I have another objection to raise against Luke Johnson’s use of the “method of convergence” to support the reliability of the Gospels or the “historical framework” of the Gospels (emphasis added by me):

As I have tried to show, the character of the Gospel narratives does not allow a fully satisfying historical reconstruction of Jesus’ ministry. Nevertheless, certain fundamental points on which all the Gospels agree, when taken together with confirming lines of convergence from outsider testimony and non-narrative New Testament evidence, can be regarded with a high degree of probability.  Even the most critical historian can confidently assert that a Jew named Jesus worked as a teacher and wonder-worker in Palestine during the reign of Tiberius, was executed by crucifixion under the prefect Pontius Pilate, and condintued to have followers after his death.  These assertions are not mathematically or metaphysically certain, for certainty is not within the reach of history.  But they do enjoy a very high level of probability.    (TRJ, p.123)

This paragraph contains a common logical fallacy concerning probability.   This logical fallacy is of great practical importance as well as theoretical importance.  In the field of project management, one important practical application of logic and probability is that of constructing realistic, accurate, detailed schedules, and evaluations of the probability that a project will be completed on time.

There is a common tendency to overestimate the probability of completing a project on schedule.  One reason for this tendency is the failure to apply the logic of probability by committing a particular logical fallacy.  For example, lets say that we have a very simple and short project that consists of just five tasks, with a one-week duration for each task.  Suppose that each task has a very good chance of completing on schdule, specifically, each task has a probability of .8 completing in the planned duration (being completed in one week or less).  Furthermore, suppose that these tasks must be worked in a particular order, and one task must be completed before the next task can be started.  Project managers create charts to display the logic of project schedules, and the chart for this simple project would look like this:

Suppose that this project had to complete in five weeks in order for the project to make a profit.  What is the probability that the project will complete on time?  Because each task in the project has a high probability of being completed in one week (or less), it is tempting to infer that there is a high probability that the project as a whole will complete on time, in five weeks (or less).  But this is a logical fallacy.

Although each individual task has a high probability of being completed in the planned duration (of one week), this does NOT mean that the entire project has a high probability of being completed in the planned duration (of five weeks).  If just one of the tasks takes longer than estimated, that could make the whole project take longer than planned.  The probability that this project will complete in five weeks (or less) is NOT .8, but rather approximately  .8 x .8 x .8 x .8 x .8 =  .64 x .64 x .8 =  .32768  or aprox. .33  or one chance in three.  In other words, it is more likely that this project will fail to complete on time than that it will complete on time.

This common logical fallacy concerning the probability of a chain of tasks completing on schedule is a particular form of the more general fallacy known as the FALLACY OF COMPOSTION:

What is true of the part is not necessarily true of the whole.  To think so is to commit the fallacy of composition.  

(With Good Reason, 4th edition, by S. Morris Engel, p.103)

Reasoning of the following form is invalid:

1.  It is highly probable that A is the case.

2. It is highly probable that B is the case.

3. It is highly probable that C is the case.

4. It is highly probable that D is the case.

Therefore:

5. It is highly probable that A and B and C and D are the case.

But in the paragraph quoted at the begining of this post, it appears that Luke Johnson reasons this way:

1. It is highly probable that claim (A) about Jesus is true.

2. It is highly probable that claim (B) about Jesus is true.

3. It is highly probable that claim (C) about Jesus is true.

4. It is highly probable that claim (D) about Jesus is true.

Therefore:

5. It is highly probable that claims (A) and (B) and (C) and (D) about Jesus are all true.

This is clearly a bit of fallacious reasoning.  Such bad reasoning about probability is tempting and quite common, but it is still bad reasoning, and Johnson appears to be encouraging his readers to engage in such fallacious reasoning about the probability of claims about Jesus.  In the paragraph quoted at the start of this post, Johnson appears to be encouraging his readers to commit the fallacy of compostion, and to reason from the high probability of individual claims about Jesus to the high probability of  conjunctions of serveral claims about Jesus.

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Here is an INDEX to posts in this series.