Explanatory Functions – 1 – Introduction

xExplanatory FunctionsThe following series discusses some issues relating to interpreting the bible.

This is post one of three.  Here are the links to the other posts.

2 Sola Scriptura and Semper Reformanda

3 Historical Evolution of Interpretations

For any large group of texts and passages there tend to be several possible interpretations for how they work together and what they mean. Lets say for example at one point in time a group of people became authors of a special unknown function y = f(x). From this function they produced the a consecutive series of numbers.

Once they had the series they duplicated several numbers and put them in a random order and the product is the set of numbers below.

4, 13, 4, 20, 4, 5, 5, 8, 4, 13, 29, 8, 5, 4, 20, 8, 5, 4, 13, 5, 8

Index 0 1 2 3 4 5
Original set 4 5 8 13 20 29

Now lets say over time various leaders in groups of people (group-a, group-b, group-c), with varying mathematical ability, made suggestions for functions that best explain the set of given numbers. This link describes the process for guessing what f(x) is, but it is not important for our purposes. These leaders developed different functions over time to explain to their audiences what they believed is the correct way to read and interpret the given set of numbers.

Group-a (y = 8)

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Group-a became quite interested in the set of numbers, suggests ‘y = 8’ best explains the series and this is what they teach to their audiences is the key to understanding the whole series of numbers. So for x = 0 to 5 this formula would yield the following series of numbers. Below this series I have displayed the original series from the unknown function so we can compare the two.

Index 0 1 2 3 4 5
y = 8 8 8 8 8 8 8
Original set 4 5 8 13 20 29

Note that some of the results produced are the same and some very close to the original set. Particularly where x = 2. But others are off. This group is not really good at maths. So they exercise a fair amount of tolerance on some results fudging them to match it up with the original set. Within this group there are sub groups and they have suggested slightly different explanatory formulas, such as ‘y = 9’ and ‘y = 7’. So within group-a there is competition over the detail of the general explanatory formula.

But, some people in the group are unhappy with the suggested general function and seek a better one arguing with the remainder of the group. This remainder keep referring to the numbers which the function does explain really well in the original set.

Group-b (y = 2x + 2)

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Group-b followed group-a and were originally part of group-a. But they broke off because they became really unhappy with the suggested formula and some of the people from group-a. Group-b suggests ‘y = 2x + 2’ best explains the series and this is what they teach their audiences is the way to understand the original set of numbers. So for x = 0 to 5 this function would yield the series, again displaying the original set below it.

Index 0 1 2 3 4 5
y = 2x + 2 2 4 6 8 10 12
Original set 4 5 8 13 20 29

This group is still not really good at maths but they are much better than the previous group. When group-b releases this formula, more people from group-a leave for group-b.

Consequently groups-a and groups-b start arguing with one another, become fearful, proud and refuse to give in to the other groups formula. While each claim the authority of the original set in their arguments, all too often they are seen to be biased and harbour a significant amount of vested interest in their own formula. Communication breaks down between groups a and b, as they both point to various numbers which justify their own formula and numbers which disagree with the others formula. The running argument leads into increasing amounts of frustration between the groups.

Their audiences place a lot of trust in their own leaders who have formulated the explanatory formulas. So the leaders of these groups themselves do not want to betray that trust by admitting their function was wrong in some respects and could be improved upon.

Group-b, like group-a before them, exercises a degree of tolerance on some results that don’t quite match up with the original set of numbers. So they fudge some taking them on faith and ignore others that do not justify their formula.

Within this group there are sub groups as well and they have suggested slightly different explanatory formulas, such as ‘y = 3x + 2’ and ‘y = 2x + 3’. So within group-b there is competition over the detail of the general explanatory formula just like there was in group-a. Hence there are arguments between groups and inside the groups struggling to gain popular attention.

A small number of people amongst group-b are unhappy with the suggested function and seek a better one arguing with the larger mass of group-b. This small number of people is the beginning of group-c.

The larger mass of group-b keeps referring to the numbers which the function does explain really well in the original set, and saying to people potentially in the early formation of group-c (who are unhappy with the explanatory function of group-b) that if they don’t like this function they should join group-a.

Group-c (y = x² + 3)

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Eventually group-c forms and produces their own explanatory formula. Group-c suggests ‘y = x² + 3’ best explains the series and this is what they teach their audiences is the best way to understand the whole set. So for x = 0 to 5 this function would yield the series shown below.

Index 0 1 2 3 4 5
y = x² + 3 3 4 7 12 19 28
Original set 4 5 8 13 20 29

Like before the formation of group-c and the promotion of its explanatory formula is fraught with outer and inner group arguments. So overall there are arguments within each group and with other groups. It can become quite difficult pinning peoples opinion down on what the best explanatory formula is.

The problem is, its really easy to rely to much on an explanatory function and neglect to know the original set.

Do you think it is easy to substitute the authority of the original set of numbers with an explanatory function?

Welcome to the arena of biblical interpretation. The original set of numbers in my example represent the scriptures. The explanatory functions best sum up what is called systematic theology. The leaders and their audiences represent the various denominations in the history of the Christian church.

Click here to go to the next post in the series.


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