophy.  I learned some basic probabilistic logic in these courses both as an undergraduate student and as a graduate student.
I did not learn about Bayes’ Theorem in the logic and critical thinking classes that I took nor in the logic and critical thinking courses that I helped teach.  So, that is a potential weakness in my educational background.  However, I have been studying Richard Swinburne’s book The Existence of God  for many years, and that has required that I develop a basic understanding of Bayes’ Theorem.  Most of what I have learned about Bayes’ Theorem comes from Swinburne, who is an expert on this subject.  Although I have not had any courses that included Bayes’ Theorem, I have learned about this theorem from a qualified expert.
 

SOME DOUBTS ABOUT DR. ERASMUS’ UNDERSTANDING OF PROBABILITY

Since Dr. Erasmus questions my credibility in terms of my educational background,  I will return the favor.  His educational background is in Information Technology (an undergraduate degree) and Philosophy (a PhD).  So far as I know, courses in Probability are NOT required for either Information Technology nor for Philosophy degrees.  So, it is not clear to me that Dr. Erasmus has had ANY classes in Probability.  I suspect that he has had some classes in logic, but logic classes don’t necessarily cover Probability calculation.  Maybe Dr. Erasmus took a Probability class or two in order to fulfill a math or logic requirement.  I don’t know.  But his degrees don’t imply that he has ANY background in probability calculation.
There are a few obvious problems with Dr. Erasmus’ short post that indicate to me that he does NOT understand probability well.
First, he provides NO EXPLANATIONS in his post.  He neither EXPLAINS my alleged error, nor EXPLAINS his own example of a probability calculation.  If he really understood probability, then I would expect him to clearly EXPLAIN both points, so the absence of any such explanations suggests to me that he doesn’t really understand what he is talking about.
Second, he contradicts himself in the counterexample that he provides.  On the one hand, he assigns an estimated probability of 0.6 to the claim that The butler is a murderer.  But then he immediately turns around and calculates a probability of 0.9 that  the butler murdered Jones.   Those two probabilities CANNOT BOTH BE CORRECT.  A third grader could see that!  But not Dr. Erasmus.
If the probability that the butler murdered Jones was truly 0.9, then the probability that The butler is a murderer must be AT LEAST 0.9; it can’t be less than 0.9.  There is some chance that the butler murdered somebody else besides Jones, so the probability that The butler is a murderer must be 0.9 plus the probability that the butler murdered someone else besides Jones.   Dr. Erasmus contradicts himself in the space of just a few paragraphs while presenting his counterexample to my reasoning.  I am not impressed by such sloppy thinking.
Third,  one of the pieces of evidence in Dr. Erasmus’ counterexample makes his example inappropriate:
The butler was the only other person in the house when Jones died.
This bit of evidence all by itself makes it highly probable that the butler murdered Jones.  The counterexample involves the murder of Jones by means of someone hitting him in the head with a brick.  If the butler was “the only other person in the house when Jones died”, then it would be nearly impossible for anyone other than the butler to have committed the murder of Jones.  This one bit of evidence makes the other evidence largely irrelevant. Given this one bit of evidence, it is already determined that it is highly probable that the butler murdered Jones.   But Dr. Erasmus fails to see this obvious point.
Furthermore, this makes the supposed counterexample a poor one, since the probability calculation concerning the resurrection of Jesus does NOT include such a bit of evidence that all by itself could settle the issue, at least not in support of the hypothesis.  Many of the claims that I consider are necessary conditions of the hypothesis “God raised Jesus from the dead”.  The falsehood of a necessary condition would thus immediately establish with certainty the falsehood of the hypothesis.  But none of the claims I consider would all by itself show the hypothesis to be true or highly probable.
Fourth,  Dr. Erasmus complains about my supposed ignorance concerning Bayes’ Theorem, but he inaccurately describes my reasoning by leaving out the fact that I make use of CONDITIONAL PROBABILITIES, which are crucial to Bayes’ Theorem.  So, Dr. Erasmus mischaracterizes my reasoning in a way that divorces my reasoning from the logic of Bayes’ Theorem.  It is very clear that I am making use of CONDITIONAL PROBABILITIES when I talk about multiplication of probabilities in the case of assessing the hypothesis that “God raised Jesus from the dead”:
========================

The main claim that God raised Jesus from the dead, (GRJ), assumes or implies various other related Christian beliefs:
(GE) God exists.
(GPM) God has performed miracles.
(JEP) Jesus was a Jewish man who existed in Palestine in the first century.
(JWC) Jesus was crucified in Jerusalem in about 30 CE.
(DOC) Jesus died on the cross on the same day he was crucified.
(JAW) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.
(JRD) Jesus rose from the dead.
[…]
The multiplication of probability applies to the claim that Jesus rose from the dead, (JRD). Suppose that the probability of (JEP) was .8, and that the probability of (JWC) was .8 given that (JEP) is true (and 0 if (JEP) is false), and suppose that the probability of (DOC) was .8 given that (JWC) is true (and 0 if (JWC) is false), and suppose that the probability of (JAW) was .6 given that (DOC) is true, then the probability of (JRD) would be approximately:
.8 x .8 x .8 x .6 = .3072
or about three chances in ten.  Thus, (JRD) could be improbable, even if the various individual claims related to it were ALL either probable or very probable.
[an excerpt from my post that Dr. Erasmus is criticizing]
=============================
If Dr. Erasmus is familiar with probability calculations, then he would know that the expression
…the probability of (JWC) was .8 given that (JEP) is true…
is a reference to CONDITIONAL PROBABILITY.  But there is no hint in Dr. Erasmus’ post that he is aware that I was making use of CONDITIONAL PROBABILITIES.
So, either he FAILED to notice this obvious and important element of my reasoning, and thus shows himself to be ignorant about probability calculations, or else he DID notice this obvious and important element of my reasoning, but he dishonestly suppressed this fact in order to make me appear to be ignorant about probability calculations.  Bayes’ Theorem is derived from a basic principle of CONDITIONAL PROBABILITY.
Fifth, Dr. Erasmus appears to infer an UNCONDITIONAL PROBABILITY, when the instance of Bayes’ Theorem that he spells out clearly only establishes a CONDITIONAL PROBABILITY:
In this case, the odds in favour of H2 is about 10:1 (ten to one), which converts to a probability of 0.9 (or 90%) for H2.
He appears to infer that the unconditional probability of H2 is 0.9, but that is NOT what his instance of  Bayes’ Theorem shows.  The left side of his instance of the equation contains CONDITIONAL PROBABILITIES:
P(H2 | C1 & C2 & C3) / P(~H2 | C1 & C2 & C3)
So, what Dr. Erasmus is calculating is the relative probability of H2 vs. not-H2, given that C1 and C2 and C3 are true. 
This tells us NOTHING about the probability of H2 if we don’t know whether C1, C2, or C3 are true!  What he has shown is merely that H2 is highly probable IF we knew for certain that C1, C2, and C3 were true.  This example is irrelevant to the case of the resurrection of Jesus, where we are not dealing with facts that are known to be true, but are instead dealing with claims that only have some degree of probability.
It might be the case that Dr. Erasmus has more “training” or education than I do about Bayes’ Theorem, but his degrees don’t show that to be the case,  and the various problems with his post (that I have pointed out above) suggest to me that he does NOT have a good understanding of probability.
To Be Continued…

bookmark_borderWhy I Reject the Resurrection – Part 6: Non-Standard Resurrection

THE NON-STANDARD RESURRECTION OBJECTION
In this post I will state one objection to the logic of my thinking about the probability of the resurrection. I will also discuss and respond to this objection.  In the next post I will state a second objection to the logic of my thinking about the probability of the resurrection.  The second objection is based on the logic of Richard Swinburne’s thinking about the probability of the resurrection.
Some of the beliefs or claims that I have focused on represent a summary of the traditional Christian view of the death and resurrection of Jesus, specifically the following three claims:
(JWC) Jesus was crucified in Jerusalem around 30 CE.
(DOC) Jesus died on the cross on the same day he was crucified.
(JAW) Jesus was alive and walking around in Jerusalem less than 48 hours after he was crucified.
A careful reader might point out that some of the details of these claims are not absolutely necessary in order for it to be the case that God raised Jesus from the dead.   
Suppose, for example, that Jesus was crucified in Jerusalem but this happened in the year 40 CE, not around 30 CE.  In that case (JWC) would be false, but it could still be the case that Jesus died on the cross, and was alive and walking around in Jerusalem less than forty-eight hours after he was crucified.  Furthermore, in this scenario Jesus died and rose again from the dead, and God, if God exists, could have caused the resurrection of Jesus in 40 CE just as well as he could have done so in 30 CE.  So, in this “non-standard” scenario, (JWC) would be false, but (GRJ) could, nevertheless, be true.
In my probability tree diagram for the resurrection, there is only one branch coming off of ~(JWC) and that branch goes to ~(GRJ).  So, the diagram implies that if it is NOT the case that Jesus was crucified in Jerusalem around 30 CE, then it is NOT the case that God raised Jesus from the dead.  But, someone might object, we can imagine a scenario where (JWC) is false, but where (GRJ) is true.  So, the diagram is mistaken, and thus any calculation of the probability of (GRJ) based on the diagram would also be mistaken.
 
 
RESPONSE TO THE NON-STANDARD RESURRECTION OBJECTION
My general reply to the non-standard resurrection objection is that such non-standard scenarios usually undermine the reliability of the Gospel accounts and thus lower the probability of the claim that God raised Jesus from the dead in that respect, thus nullifying whatever modest increase in probability they provide by pointing to non-standard scenarios that support this claim.
Although this objection does not obviously apply to the claim that Jesus existed, it does have some relevance to that general issue:
JE.  Jesus existed.
On the one hand, if we understand the word “Jesus” too broadly, then it will fail to pick out just ONE specific person, which would mean that (JE) was neither true nor false.  On the other hand, if we understand the word “Jesus” too narrowly, then it will unreasonably exclude too many potential candidates, which would mean that the falsehood of this claim would be compatible with the existence of a person who most reasonable people would consider to be the Jesus talked about in the Gospels.
If we understand the word “Jesus” in this context to simply mean “the Jewish man named ‘Jesus’ who lived in Palestine in the first century”, then (JE) will be neither true nor false, because there were in fact MANY Jewish men named ‘Jesus’ who lived in Palestine in the first century.  The expression “the Jewish man named ‘Jesus’ who lived in Palestine in the first century” is about as meaningful as the expression “the white man named ‘David’ who lived in California in the 20th century”.  There are thousands of such men, so this expression fails to pick out just ONE man.  So, we must understand the meaning of the word “Jesus” in a way that is likely to narrow down to just ONE man.
If, on the other hand, we understand the word “Jesus” in this context to mean “the person who matches up perfectly to every claim and every detail in all four canonical Gospels about the character named ‘Jesus’,” then probably no one could possibly fit this description, because the Gospels appear to make conflicting and contradictory claims about Jesus and what Jesus said and did.
Furthermore, even if we set aside any conflicting events or details about Jesus in the Gospels, there seems to be no good reason to insist on such a narrow understanding of the word “Jesus”.  If there was one particular man who was Jewish and who lived in Palestine in the first century and whose life was a match for most of the events and details of the Gospels, then that man is clearly a good candidate for being the “Jesus” who was discussed in the Gospels, even if there are some events or details in the Gospels that did not occur in the life of that man.
In short, the claim (JE) could be subject to the non-standard resurrection objection, if the word “Jesus” was interpreted too narrowly, requiring that a good candidate for being “Jesus” matches every little detail in all four Gospels concerning the “Jesus” character.  In that case, even if (JE) were false, there could still be a Jewish man who lived in Palestine in the first century who was a close enough match with the “Jesus” character in the Gospels for a reasonable person to conclude that this man was indeed the man whom the Gospels describe with fair, but not complete, accuracy.
The first claim that is obviously subject to the non-standard resurrection objection is about the crucifixion:
JWC.  Jesus was crucified in Jerusalem around 30 CE.
There are other possibilities that could still support the ultimate conclusion that God raised Jesus from the dead.
One possibility, mentioned above, is that Jesus was crucified in Jerusalem, but this occurred in 40 CE, not “around 30CE”.  Jesus did not have to die in 30 CE in order for God, if God exists, to raise him from the dead.  However, if Jesus was crucified in 40 CE, then Pilate would not have presided over the trial of Jesus, nor would Pilate have ordered Jesus to be crucified, nor would Pilate have granted permission for anyone to remove the body of Jesus from the cross and bury his body in a tomb.   Pilate ceased to be the Roman governor of Judea in 36 CE, so he would not have presided over a trial of Jesus, if that trial occurred in 40 CE.  But if Pilate had no role in Jesus’ trial, crucifixion, and burial, then large portions of the passion narratives in the Gospels are works of fiction, or are at best highly unreliable third and fourth hand accounts of those events.
But if the passion narratives in the Gospels are works of fiction or highly unreliable accounts of those events, then that undermines the credibility of the Gospels concerning the other historical claims:
DOC.  Jesus died on the cross on the same day he was crucified.
JAW.  Jesus was alive and walking around in Jerusalem less than 48 hours after he was crucified.
If the trial of Jesus before Pilate is fictional, then it is quite likely that other events and details in the Passion Narratives are also fictional.  We would have little reason to believe DOC or JAW with any significant degree of certainty, if the trial of Jesus before Pilate is fictional.  So, although it is indeed a possibility that Jesus existed and that Jesus was crucified in 40 CE rather than around 30 CE, such a non-standard scenario would fail to make it more probable that God raised Jesus from the dead, because this scenario implies that the Gospel accounts of the alleged death and resurrection of Jesus are historically unreliable and may be largely or completely fictional.
If we move the date of the crucifixion even further, it would totally destroy the credibility of the Gospels.  Suppose that Jesus was crucified in the year 120 CE.  Pilate would be dead by then, so we again would have a large chunk of fiction in the Passion Narratives.  But an even bigger problem than that is that the Gospels were written in the second half of the first century, so all four Gospels had already been written PRIOR to the crucifixion of Jesus, based on this non-standard scenario.  That would clearly destroy any credibility the Gospel accounts have.  A reasonable person will place no confidence in an historical account that was written decades PRIOR to the events that it supposedly describes.
What if the crucifixion took place in 30 CE, but not in Jerusalem?  In that case, (JWC) would be false, but it could still be the case that God raised Jesus from the dead, because God, if God exists, is omnipotent and omnipresent, so God could perform a resurrection anywhere that he wants to.   Suppose that Jesus was crucified in 30 CE in Tiberias, on the western shore of the Sea of Galilee.  In that case (JWC) would be false, but it would still have been possible for Jesus to die on the cross and for God to raise Jesus from the dead.
Once again, this does show that it is possible for (JWC) to be false and yet for (GRJ) to be true.  However, if Jesus had been crucified in Tiberias in 30 CE, then Pilate would not have presided over Jesus’ trial, because Pilate was not the Roman governor of that area of Palestine.  So, this non-standard crucifixion scenario implies that a good chunk of the Passion Narratives are fictional, and thus implies that the Gospels, and the Passion Narratives in particular are historically unreliable.
Furthermore, it is not just the trial of Jesus that is clearly set in Jerusalem.  Jesus and his disciples have come to celebrate Passover in Jerusalem along with hundreds of thousands of other devout Jews.  The Last Supper was in Jerusalem.  The temple guard played a role in Jesus’ arrest.  The Jewish temple was in Jerusalem.  The high priest and the priesthood of the Jewish temple are involved in bringing about the crucifixion of Jesus, according to the Gospels.  So, if the crucifixion of Jesus took place in Tiberias rather than Jerusalem, then that implies that the Passion Narratives are either mostly or completely fictional, and thus that no reasonable person could place any confidence in the historical accuracy of the events and details presented in the Passion Narratives.
What if Jesus was executed in Jerusalem in 30 CE, but he was beheaded with a sword or an ax, and was not crucified?  Once again, God, if God exists, could still raise Jesus from the dead, no matter how Jesus had been killed.  However, if Jesus was beheaded rather than crucified, then the Gospel accounts of Jesus trial, crucifixion, and burial, are either mostly or completely fictional, because the cross and the crucifixion are ubiquitous throughout the Passion Narratives.
At Jesus trial, people cry out “Crucify him!” according to the Gospels.  Jesus carries his cross to the execution site, according to the Gospels.  Jesus was crucified according to the Gospels.  People speak to Jesus on the cross, and watch Jesus on the cross, and Jesus speaks to people from the cross.  After Jesus allegedly dies, Joseph of Arimathea removes Jesus from the cross.  If there was no crucifixion, then all of this is fiction.   So, if we assume this non-standard scenario, where Jesus is beheaded rather than crucified, then the credibility of the Gospel accounts of Jesus’ trial, death and burial is completely destroyed.
I think walking through these examples of non-standard death and resurrection scenarios concerning (JWC) is sufficient to show the strength of my reply to the non-standard resurrection objection.  The further one departs from the traditional Christian story about the alleged death, burial,  and resurrection of Jesus, the more one undermines the credibility of the Gospel accounts, which is the primary evidence we have for the historical claims required to show that Jesus rose from the dead and that God raised Jesus from the dead.  
Therefore, although such non-standard resurrection scenarios do show that it is possible for one or more of the main historical claims to be false and yet for the ultimate conclusion (GRJ) to be true, this objection is weak because such non-standard scenarios usually also undermine the credibility of the Gospel evidence, and thus these scenarios fail to significantly increase the probability that God raised Jesus from the dead, relative to the results of probability calculations that make use of my probability tree diagram of the resurrection.

bookmark_borderWhy I Reject the Resurrection – Part 5: Multiplication of Probabilities

INTRODUCTION
In this post I will spell out the basic logic of my current thinking about the probability of the resurrection.
First, I give an example of a probability tree diagram and calculation where the events are independent of each other (coin tosses).  Next, I give an example of a probability tree diagram and calculation where the events are NOT independent (card draws).  Third, I present a probability tree diagram and calculation for the claim that God raised Jesus from the dead.
 
PROBABILITY TREE DIAGRAMS
1. Probability Tree Diagram of Coin Tosses (click on image for a clearer view of the diagram):

 
 
 
 
 
 
 
 
Coin tosses are independent events.  Whether you get heads or tails on the first coin toss has no impact on the probability of getting heads on the second toss.  With a fair coin, the probability is always .5 that heads will be the outcome of a toss.
The above diagram represents a series of two coin tosses.
H1.  The outcome of toss 1 is HEADS.
H2. The outcome of toss 2 is HEADS.
The probability that heads will be the outcome of the first toss and also the outcome of the second toss can be calculated by multiplying the probability of getting heads on the first toss times the probability of getting heads on the second toss.
P[(H1) & (H2)] =  P(H1) x P(H2)
= .5  x  .5
= .25
So, the probability of getting heads on both tosses is .25.
2. Probability Tree Diagram of Card Draws (click on image for a clearer view of the diagram):

 
 
 
 
 
 
 
 
Card draws (without replacing the card that was drawn back into the deck prior to drawing the next card) are NOT independent events.  Whether you get a RED card on the first draw impacts the probability of getting a RED card on the second draw.
For example, if you get a RED card on the first draw, then there is one less card in the deck and one less RED card remaining in the deck.  So, although the probability of getting a RED card on the first draw is 26/52 = .5, the probability of getting a RED card on the second draw (after getting a RED card on the first draw) is less than .5, namely  25/51 =  .4902  (rounded to four decimal places).
The above diagram represents a series of two card draws.  The probability that a RED card will be the outcome of the first draw and also the outcome of the second draw can be calculated by multiplying the probability of getting a RED card on the first draw (.5) times the probability of getting a RED card on the second draw given that the first card drawn was RED (.4902).  So, the probability of getting heads on both tosses is equal to .5 x .4902, which is equal to: .2451 (rounded to four decimal places).
Although the outcomes of the draws are NOT independent events, we can still use multiplication of probabilities in the calculation, but the probability of the second draw must be understood in terms of a CONDITIONAL PROBABILITY:
R1.  The first card drawn is a RED card.
R2.  The second card drawn is a RED card.
To calculate the probability of getting a RED card on the first draw and a RED card on the second draw, we need to multiply the probability of (R1) times the probability of (R2) given that (R1) is the case:
P[(R1) & (R2)] = P(R1) x P[(R2)|(R1)]
P[(R1) & (R2)] = 26/52  x   25/51
= .5  x  .4902
= .2451
 
3. Probability Tree Diagram of The Resurrection:

 
 
 
 
 
 
 
 
The first branch of the tree diagram concerns the probability of the existence of God:
GE.  God exists.
Either (GE) is true or it is not.  If it is not the case that God exists, then it is also not the case that God raised Jesus:
GRJ. God raised Jesus from the dead.
So, if ~(GE) is the case, then it is certain that ~(GRJ) is the case.
However, if God exists, then it is possible that God has performed miracles, but the existence of God does not imply that God has performed miracles.  It is possible that God exists but does not perform miracles (other than having created the universe).
GPM.  God has performed miracles.
Either (GPM) is the case or it is not.  If it is not the case that God has performed miracles, then it is also not the case that God raised Jesus from the dead.  So, if ~(GPM) is the case, then it is certain that ~(GRJ) is the case.
Either Jesus existed or it is not the case that Jesus existed.
JE.  Jesus existed.
If it is not the case that Jesus existed, then it is not the case that God raised Jesus from the dead.  So, if ~(JE) is the case, then it is certain that ~ (GRJ) is the case.
However, if Jesus did exist, then it is possible that he was crucified in Jerusalem around 30 CE, as the Gospels indicate:
JWC.  Jesus was crucified in Jerusalem around 30 CE.
If Jesus was crucified in Jerusalem around 30 CE, then he might have died on the cross the same day he was crucified, as the Gospels indicate:
DOC.  Jesus died on the cross the same day he was crucified.
If Jesus died on the cross, then he might have been alive again less than 48 hours later, as the Gospels indicate:
JAW.  Jesus was alive and walking around in Jerusalem less than 48 hours after he was crucified.
If God raised Jesus from the dead, then the following claims are true:
(GE), (GPM), (JE), (JWC), (DOC), and (JAW)
However, even if all of these claims are true, it does not follow that God raised Jesus from the dead, because it is also possible that Jesus rose from the dead but this event was NOT caused by God but by some other being or force.
It is important to note that the probability calculation for this probability tree is more like the card draw example than the coin toss example.  These claims and events are NOT independent of each other.
For example, if it is NOT the case that God exists, then that impacts the probability of the claim that  God has performed miracles; if there is no God, if (GE) is NOT the case, then the probability of (GPM) would be ZERO.   If it is NOT the case that Jesus existed, then it is also NOT the case that Jesus was crucified in Jerusalem around 30 CE.  If (JE) is NOT the case, then the probability of (JWC) would be ZERO.
Because these claims and events are not independent, we need to use conditional probability when determining the probability of each branch of the tree diagram.  It would be incorrect to simply multiply the probability of the existence of God times the probability that God has performed miracles:
P[(GE) & (GPM)] =  P(GE)  x  P(GPM)  
Rather, we need to use the probability that God has performed miracles GIVEN that God exists.  This conditional probability is written like this:
P[(GPM)| (GE)]
The proper equation for the combination of these two claims is this:
P[(GE) & (GPM)] = P(GE)  x  P[(GPM)|(GE)] 
As we follow the branches of the probability tree diagram to get to the final branch between (GRJ) and ~(GRJ), we need to understand that more and more assumptions are being added to the condition of the conditional probability.  When we get to the final branch of the probability tree diagram, the probability of (GRJ) that we use as a factor in the calculation, is the probability of (GRJ) GIVEN that (GE) and (GPM) and (JE) and (JWC) and (DOC) and (JAW) are true:
P[(GRJ) | (GE) & (GPM) & (JE) & (JWC) & (DOC) & (JAW)]
This, of course, must be multiplied times the probability that all of those conditions or assumptions are true:
P[(GE) & (GPM) & (JE) & (JWC) & (DOC) & (JAW)]
Because these various conditions or assumptions are NOT independent of each other, we must also understand that the probability of the conjunction of these conditions or assumptions also requires the use of conditional probabilities.  But the overall equation for the probability of the resurrection can be written in this “short” form:
P(GRJ) =
P[(GRJ) | (GE) & (GPM) & (JE) & (JWC) & (DOC) & (JAW)]   x   P[(GE) & (GPM) & (JE) & (JWC) & (DOC) & (JAW)]
The probability of the resurrection of Jesus is equal to the probability of the resurrection of Jesus GIVEN the various assumptions outlined here TIMES the probability of the conjunction of the truth of all those various assumptions.
 
THE NEXT POST
In the next post after this one, I will consider two objections to this logic.
The first objection seems to me to be correct, but I believe it to be a relatively minor problem with my logic. The second objection is based on the logic of Richard Swinburne’s thinking about the resurrection, and that objection, it seems to me, is potentially a more serious objection that might point to a major problem with my logic.
I don’t know if the second objection is correct, so I’m not ready to abandon the basic logic of my current thinking about the resurrection, but I do need to either come up with a plausible reply to this second objection or else make some modifications to the logic of my current thinking about the probability of the resurrection.

bookmark_borderWhy I Reject the Resurrection – Part 4: Skepticism about the Supernatural

SKEPTICAL CLAIMS ABOUT SUPERNATURAL BELIEFS
Two points from my List of Key Points about the resurrection relate directly to skepticism about the supernatural:

1. Nobody KNOWS that supernatural beings exist.

2. Nobody KNOWS that supernatural events occur.

There are two more related points that should be added to the above two points:

21. Nobody KNOWS that supernatural powers exist.

22. Nobody KNOWS that supernatural forces exist.

One form of skepticism about (1) and (2) concerns the question of the TRUTH of supernatural claims:

10. It is IMPROBABLE that any supernatural being exists.

11. It is IMPROBABLE that any supernatural events occur.

So, we can add two more improbability claims in relation to the two added skeptical claims:

23. It is IMPROBABLE that any supernatural powers exist.

24.  It is IMPROBABLE that any supernatural forces exist.

In my previous comments about skepticism (see Skepticism about the Resurrection), I point out two different forms of qualified skepticism:

  • Denial that beliefs or claims in area X are JUSTIFIED/WARRANTED.
  • Denial that beliefs or claims in area X are TRUE.

So, in addition to the four improbability claims above, (10), (11), (23), and (24), we can add four skeptical claims about the lack of justification/warrant for supernatural claims:

25. Nobody has a JUSTIFIED/WARRANTED belief that supernatural beings exist.

26. Nobody has a JUSTIFIED/WARRANTED belief that supernatural events occur.

27. Nobody has a JUSTIFIED/WARRANTED belief that supernatural powers exist.

28. Nobody has a JUSTIFIED/WARRANTED belief that supernatural forces exist.

 
REASONS FOR SKEPTICISM ABOUT THE SUPERNATURAL
My main reasons for skepticism about the supernatural may be summarized this way:

 
 
 
 
 
 
 
Skepticism about the supernatural may be based on a combination of science and cynicism, and cynicism itself is supported by science.
I’m not claiming that all skeptics think this way.  Rather, this is a representation of my own thinking, of why I am a skeptic. This is a summary or overview of how I would defend skepticism, especially skepticism about the supernatural.
 
CYNICISM
By “cynicism” I mean a collection of negative beliefs about human thinking and behavior that provide reasonable grounds for suspicion and doubt about the rationality and truthfulness and reliability of human beings in general, such as:

30. Many people are stupid.

31. Many people are ignorant.

32. Many people are uncritical  or sophistic thinkers.

33. Many people are influenced by egocentric and sociocentric biases.

34. Many people form important beliefs based on indoctrination, propaganda, or group think.

35. Many people are dishonest or deceptive.

36. Many people have false beliefs based on unreliable memories. 

37. Many people have false beliefs based on unreliable eyewitness testimony.

38. Many people have false beliefs based on cognitive biases.

39. Many people are mentally handicapped or are mentally ill or are addicted to alcohol or drugs.

Here is one simple fact that strongly supports cynicism:  nearly half of Americans who voted in the last presidential election (46% of voters) voted for Donald Trump.  Here is a related fact that is almost as depressing: 72% of Republicans say that Donald Trump is a good role model for children, and only 22% of Republicans say that he is NOT a good role model for children.
 
SCIENCE SUPPORTS CYNICISM
Psychology, Sociology, and other human sciences provide empirical data and empirically confirmed theories and generalizations about human thinking and human behavior that generally support a cynical view about human thinking and human behavior.  Thus, scientific investigation supports cynicism, in the sense that I have explained above.
 
SCIENCE CASTS DOUBT ON SUPERNATURAL BELIEFS
Many ancient supernatural beliefs have been cast into doubt by scientific investigation into the relevant phenomena.  Many contemporary supernatural beliefs have also been cast into doubt by scientific investigation into the relevant phenomena.  Whenever careful objective scientific investigation is conducted into alleged supernatural phenomena, it turns out that either the phenomena doesn’t actually exist, or it exists but is the product of deception and/or that the phenomena has a natural explanation and can be reproduced by natural means.  As the years go by, more and more phenomena can be given plausible natural scientific explanations, and fewer and fewer phenomena remain as potential candidates for having a supernatural cause or explanation.

40. Science casts doubt on belief in supernatural agents.

41. Science casts doubt on belief in supernatural events.

42. Science casts doubt on belief in supernatural powers.

43. Science casts doubt on belief in supernatural forces.

bookmark_borderWhy I Reject the Resurrection – Part 3: Improbability of the Resurrection

IMPROBABILITY
Some Christians believe that it is certain that God raised Jesus from the dead; other Christians believe that it is very probable but not certain that God raised Jesus from the dead.  Some people believe that it is probable but not very probable that God raised Jesus from the dead.
Some skeptics believe that it is certain that the claim God raised Jesus from the dead is FALSE, but other skeptics believe that it is very improbable that God raised Jesus from the dead but not certain that this claim is FALSE.  Some people believe that it is improbable but not very improbable that God raised Jesus from the dead.

  • A belief that is certain has a probability of:  1.0
  • A belief that is as probable as not has a probability of:  .5
  • A belief that is certainly false has a probability of:  0

We can make probability evaluations more precise by defining numeric values for some common probability expressions:
1. It is certain that X is false:
the probability of X  is 0.
2. It is very improbable that X is true but not certain that X is false:
the probability of X is less than .2 but is greater than 0.
3. It is improbable but not very improbable that X is true:
the probability of X is less than .4 but is at least .2.
4. It is about as probable as not that X is true:
the probability of X is at least .4 but is less than .6.
5. It is probable but not very probable that X is true:
the probability of X is at least .6 but is less than .8.
6. It is very probable but not certain that X is true:
the probability of X is at least .8 but is less than 1.0.
7. It is certain that X is true:
the probability of X is 1.0.
 
RESURRECTION
See comments in the “Resurrection” section of Part 2 of this series.
 
IMPROBABILITY OF THE RESURRECTION
The main claim that God raised Jesus from the dead, (GRJ), assumes or implies various other related Christian beliefs:

(GE) God exists.

(GPM) God has performed miracles.

(JEP) Jesus was a Jewish man who existed in Palestine in the first century.

(JWC) Jesus was crucified in Jerusalem in about 30 CE.

(DOC) Jesus died on the cross on the same day he was crucified.

(JAW) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.

(JRD) Jesus rose from the dead.

If any of these claims are improbable, then (GRJ) is also improbable.  If (GE) is improbable, then (GRJ) is improbable.  If (GPM) is improbable, then (GRJ) is improbable.  If (JEP) is improbable, then (GRJ) is improbable, if (JWC) is improbable, then (GRJ) is improbable, and so on.  Conversely, each of these claims must AT LEAST be probable in order for (GRJ) to be probable.
Furthermore, because we must in general multiply probabilities of individual events to obtain the probability of a complex event, even when each individual event is probable, the complex event (or claim) which consists in the conjunction of those various individual events (or claims) might well be improbable.
The probability of rolling a die and getting an even number (2, 4, or 6) is .5, but the probability of rolling a die twice and getting an even number on both rolls is .5 x .5 or .25.  The probability of rolling a die three times and getting an even number on all three rolls is .5 x .5 x .5 = .125, just a little over one chance in ten.
The multiplication of probability applies to the claim that Jesus rose from the dead, (JRD). Suppose that the probability of (JEP) was .8, and that the probability of (JWC) was .8 given that (JEP) is true (and 0 if (JEP) is false), and suppose that the probability of (DOC) was .8 given that (JWC) is true (and 0 if (JWC) is false), and suppose that the probability of (JAW) was .6 given that (DOC) is true, then the probability of (JRD) would be approximately:
.8 x .8 x .8 x .6 = .3072
or about three chances in ten.  Thus, (JRD) could be improbable, even if the various individual claims related to it were ALL either probable or very probable.

bookmark_borderWhy I Reject the Resurrection – Part 2: Skepticism about the Resurrection

SKEPTICISM
Skepticism is the denial of knowledge.  Universal skepticism denies the possibility of any kind of knowledge, or the actual existence of any kind of knowledge.  Qualified forms of skepticism deny the possibility of knowledge in particular areas, or the actual existence of knowledge in particular areas, such as religious knowledge or knowledge of the future.
Knowledge is traditionally understood to be Justified True Belief, because one can have a true belief by accident or luck, but such true beliefs don’t count as knowledge.  ALL known beliefs are true beliefs, but SOME true beliefs are not known beliefs.  Traditionally, the difference between true beliefs that makes some of them known beliefs, is that the person who has the belief is JUSTIFIED in holding that belief.  To be justified in holding a belief means that one has GOOD REASON to be confident that the belief in question is a true belief.
According to foundationalism (a view of the nature of knowledge) some beliefs count as knowledge even though they are not based on or inferred from other beliefs.  Some beliefs are thought to count as knowledge even though those beliefs are not based on or inferred from other beliefs, but are produced naturally by our minds as the result of particular sensory input or experiences.
Because talking about beliefs being “justified” suggests that no belief counts as knowledge unless one can produce a “justification” or good reason for accepting that belief, the term “justified” can be objected to as carrying a bias against the possibility that some beliefs count as knowledge even though no “justification” or good reason can be given for accepting the belief in question.  The term “justified” also suggests that there are intellectual duties that must be satisfied in order for a belief to count as knowledge, but some philosophers object to the idea that intellectual duties must be satisfied in order for a belief to count as knowledge.
The Christian philosopher Alvin Plantinga suggests the use of the term “warranted” in place of the term “justified” as whatever it is that makes some true beliefs count as knowledge and the lack of which makes other true beliefs fail to count as knowledge.  Whether we use the term “warranted” or “justified”, it is clear that not all true beliefs are known beliefs, and that having a true belief by accident or by good luck falls short of being knowledge.
One can deny knowledge in area X, either by denying that there are any true beliefs in area X, or by denying that there are any justified/warranted beliefs in area X.  Both qualified kinds of skepticism can occur in a stronger or weaker form.
One strong form of qualified skepticism denies the possibility of there being any true beliefs in area X, and the related weak form of qualified skepticism simply denies that there are in fact any true beliefs in area X.  Another strong form of qualified skepticism denies the possibility of there being any justified/warranted beliefs in area X, and the related weak form of qualified skepticism simply denies that there are in fact any justified/warranted beliefs in area X.
 
THE RESURRECTION
By “the resurrection” I mean, the traditional Christian belief that:

(GRJ) God raised Jesus from the dead.

This belief is understood in the context of other traditional Christian beliefs:

(GE) God exists.

(GPM) God has performed miracles.

(JEP)  Jesus was a Jewish man who existed in Palestine in the first century.

(JWC)  Jesus was crucified in Jerusalem in about 30 CE.

(DOC) Jesus died on the cross on the same day he was crucified.

(JAW) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.

(JRD) Jesus rose from the dead.

 
In his book The Resurrection of God Incarnate (hereafter: ROGI), Richard Swinburne accurately characterizes the traditional Christian belief in the resurrection of Jesus:
…the Resurrection of Jesus understood in the traditional sense–of Jesus being dead for thirty-six hours and then coming to life again in his crucified body (in which he then had superhuman powers; e.g. he was able to appear and disappear).  (ROGI, p.1)
[In raising Jesus, God was] interfering in the operation of the natural laws by which he controls the universe.  For the coming-to-life again of a body dead for thirty-six hours is undoubtedly a violation of natural laws.  (ROGI, p.1-2)
The traditional Christian belief in the resurrection includes or implies: (GE), (GPM), (JEP), (JWC), (DOC), (JAW), (JRD), and (GRJ), and also the belief that God raising Jesus involved the violation of natural laws or interference in the operation of natural laws.
 
SKEPTICISM ABOUT THE RESURRECTION
Universal skepticism denies all knowledge, and so it denies that anyone knows that God raised Jesus from the dead.  But universal skepticism is implausible and indiscriminate, so it is not very interesting.  Qualified forms of skepticism can be more plausible.  One sort of qualified skepticism denies that people know that God exists.  If nobody knows that God exists, then nobody knows that God raised Jesus from the dead.
Skepticism about the resurrection, however, does not have to be based on skepticism about the existence of God.  One can be a skeptic about the existence of Jesus, or a skeptic about Jesus alleged death on the cross, or a skeptic about whether Jesus was alive and walking around in Jerusalem on Easter Sunday.  If nobody knows that Jesus existed, then nobody knows that Jesus rose from the dead, and nobody knows that God raised Jesus from the dead.  If nobody knows that Jesus was alive and walking around in Jerusalem on Easter Sunday, then nobody knows that Jesus rose from the dead, and nobody knows that God raised Jesus from the dead.
Skepticism about the resurrection could also be based on skepticism about supernatural powers or events, or skepticism about miracles.  For further discussion on skepticism about the supernatural, see Part 4 of this series.
A qualified form of skepticism can deny that people have a JUSTIFIED/WARRANTED BELIEF that Jesus existed, or that Jesus died on the cross, or that Jesus was alive on Easter Sunday.  Such skepticism could be argued on the grounds that Christians have failed to provide solid reasons and evidence showing that Jesus existed, or that Jesus died on the cross, or that Jesus was alive on Easter Sunday.  Or such a form of skepticism might be argued for more generally on the grounds that the available evidence, primarily the New Testament writings, is unreliable and insufficient to establish these beliefs related to the alleged resurrection of Jesus.
A qualified form of skepticism can deny that people have a TRUE BELIEF that Jesus existed, or that Jesus died on the cross, or that Jesus was alive on Easter Sunday.  Such skepticism could be argued on the grounds that the available evidence proves one or more of these beliefs to be FALSE, or that the available evidence shows one or more of these beliefs to be PROBABLY FALSE.

bookmark_borderWhy I Reject the Resurrection – Part 1: List of Key Points

SKEPTICISM ABOUT THE RESURRECTION
1. Nobody KNOWS that supernatural beings exist.
2. Nobody KNOWS that supernatural events occur.
3. Nobody KNOWS that God exists.
4. Nobody KNOWS that miracles occur.
5. Nobody KNOWS that Jesus existed.
6. Nobody KNOWS that Jesus died on the cross.
7. Nobody KNOWS that Jesus was alive on Easter morning.
8. Nobody KNOWS that Jesus rose from the dead.
9. Nobody KNOWS that God raised Jesus from the dead.
 
IMPROBABILITY OF THE RESURRECTION
10. It is IMPROBABLE that any supernatural being exists.
11. It is IMPROBABLE that any supernatural events occur.
12. It is IMPROBABLE that God exists.
13. It is IMPROBABLE that miracles occur.
14. There is a SIGNIFICANT PROBABILITY that Jesus did not exist.
15. IF Jesus did not exist, THEN it is CERTAIN that Jesus did not die on the cross, and did not rise from the dead.
16. IF Jesus existed and Jesus died on the cross, THEN it is IMPROBABLE that Jesus was alive on Easter morning.
17. IF Jesus existed and was alive on Easter morning, THEN it is IMPROBABLE that Jesus died on the cross.
18. IF God does not exist, THEN it is CERTAIN that the claim that “God raised Jesus from the dead” is a FALSE claim.
19. IF God does exist, THEN it is IMPROBABLE that God raised Jesus from the dead.
20. It is  IMPROBABLE that God raised Jesus from the dead (based on 12, 18, and 19).