New Testament Note 75

New Testament Note 75 March 2, 2019

 

Vista House, Washington
As long as we’re building houses on solid rock, I would like mine to be built in a place that looks something like this one, overlooking the Columbia River.  (Wikimedia Commons public domain photo)

 

Matthew 7:24-27

Compare Luke 6:47-49

 

The image of the house built upon a rock is a memorable one, and clearly understandable.

 

The fundamental point, obviously, is that we should found our lives upon the truth about God.

 

It can be extended, though, to illustrate (among other things) the idea that, even if your reasoning is otherwise sound, if you’re basing your argument on faulty premises it’s not going to be very solid or reliable.  Thus, for instance, the following syllogism is logically valid:

 

All elephants are yellow and furry.

Jumbo is an elephant.

Therefore, Jumbo is yellow and furry.

 

However, since the first premise is factually untrue, the conclusion is likewise false, even though its derivation from premises one and two is entirely respectable.

 

I’ve always been struck by the notorious case of the illustrious German mathematician, philosopher, and logician Gottlob Frege (d. 1925) and his Grundgesetze der Arithmetik (“Basic Laws of Arithmetic”).  I quote from the Wikipedia entry on Frege:

 

In a famous episode, Bertrand Russell wrote to Frege, just as Vol. 2 of the Grundgesetze was about to go to press in 1903, showing that Russell’s paradox could be derived from Frege’s Basic Law V. It is easy to define the relation of membership of a set or extension in Frege’s system; Russell then drew attention to “the set of things x that are such that x is not a member of x“. The system of the Grundgesetze entails that the set thus characterised both is and is not a member of itself, and is thus inconsistent. Frege wrote a hasty, last-minute Appendix to Vol. 2, deriving the contradiction and proposing to eliminate it by modifying Basic Law V. Frege opened the Appendix with the exceptionally honest comment: “Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion.”

 

Sometimes, we’re in such a hurry to set forth our arguments that we fail to notice the quite problematic assumptions at their base.  It’s essential to get the fundamentals right.  There’s plenty of time, after that, to work out their implications.  I suppose that another way of putting this is to recommend that we always devote sufficient time to the roots before we focus on the branches, or to planning before execution.

 

 

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