bookmark_borderDebate: External Evidence for Jesus – Part 5A: Five Principles

Joe Hinman’s fifth argument for the existence of Jesus is presented in three sections:
5A. Historical Methods
5B. Big Web of Historicity
5C. Jesus Myth Theory Cannot Account for the Web
I will comment on, and raise objections to, points in each of these three sections, but this post will only cover part of the section on “Historical Methods”.  Specifically, I will cover the five high-level principles of historical investigation proposed by Hinman in his discussion of “Historical Methods”.
5A. Hinman on Historical Methods: Five General Principles
Hinman advocates the following five general principles of historical investigation:
P1. The document, not the people, is the point.
P2. Supernatural content does not negate historic aspects.
P3. What people believed tells us things, even if we don’t believe it.
P4. Everyone is biased.
P5. The historicity of a single persona cannot be examined apart from the framework.
 
Hinman’s first principle of historical investigation is this:
P1. The document, not the people, is the point.
I don’t know what (P1) means, and Hinman’s discussion of this idea does not make it any clearer.  Hinman’s discussion of (P1) makes a number of assertions that are interesting and worth thinking about, but I will comment on those more specific points in my next post on “Historical Methods”.  I won’t criticize what I don’t understand, so Hinman needs to clarify this principle before I will attempt to evaluate it.
The second principle put forward by Hinman is a bit clearer:
P2. Supernatural content does not negate historic aspects.
A comment by Hinman provides further clarification of (P2):
Historians do not discount sources merely for supernatural contents.  Even when they don’t believe the supernatural details, they don’t just deny everything the source says.
This is certainly a true point about how historians work, and I have no problem with the basic point.  However, there are some qualifications that I would add to this principle.
First, the Gospels don’t just have a few “supernatural details”.  They are filled with supernatural beings and events, from start to finish.  Here are a few supernatural elements from the beginnings of two Gospels (Matthew and Luke):

  • An angel visits Mary to tell her that she will become pregnant by the power of God, not by the usual biological process of sexual reproduction (Luke 1:26-38).
  • Mary miraculously becomes pregnant without first having sex with a man (Matthew 1:18-25).
  • An angel appears to some shepherds near Bethlehem to announce the birth of the Messiah, when Jesus is born there (Luke 2:1-20).
  • A multitude of angels appear to the shepherds and praise God (Luke 2:1-20).
  • A star indicates to some wise men from the East that a great king has been born in Palestine (Matthew 2:1-12).
  • The same star miraculously guides the wise men to the specific house where Mary and the baby Jesus were staying (Matthew 2:1-12).
  • Joseph, the husband of Mary, has a dream in which an angel warns him to take Mary and the baby Jesus away from Palestine, and Joseph follows this warning thus saving the baby Jesus from being killed in a mass slaughter of infants in Bethlehem by king Herod. (Matthew 2:13-23).

We have at least seven supernatural events surrounding the birth of Jesus in just the opening chapters of Matthew and Luke.  After that the miracles and supernatural events just keep on coming:  Jesus turns water into wine, Jesus heals the blind, the lame, and the deaf.  Jesus raises dead people back to life.  Jesus walks on water, calms a huge storm with a command, and feeds thousands of people with a few fishes and a few loaves of bread.  Jesus is levitated to the top of the temple by the devil and argues with the devil.  Jesus is transfigured and has a conversation with Moses and Elijah.  Jesus reads people’s minds.   Jesus miraculously causes huge collections of fish to congregate in the nets of his disciples.  Jesus dies and then comes back to life less than 48 hours later.  He then walks through a locked door, instantly vanishes from sight at will, and is able to levitate himself up into the sky.
The Gospels do not just contain a few “supernatural details”.  They are filled with supernatural beings (angels and demons and spirits) and supernatural events (miraculous healings, resurrections, mind reading, and nature miracles like levitation, walking on water, and controlling the weather).
Second, the supernatural elements in the Gospels are often essential to the stories related in the Gospels.  If we strip out all of the supernatural beings and events from the birth narratives, for example, there is not much left over.  If 75% of the assertions in the birth narratives are fictional, then why believe the 25% that remains?
It is possible that the very minimal historical claim “Jesus was born in Bethlehem” could be true, but given the general unreliability of the birth narratives (due in part to their being filled with supernatural beings and events), this also casts doubt on the tiny bit of historical “information” that remains after stripping out all of the clearly fictional B.S.  Given that Christians believed that the Old Testament predicted that the Messiah would be born in Bethlehem, and given that most of the other assertions in the birth narratives are historically dubious, we ought to be very skeptical about the claim “Jesus was born in Bethlehem” even though this claim does not, by itself, involve any supernatural elements.  It might represent prophecy that was used to formulate “history”.
What remains of the story of Jesus at the wedding in Cana if we delete his miracle of turning water into wine? Not much: Jesus went to a wedding in Cana. What remains of the story of Jesus walking on water on the sea of Galilee if we remove the walking on water part?  Not much: Jesus went in a boat with some of his disciples on the sea of Galilee. What remains of the transfiguration story if we remove the part about how Jesus began to shine like a bright light and if we remove the appearance of Moses and Elijah?  Not much: Jesus prayed with some of his disciples on a mountain top.  In a few stories the supernatural beings or events might be a detail that can be ignored, but in many cases the supernatural being or event plays an important role in the story, so that removing the supernatural element guts the story or seriously changes the meaning of the story or makes the story illogical and incoherent.
As David Friedrich Strauss argued long ago in The Life of Jesus, the attempt of skeptics to strip out all of the supernatural elements of the Gospels while still maintaining the basic historicity of the Gospel accounts makes no sense.  It makes far more sense to admit that Gospels are filled with legends and myths and fictional stories, and that only a few bits and pieces here and there, at best, are factual and historical.
Third, the assertion of this principle borders on a STRAW MAN fallacy.  There is the suggestion here that Jesus skeptics doubt the historicity of the Gospels ONLY because the Gospel stories contain supernatural elements.  Skeptics do NOT doubt the historicity of the Gospels ONLY because of there are a few supernatural details in them, nor do skeptics doubt the historicity of the Gospels ONLY because the Gospels are filled with supernatural beings and events.
Take the birth narratives in Matthew and Luke for example.  They include many supernatural elements, both supernatural beings (angels), and supernatural events (virgin birth, a star that guides people to a specific location).  These supernatural elements are one reason for doubting the historicity of these stories, but there are other reasons as well.  The Gospels of Matthew and Luke use Mark as a primary source of information about Jesus, but there is no birth story in Mark.  When Matthew and Luke follow the narrative framework in Mark, they generally agree with each other, but when they provide birth stories, their stories contradict each other, indicating that when they depart from the information in Mark, at least one of the two Gospels provides a fictional birth story, and perhaps both birth stories are fictional.
There are also some historically improbable details in both accounts beyond the supernatural elements.  The census in Luke is historically improbable for various reasons.  The slaughter of the innocents story in Matthew is historically improbable.  The relocation of the holy family to Egypt is historically improbable.  The fact that both Matthew and Luke place the birth of Jesus in Bethlehem in accordance with an alleged messianic prophecy, casts doubt on the historicity of that key shared claim between the two birth stories.
So, the rejection of the birth stories as legends or myths is not based ONLY on the fact that these stories are filled with supernatural elements.  There are other good reasons that point to the same conclusion.  Similar reasoning applies to skepticism about other parts of the Gospels.
Hinman’s third principle of historical investigation is a bit vague:
P3. What people believed tells us things, even if we don’t believe it.
I’m not sure what Hinman is getting at here, but taken straightforwardly, this principle seems obviously correct.  Using an historical document to determine what early Christians believed about God or Jesus “tells us things”, even if the historian rejects some or all of those beliefs.  At the very least, this tells us what early Christians believed about God or Jesus!  
This information about the beliefs of early Christians can also help historians to better analyze and evaluate particular Gospel stories and passages.  If early Christians believed that Jesus lived a perfectly sinless life, then historians could anticipate and look for places where the Gospels of Matthew and Luke modify some story or passage from Mark in order to make Jesus appear to be sinless, and to the extent that historians do find such modifications of Mark by Matthew and Luke, this provides further evidence that early Christians believed Jesus was sinless and also provides evidence that Matthew and Luke alter information from their sources to make the story or quotation fit better with their theological beliefs or the theological beliefs of their early Christian readers.
One of the things that the Gospels tell us is that early Christians were gullible and superstitious, at least if we assume that early Christian believers read the Gospels literally.  They believed in astrological signs, in angels, in demons, in demon possession, in the devil, in faith healing, in prophetic dreams, in levitation, in mind reading, in spirits of the dead, in raising the dead, in prophecy.  They believed all of these things without demanding strong evidence for claims of such events; they believed such things on the basis of hearsay and testimonial evidence,  on the basis of contradictory reports in the canonical Gospels, and without conducting serious skeptical investigations into the facts.  This is an important fact about early Christians that we can learn from reading the Gospels.  We can learn of the gullibility of early Christian believers even if we reject some or all of the beliefs that they formed in gullible and uncritical ways.
We can also learn that the early Christians were either not particularly good at logical and critical thinking or else were generally ignorant about the contents of the OT, because they were not skeptical about Jesus being a true prophet and the divine Son of God in spite of the various contradictions between Christian doctrines and the teachings of the Old Testament (e.g. OT: God rewards those who obey his commandments with wealth, health, peace and happiness in this life, but provides only a dark and miserable afterlife for good and evil people alike.  NT: God allows people who have faith in him and Jesus to suffer poverty, disease, hunger, and persecution in this life, but will provide a life of eternal bliss to those people in the next life.)
That early Christians were not particularly good at logical and critical thinking is also supported by their acceptance of various logical contradictions within Christian theology (e.g. For God so loved the world that God planned to send most humans to suffer torture in hell for all eternity).  Of course it is possible that a few early Christians were bothered by such contradictions, but not enough were bothered so that there would be apologetic points on these issues built into the Gospels (or the letters of Paul).
That early Christians were not particularly good at logical and critical thinking is also supported by their apparent acceptance of unclarity of Jesus’ teachings and the teachings of Paul on central issues (e.g.  “What must I do to be saved?”  Protestants disagree with Catholics on the answer to this fundamental question, and Protestants disagree with each other on the answer to this fundamental question.  These disagreements between various Christian denominations are the result of the unclarity and inconsistencies in the teachings of Jesus, in the teachings of Paul, and inconsistencies between the teachings of Jesus and the teachings of Paul.).
We can, however, also learn things that help the case for an historical Jesus.  If the Gospels and other early Christian writings show that Christians viewed the crucifixion of Jesus as something that was very shameful, then that could provide evidence in support of the historicity of the crucifixion of Jesus.  Why invent a story about the death of Jesus that is so shameful?  I don’t necessarily accept this argument from embarassment, but it is an example of how knowledge about the beliefs of early Christians can be used in support of the historicity of Jesus or of a particular event in the life (or death) of Jesus.
The fourth principle that Hinman advocates is quite brief:
P4. Everyone is biased.
Based on Hinman’s discussion of (P4) and (P5) it appears that this principle is given in part as a reply to an objection about an alleged bias of scholars on the issue of the historicity of Jesus.  Here are two plausible claims about NT scholars along such lines:

  • The vast majority of NT scholars have a significant bias in favor of the historicity of Jesus.
  • Most NT scholars have a strong bias in favor of the historicity of Jesus. 

So, one question to keep in mind is whether (P4) provides a strong reply to such criticisms about NT scholars.
The principle (P4) is a bit vague and ambiguous.  Here are a couple of different possible interpretations of (P4):
P4a. Everyone has a bias on some issue or other.
P4b. For any given theory, everyone is either biased in favor of the theory or biased against the theory.
Principle (P4a) is no doubt true, but it is insignificant and unhelpful in this context, because it leaves open the possibility that some people have a bias when it comes to the issue of the historicity of Jesus and other people do NOT have a bias on this issue.  Because (P4a) leaves this possibility open, it does not help us any in dealing with this particular issue; it fails to provide a strong reply to the above criticisms about NT scholars.
Principle (P4b) on the other hand, would certainly be of some significance to the issue of the historicity of Jesus, but, alas, (P4b) is a very broad generalization that is clearly false.  So, principle (P4b) is of no use, and fails to provide a strong reply to the above criticisms of NT scholars, because (P4b) is false.
We could try to rescue (P4b) by narrowing the scope to focus exclusively on the issue of the historicity of Jesus:
P4c. Everyone is either biased in favor of the historicity of Jesus or is biased against the historicity of Jesus.
But (P4c) is still somewhat dubious.  The issue of the historicity of Jesus is more controversial than many other issues, but controversiality is based on the feelings and attitudes of people in general, and there are almost always exceptions to such general psychological phenomena.  In other words, although most people have strong feelings about this issue, it seems fairly certain that there are at least a few people who don’t have strong feelings or opinions about the historicity of Jesus.  So, in order to rescue the (P4c) in terms of truth, we would need to either qualify the degree of bias that is being asserted or revise the quantification in terms of the proportion of people in scope:
P4d.  Everyone is either biased at least a tiny bit in favor of the historicity of Jesus or biased at least a tiny bit against the historicity of Jesus.
P4e.  Most people are either significantly biased in favor of the historicity of Jesus or significantly biased against the historicity of Jesus.
These generalizations are at least plausible.  However, (P4d) leaves open the possibility that some people (e.g. NT scholars) have a strong bias in favor of the historicity of Jesus, while other people (e.g. Jesus skeptics) have only a tiny bit of bias against the historicity of Jesus.  This would clearly not help Hinman’s case for the existence of Jesus, and fails to provide a strong reply to the above criticsims about NT scholars.
Also, (P4e) leaves open the possibility that some people (e.g. NT scholars) have a strong bias in favor of the historicity of Jesus, while a few people (e.g. Jesus skeptics) have no significant bias on this issue.  Again, this would not be of help for Hinman’s case, and fails to provide a strong reply to the criticisms of NT scholars.
I have considered a number of different possible interpretations of principle (P4).  The principle is false or dubious on some of those interpretations, and on the interpretations where the principle is true or plausible, it is either insignificant and unhelpful or appears to be of no help to Hinman’s case, and fails to provide a strong reply to the above criticisms of NT scholars.
If Hinman wants to continue to advocate this principle, he needs to clarify it in terms of the quantification of the portion of people who are being characterized and he needs to clarify it in terms of the scope of issues to which it applies, and he needs to clarify it in terms of the degree of bias that is being alleged (because there is a big difference between a strong bias and a very tiny bit of bias).  Principle (P4) cannot be rationally evaluated unless and until it is re-stated in a much clearer and more specific form.
As with (P4), the final principle is in need of clarification:
P5. The historicity of a single persona cannot be examined apart from the framework.
What matters in this context is whether this principle applies to (or is correct in terms of) the issue of the historicity of Jesus, so we can focus on this instantiation of (P5): ”
IP5. The historicity of Jesus of Nazareth cannot be examined apart from the framework.
The term “the framework” is unclear and vague.  However, based on Hinman’s discussion of this principle, this phrase appears to refer to the view or theory that Jesus existed, that Jesus was a flesh-and-blood historical person.  Given this understanding of “the framework”, the principle is still ambiguous.  Here are two different possible interpretations:
IP5a. The historicity of Jesus of Nazareth cannot be examined apart from assuming that Jesus of Nazareth was a flesh-and-blood historical person.
IP5b. The historicity of Jesus of Nazareth cannot be examined apart from examining the issue of  whether Jesus of Nazareth was a flesh-and-blood historical person.
Principle (IP5a) clearly involves circular reasoning.  If one simply assumes that Jesus was a flesh-and-blood historical person, then one begs the question of the historicity of Jesus.  So, we must reject (IP5a) because it is an unreasonable and illogical principle.
Principle (IP5b), on the other hand, is completely and undeniably true.  But it is true because it is a trivial and uninformative tautology.  The question of the historicity of Jesus of Nazareth just is the question of whether Jesus of Nazareth was a flesh-and-blood historical person.  So, this principle is of no significant help or use (other than to clarify the question at issue for those who are ignorant or confused).
There is one other interpretation, which seems both plausible and significant:
IP5c. The historicity of Jesus of Nazareth cannot be examined apart from treating this question as a question about which framework or theory among available alternatives best accounts for all of the available evidence (e.g. the theory that Jesus was a flesh-and-blood historical person vs. the theory that Jesus was just a myth).
Because this interpretation is both plausible and significant, the Principle of Charity indicates that this is the best interpretation, at least of the possible interpretations considered so far.
I have no objection to (IP5c).  However, it is obvious to any intelligent and informed Jesus skeptic that (IP5c) is true, and intelligent and informed Jesus skeptics usually think and argue in keeping with (IP5c).  G.A. Wells, Earl Doherty,  Robert Price, and Richard Carrier all accept this principle and they all think and argue in keeping with this principle, at least most of the time.  So, emphasis on this principle appears to me to be bordering on a STRAW MAN fallacy.
Jesus skeptics do NOT argue that because this or that Gospel story is historically problematic, therefore Jesus is just a myth.  The case against the historicity of Jesus is much broader than that and deals with a wide range of evidence both from the NT and from external (non-biblical) historical sources. Emphasis of this principle is a way of suggesting that Jesus skeptics and Jesus mythicists are idiots who don’t think and argue in keeping with this principle, but that suggestion is false and slanderous.  There are some stupid and unreasonable Jesus skeptics, but the major published Jesus skeptics accept (IP5c) and generally conform their thinking to this principle.

bookmark_borderWilliam Lane Craig’s Logic Lesson – Part 4

In the March Reasonable Faith Newsletter William Craig asserted this FALSE principle about valid deductive arguments that have premises that are probable:
… in a deductive argument the probability of the premises establishes only a minimum probability of the conclusion: even if the premises are only 51% probable, that doesn’t imply that the conclusion is only 51% probable. It implies that the conclusion is at least 51% probable.
There are a variety of natural tendencies that people have to reason poorly and illogically when it comes to reasoning about evidence and probability.  So, it is worth taking a little time to carefully review Craig’s mistake in order to LEARN from his mistake, and to understand how the logic really works in this case, so that we can avoid making the same mistake ourselves, and so that we can more readily notice and identify when others make similar mistakes in their reasoning.
One way that Craig’s principle can fail is because of the fact that a valid deductive argument can have multiple premises and because standard valid forms of deductive inferences/arguments require that ALL premises be true in order to work, in order to logically imply the conclusion.  In the case of a valid deductive argument with multiple premises that are probable rather than certain, it is usually the case that ALL of the premises must be true in order for the argument to logically imply the conclusion.
If the probable premises of such an argument are independent from each other (so that the truth or falsehood of one premise has no impact on the probability of the truth or falsehood of other premises in the argument), then the simple multiplication rule of probability applies, because what matters in this case is that the CONJUNCTION of all of the probable premises is true, and the probability of the conjunction of the premises of such an argument is equal to the product of the individual probabilities of each of the probable premises.  This means that the premises of a valid deductive argument can each have probabilities of .51 or greater while the conclusion has a probability of LESS THAN .51.  Examples of such arguments were given in Part 2 of this series of posts.
Another way that Craig’s principle can FAIL is based on situations where one or more premises of a valid deductive argument have dependencies with other premises in the argument.
Here is an example of a valid deductive argument with a premise that has a dependency on another premise :
1. I will get heads on the first random toss of this fair coin.
2. I will get tails on the first random toss of this fair coin. 
THEREFORE:
3. I will get heads on the first random toss of this fair coin, and I will get tails on the first random toss of this fair coin.
The probability of (1) is .5, and the probability of (2) is also .5 (considered on its own).  However, these two premises are mutually exclusive.  If (1) is true, then (2) must be false, and if (2) is true, then (1) must be false.  Thus, the conclusion (3) asserts a logical contradiction, and thus the probability that (3) is true is 0.   In the case of this argument, we cannot simply multiply the probability of (1) , considered by itself, times the probability of (2), considered by itself, in order to determine the probability of the CONJUNCTION of (1) and (2).
We have to multiply the probability of (1) times the probability of (2) GIVEN THAT (1) is the case.   Because the truth or falsehood of (1) impacts the probability of the truth or falsehood of (2), we cannot use the simple multiplication rule with this argument.  We must use the general multiplication rule:
The probability of the conjunction of A and B is equal to the product of the probability of A and the probability of B given that A is the case.
Here is the mathematical formula for the general multiplication rule of probability:
P(A & B) =  P(A) x P(B|A)
NOTE: The general multiplication rule can be used whether or not there is a dependency relationship between the premises of an argument.  If there is no dependency relationship between A and B, then the probability of B given that A is the case will be the SAME as the probability of B considered by itself.
Since the truth of (1) clearly excludes the possibility of the truth of (2), the probability of (2) GIVEN THAT (1) is the case is 0.  The probability of the conjunction of (1) and (2) is thus equal to:  .5   x  0  =  0.  So, the probability of the conclusion (3) is 0, even though the probability of (1) is .5.
This demonstrates how the probability of the conclusion of a valid deductive argument can be LESS THAN the probability of a premise in the argument (considered by itself).  The main reason why the probability of (3) is 0 is that there is a logical incompatability between premise (1) and premise (2) which rules out the possibility of it being the case that BOTH premises are true.  The truth or falsehood of (1) has an impact on the probability of the truth or falsehood of (2), so there is a dependency between the truth or falsehood of these premises.
Considered by itself, premise (2) has a probability of .5, but for the argument to work, both premises have to be true, and the probability of (2) can be impacted by whether (1) is true or false, so we need to assess the probablity of (2) on the assumption that (1) is true, and when we do so, the probability of (2) in that scenario is reduced from .5 down to 0.  Therefore, it is this dependency relationship between (2) and (1) that results in the conclusion having a probability that is extremely low, as low as probabilities can get: 0.
The same mathematical relationship holds when the probability of an individual probable premises is greater than .5:
4. I will not roll a six on the first random roll of this fair die.
5. I will roll a six on the first random roll of this fair die.
THEREFORE:
6. I will not roll a six on the first random roll of this fair die, and I will roll a six on the first random roll of this fair die.
The probability of (4) considered by itself is 5/6 or about .83, and the probability of (5) considered by itself is 1/6 or about .17.  However, these two premises are mutually exclusive. If (4) is true, then (5) must be false, and if (5) is true, then (4) must be false. Thus, the conclusion (6) asserts a logical contradiction, and thus the probability that (6) is true is 0. In the case of this argument, we cannot simply multiply the probability of (4) considered by itself, times the probability of (5) considered by itself, in order to determine the probability of the CONJUNCTION of (4) and (5).
Because there is a dependency relationship between (4) and (5), we must use the general multiplication rule to determine the probability of the conclusion.  The probability of the conjunction of (4) and (5) is equal to the product of the probability of (4) and the probability of (5) given that (4) is the case:
P[(4) & (5)] =  P[(4)]  x  P[(5)|(4)]
=  5/6  x   0 =  0
Thus, because of the dependency relationship between (4) and (5), the probability of the conclusion is reduced to 0, even though the probability of premise (4) considered by itself is 5/6 or about .83, which is GREATER THAN .51.  This argument is therefore another counterexample to Craig’s principle.  It is a valid deductive argument which has a probable premise with a probability GREATER THAN .51 but where the probability of the conclusion is LESS THAN .51.
The dependency relationship between premises need not be as strong as in the above examples. So long as the truth or falsehood of one premise impacts the probability of some other premise in the argument, Craig’s principle about valid deductive arguments can  FAIL.
Here is a counterexample against Craig’s principle that involves a dependency relationship that is weaker than in the above examples (something less than being mutually exclusive):
10. I will not select a heart card on the first randomly selected card from this standard deck.
11. I will not select a diamond card on the first randomly selected card from this standard deck.
THEREFORE:
12. I will not select a heart card on the first randomly selected card from this standard deck, and I will not select a diamond card on the first randomly selected card from this standard deck.
The probability of (10) considered by itself is .75, and the probability of (11) considered by itself is .75.  However, there are dependency relationships between these premises which make the conjunction of the premises less probable than if we simply multiplied these probabilities of each premise considered by itself.
If we ignored the dependency then the probability of the conjunction of the three premises would be calculated this way: .75  x  .75  = .5625 or about .56.  But to properly determine the probability of the conjunction of the three premises, we need to use the following equation (based on the general multiplication rule):
P[(10) & (11)] =  P[(10)]  x  P[(11)|(10)]  
=  3/4   x   2/3    =   6/12  =  1/2  =  .50
Thus, the probability of the conclusion of this argument is .50, which is LESS THAN .51.
The probability of premise (10) considered by itself is 3/4 or .75, and the probability of (11) is 3/4 considered by itself, which is GREATER THAN .51, and the probability of (11) given that (10) is the case is 2/3 or about .67, which is still GREATER THAN .51, but the probability of the conclusion of this argument is LESS THAN .51, so this argument is a counterexample to Craig’s principle, and part of the reason why the probability of the conclusion is so low is that there is a depenedency relationship between the premises.
Here is a final counterexample based (in part) on there being a dependency between premises:
14. I will not roll a six on the first random roll of this fair die.
15. I will not roll a five on the first random roll of this fair die. 
16. I will not roll a four on the first random roll of this fair die.
THEREFORE:
17. I will not roll a six on the first random roll of this fair die, and I will not roll a five on the first random roll of this fair die, and I will not roll a four on the first random roll of this fair die.
Each of the premises in this argument has a probability of 5/6 or about .83 when considered by itself.  If we ignored the dependency relationship between these premises, then we would calculate the probability of the conjunction of premises (14), (15), and (16) simply by multiplying these probabilities:  5/6  x  5/6  x  5/6   =  125/216   which approximately equals .5787 or about .58.  However, because there are dependencies between these premises, we must use the general multiplication rule.  Here is a formula for this argument that is based on the general multiplication rule:
P[(14) & (15) & (16)] =  
P[(14)]  x  P[(15)|(14)]  x  P[(16)|[(14) & (15)]]  
= 5/6  x  4/5  x  3/4  =   60/120  =  1/2  =  .50
Thus, the probability of the conclusion (17) is 1/2 or .50 which is LESS THAN .51.
So, the probability of each premise (considered by itself) is greater than .51, and the probability of premise (16) given that all the other premises are true is 3/4 or  .75, which is still greater than .51, but the probability of the conclusion (17) is LESS THAN .51, so Craig’s principle FAILS in this case, and thus Craig’s principle is shown to be FALSE.

bookmark_borderWilliam Lane Craig’s Logic Lesson – Part 3

I had planned to discuss counterexamples (to Craig’s principle) that were based on dependencies existing between the premises in some valid deductive arguments.  But I am putting that off for a later post, in order to present a brief analysis of some key concepts.
It seems to me that an important part of understanding the relationship between valid deductive arguments and probability is keeping in mind the distincition between necessary conditions and sufficient conditions. So, I’m going to do a brief analysis of this relationship.
SUFFICIENT CONDITIONS ESTABLISH A MINIMUM PROBABILITY
1. IF P, THEN Q.
Claim (1) asserts that P is a SUFFICIENT CONDITION for Q.
Assuming that (1) is true, the probability of P establishes a MINIMUM probability for Q.
If the probability of P was .60, then assuming that (1) is true, the minimum probability for Q would also be .60, because whenever P is true, so is Q.
However, (1) is compatible with Q being true even if P is false. There could be some OTHER reason for Q being true:
2. IF R, THEN Q.
If (2) is also true, and if R has some chance of being true even when P is false, then the probability of Q would be GREATER THAN the probability of P.  In this scenario the probability of Q would be GREATER THAN .60.
Suppose that the truth of R is independent of the truth of P. Suppose that the probability of R is .80. We can divide this scenario into two cases:
Case I. P is true.
Case II. It is not the case that P is true.
There is a probability of .60 that case I applies, and if it does apply, then Q is true. This gives us a minimum baseline probability of .60 for Q.
But we must add to this probability any additional probability for Q being true from case II.
There is a probability of .40 that case two applies, and if it does apply then there is a .80 probability that R is true (since the probability of R is not impacted by the truth or falsehood of P).  Since R implies Q, there is (in this second case) a probability of at least .80 that Q is true. So, we multiply the probability that case II applies times the probability of Q given that case II applies to get the (minimal) additional probability: .40 x .80 = .32.
To get the overall minimal probability of Q, we add the probability of Q from case I to the (minimal) probability of Q from case II: .60 + .32 = .92 or about .9.
NOTE: The actual probability of Q might be higher than .92, if there is some chance that Q was true even if both P and R were false.
NECESSARY CONDITIONS ESTABLISH A MAXIMUM PROBABILITY
3. IF Q, THEN P.
Claim (3) asserts that P is a NECESSARY CONDITION for Q.
Assuming that (3) is true, the probability of P establishes a MAXIMUM probability for Q.
If the probability of P is .60, then assuming that (3) is true, the maximum probability of Q would be .60, because whenever P is false, Q must also be false.
However, (3) is compatible with Q being false even when P is true. There could be some OTHER reason why Q is false:
4. IF Q, THEN S.
If (4) is also true, and if S has some chance of being false even when P is true, then the probability of Q would be LESS THAN the probability of P. In this scenario, the probability of Q would be LESS THAN .60.
Suppose that the truth of S is independent of the truth of P. Suppose that the probability of S is .20.  We can immediatly infer that the maximum probability of Q is .20, because the truth of S is a necessary condition for Q.  However, the combination of (3) and (4) reduces the maximum probability of Q even further.
We can divide this scenario into two cases:
Case I. P is true.
Case II. It is not the case that P is true.
Let’s consider case II first.  There is a probability of .40 that case II applies (because there is a probability of .60 that case I applies and the combined probabilities of both cases = 1.0), and if it does apply, then Q would be false (because P is a necessary condition of Q).  This establishes a baseline minimum probability of .40 for the falsehood of Q.
But we must add to this probability any additional probability for Q being false from case I.
There is a probability of .60 that case I applies, and if it does apply, then there is a .20 probability that S is true (because the probability of S is not impacted by the truth or falsehood of P), thus if case I applies, then there is a probability of .80 that S is false, and thus a minimum probability of .80 that Q is false (because S is a necessary condition of Q).  We meed to multiply the probability that case I applies times the (minimal) probability that Q is false given that case I applies:   .60 x .80 = .48.
Now we must add the probability of the falsehood of Q from case II with the (minimum) probability of the falsehood of Q from case I to get the overall minimum probablilty of the falsehood of Q:  .40 + .48 = .88.  The overall minimum probability of the falsehood of Q is .88, and this implies that the overall MAXIMUM probability of Q is .12.
NOTE: The actual probability of Q could be lower than the maximum probability, if there is some chance that Q was false even if both P and S were true.

bookmark_borderWilliam Lane Craig’s Logic Lesson – Part 2

I admit it.  I enjoyed pointing out that William Lane Craig had made a major blunder in his recent discussion of the logic of deductive arguments (with premises that are probable rather than certain).
However, there are a variety of natural tendencies that people have to reason poorly and illogically when it comes to reasoning about evidence and probability.  The fact that a sharp philosopher who is very experienced in presenting and analyzing arguments could make such a goof just goes to show that it is easy for people to make logical mistakes and to reason illogically, especially when reasoning about evidence and probability.
So, I think it is worth taking a little time to carefully review Craig’s mistake in order to LEARN from his mistake, and to understand how the logic really works in this case, so that we can avoid making the same mistake ourselves, and so that we can more readily notice and identify when others make similar mistakes in their reasoning.
In the March Reasonable Faith Newsletter Craig asserted a FALSE principle about valid deductive arguments that have premises that are probable:
… in a deductive argument the probability of the premises establishes only a minimum probability of the conclusion: even if the premises are only 51% probable, that doesn’t imply that the conclusion is only 51% probable. It implies that the conclusion is at least 51% probable.
 
One way that this principle can fail is because of the fact that a valid deductive argument can have multiple premises and because standard valid forms of deductive inferences/arguments require that ALL premises be true in order to work, in order to logically imply the conclusion.  In the case of a valid deductive argument with multiple premises that are probable rather than certain, it is usually the case that ALL of the premises must be true in order for the argument to logically imply the conclusion.
If the probable premises of such an argument are independent from each other (so that the truth or falsehood of one premise has no impact on the probability of the truth or falsehood of other premises in the argument), then the simple multiplication rule of probability applies, because what matters in this case is that the CONJUNCTION of all of the probable premises is true, and the probability of the conjunction of the premises of such an argument is equal to the product of the individual probabilities of each of the probable premises:
P
Q
THEREFORE:
P and Q
If the probability of P is .5, and the probability of Q (given that P is the case) is .5, then the probability of the conjunction “P and Q” is .25..  Here is an example of such a valid deductive argument:
1. I will get heads on the first random toss of this fair coin.
2. I will get heads on the second random toss of this fair coin. 
THEREFORE:
3. I will get heads on the first random toss of this fair coin, and I will get heads on the second random toss of this fair coin.
The probability of (1) is .5, and the probability of (2) given that (1) is the case is also .5 (because these two events are independent–what comes up on the first toss has no impact on what comes up on the second toss), so the probability of the conjunction of (1) and (2) is .25.  Thus, the probability of (3) is .25.  This example shows that the probability conferred on the conclusion of such an argument can be LESS THAN the probability of any individual premise of the argument.  This is because when you multiply one number that is greater than zero but less than 1.0 by another number that is greater than zero but less than 1.0, the product is LESS THAN either of those factors.
The same mathematical relationship holds when the probability of the individual probable premises is greater than .5:
4. I will not roll a six on the first random roll of this fair die.
5. I will not roll a six on the second random roll of this fair die.
THEREFORE:
6. I will not roll a six on the first random roll of this fair die, and I will not roll a six on the second random roll of this fair die.
The probability of (4) is 5/6 or about .83, and the probability of (5) given that (4) is the case is also 5/6 or about .83 (because these events are independent).  Since both premises have to be true in order to logically imply the conclusion, the multiplication rule applies in this case, so the probability of the CONJUNCTION of (4) and (5) is equal to the product of the probabilities of each individual premise:  .83 x .83 = .6889  or about .69, which is LESS THAN the probability of each of the individual premises.
Based on this sort of mathematical relationship, we can devise an example on which Craig’s principle will FAIL:
7. I will not roll a six or a five on the first random roll of this fair die.
8. I will not roll a six or a five on the second random roll of this fair die.
THEREFORE:
9. I will not roll a six or a five on the first random roll of this fair die, and I will not roll a six or a five on the second random roll of this fair die.
The probability of (7) is 4/6 or about .67, and the probability of (8) given that (7) is the case is also 4/6 or about .67 (because these are independent events).  The probability of the conjunction of (7) and (8) is equal to the product of their individual probabilities: .67 x .67 = .4489 or about .45.  To be more exact the probability of the conjunction of (7) and (8) is equal to: 4/6  x 4/6 = 16/36 = 4/9 = .44444444…  Thus, although the probability of each premise is greater than .51, the probability of the conclusion (9) is less than .51.  Therefore, Craig’s principle FAILS in this case.  Thus, his principle is FALSE.
Here is one more similar counterexample against Craig’s principle:
10. I will not select a heart card on the first randomly selected card from this standard deck.
11. I will not select a heart card on the second randomly selected card from this standard deck (after replacement of the first card back into the deck).
12. I will not select a heart card on the third randomly selected card from this standard deck (after replacement of the first and second cards back into the deck).
THEREFORE:
13. I will not select a heart card on the first randomly selected card from this standard deck, and I will not select a heart card on the second randomly selected card from this standard deck (after replacement of the first card back into the deck), and I will not select a heart card on the third randomly selected card from this standard deck (after replacement of the first and second cards back into the deck).
The probability of (10) is .75, and the probability of (11) given (10) is .75, and the probability of (12) given both (10) and (11) is also .75.  The probability of the conjunction of these three premises equals:  .75 x .75 x .75 = .421875 or about .42. Thus, the probability of the conclusion (13) is .421875 or about .42, which is LESS THAN .51, even though each of the premises has a probability that is GREATER THAN .51.
Here is my final counterexample based on the multiplication rule:
14. I will not roll a six on the first random roll of this fair die.
15. I will not roll a six on the second random roll of this fair die. 
16. I will not roll a six on the third random roll of this fair die.
17. I will not roll a six on the fourth random roll of this fair die.

THEREFORE:
18. I will not roll a six on the first random roll of this fair die, and I will not roll a six on the second random roll of this fair die, and I will not roll a six on the third random roll of this fair die, and I will not roll a six on the fourth random roll of this fair die.
Each of the premises in this argument has a probability of 5/6 or about .83.  The events referenced in the premises are independent from each other, so the probability of the conjunction of premises (14), (15), (16), and (17) is equal to:  
5/6  x  5/6  x  5/6  x  5/6 =  625/1,296 = .4822530864…  or about .48.  So, the probability of each premise is greater than .51, but the probability of the conclusion (18) is less than .51, so Craig’s principle FAILS in this case, and thus Craig’s principle is shown to be FALSE.
There is another way that Craig’s principle can FAIL, and that is because one probable premise in a valid deductive argument can have a dependency on another probable premise in the argument, and this can result in conferring a probability on the conclusion that is less than the probability of the individual premises.  I will explore this second issue with Craig’s principle in the next installment.

bookmark_borderWilliam Lane Craig’s Logic Lesson

The March Newsletter from Reasonable Faith just came out, and it includes a brief lesson in logic from William Lane Craig. However, the lesson presents a point that is clearly and obviously WRONG, and it promotes bad reasoning that could be used to rationalize UNREASONABLE beliefs.  It appears that WLC is himself in need of some basic lessons in logic.
William Craig recently debated a professor of philosophy named Kevin Scharp at Ohio State University, and in the current Reasonable Faith Newsletter, Craig criticizes what he takes to be Scharp’s main objection to Craig’s apologetic arguments:
What was odd about Prof. Sharp’s [correct spelling: Scharp] fundamental critique was that, apart from the moral argument, he did not attack any of the premises of my arguments. Rather his claim was that all the arguments suffer from what he called “weakness.” For even if the arguments are cogent, he says, they only establish that God’s existence is more probable than not (say, 51% probable), and this is not enough for belief in God. 
Why did he think that the arguments are so weak? Because I claim that in order for a deductive argument to be a good one, it must be logically valid and its premises must be more probable than their opposites. Prof. Sharp [sic] apparently thought that that is all I’m claiming for my arguments. But in our dialogue, I explained to him that that was a mistake on his part. My criteria were meant to set only a minimum threshold for an argument to be a good one. I myself think that my arguments far exceed this minimum threshold and provide adequate warrant for belief in God. I set the minimum threshold so low in order to help sceptics like him get into the Kingdom! 
This reply makes a fair point.  Establishing a minimum threshold for an argument to be considered “good” does not imply that no good arguments have premises that exceed this minimum.  Thus, when Craig claims that his deductive arguments for God’s existence are “good” arguments, he is NOT saying that the premises in these arguments each have a probability of only .51.
But then Craig goes further and provides this short lesson in logic (or lesson in illogic, as I shall argue):
Besides, I pointed out, in a deductive argument the probability of the premises establishes only a minimum probability of the conclusion: even if the premises are only 51% probable, that doesn’t imply that the conclusion is only 51% probable. It implies that the conclusion is at least 51% probable. Besides all this, why can’t a person believe something based on 51% probability? The claim that he can’t seems to me just a matter of personal psychology, which varies from person to person and circumstance to circumstance.
Thus, Prof. Sharp’s [sic] fundamental criticism was quite misconceived, and since he never attacked the arguments themselves, he did nothing to show that the arguments I defended are, in fact, weak.
Craig’s claim that “even if the premises [in a deductive argument] are only 51% probable” this “implies that the concusion is at least 51% probable” is clearly and obviously false.  This is, for me, a jaw-dropping mistaken understanding of how deductive arguments work.
First of all, deductive arguments can have multiple premises.  If multiple premises in a deductive argument each have a probability of only .51, then it is OBVIOUSLY possible for such arguments to FAIL to establish that the conclusion has a probability of “at least” .51.  For example, consider the following valid deductive argument form:
1. P
2. Q
3. IF P & Q, THEN R
THERFORE:
4. R
Suppose that the probability of P is .51 and that the probability of Q (given that P is the case) is also .51.  Suppose that we know premise (3) with certainty.  What is the probability conferred on the conclusion by this argument?   In order for this deductive argument to confer any probability to the conclusion, BOTH P and Q must be true.  Thus it only takes ONE false premise to ruin the argument.  The probability of the conclusion would NOT be .51 but would, rather, be .51 x .51 = .2601  or about .26.   This is a simple and obvious counter-example to Craig’s claim.
Another problem is that there is almost always other relevant information that could impact the probability of the conclusion of an argument.  So, one might well be able to construct additional relevant deductive arguments AGAINST the conclusion in question.
Suppose that X implies that R is not the case, and Y implies that R is not the case, and Z implies that R is not the case.  Then we could construct three additional deductive arguments against R:
5. X
6. IF X, THEN it is not the case that R.
THEREFORE:
7. It is not the case that R.
===============
8. Y
9. IF Y, THEN it is not the case that R.
THEREFORE:
7. It is not the case that R.
===============
10. Z
11. IF Z, THEN it is not the case that R.
THEREFORE:
7. It is not the case that R.
Suppose that the probability of X is .9, and the probability of Y is  .9, and the probability of Z  is .9.   Suppose that the truth of X, Y, and Z are independent of each other.  Suppose that the conditional premises in each of the above arguments is known with certainty.  In this case, what probability is conferred on the conclusion that “It is not the case that R”?
Let’s (temporarily) ignore the prevous deductive argument in support of R, and imagine that X, Y, and Z are the only relevant facts that we have regarding the truth or falsehood of R.  Each of these three valid deductive arguments would, then, individually confer a probability of .9 on the conclusion that “It is not the case that R”.  Therefore, if we combine the force of these three arguments, they will confer a probabilty that is GREATER THAN .9 on the conclusion that “It is not the case that R”.  All we need is for ONE of the premises (X, Y, or Z) to be true, in order for the negative conclusion to be secured, and each of the three premises is very likely to be true.
We can analyze the probabilty calculation into three cases in which at least one of the three premises is true:
I. X is true  (probability = .9)
II. X is not true, but Y is true  (probability = .1 x .9 =  .09)
III. X is not true, and Y is not true, but Z is true (probability = .1 x .1 x .9 = .009)
Add the probabilities of these three cases together to get the total probability conferred on the negative conclusion:
.9 + .09 + .009 = .999
Thus, the combined force of these three deductive arguments would make it nearly certain that “It is not the case that R”, assuming that these three arguments encompassed ALL of the relevant evidence.
But we also have the posititive evidence of P and Q to consider, which will, presumably increase the probability that R is the case and reduce the probability of the negative conclusion that “It is not the case that R”.
Adding in this additional relevant evidence, however, could make the overall probability calculation significantly more complex.  It all depends on whether the truth of P is independent of the truth of X, Y, and Z, and whether the truth of Q is independent of the truth of X, Y, and Z, and whether the truth of the conjunction “P and Q” is independent of the truth of X, Y, and Z.  If there are dependencies between the truth of these claims, then that will rquire additional complexity in the probability calculation.
If for the sake of simplicity, we assume that the truth of P is independent of the truth of X, Y, and Z, and the truth of Q is independent of X, Y, and Z, and the truth of “P and Q” is independent as well, we can at least conclude (without needing to do any calculations) that the overall probability of R will be greater than .001 and less than .2601, in which case Craig’s claim that the probability of the conclusion must be “at least 51%” is clearly false in this case, in part because of additional relevant evidence against the conclusion.
Thus, there are two major, and fairly obvious, problems with WLC’s claim: (1) deductive arguments with multiple premises can confer a probability on the conclusion that is LESS than the probability of any particular premise in the argument, and (2) there is almost always OTHER relevant information/data that impacts the probability of the conclusion of a particular deductive argument (which has premises that are only probable), and consideration of this additional evidence might very well lower the all-things-considered probability of the conclusion.
These two points are fundamental to understanding the logic of deductive arguments for the existence of God, so Craig’s apparent confusion about, or ignorance of, these points is shocking.