Logical Gal and what makes a good definition

8 Oct

Stop

Have you ever felt sheepish after jumping down someone’s throat….

for incorrectly assessing your conversational partner’s point of view?  Come to find out, you had been thinking about X and they had meant Y.  And it all hinged on a TERM!  Before you and I engage in a discussion, we need to clarify and clear away the fog by defining our terms precisely!

That’s rule # 1

And we always follow the rules, right? Smiley Face

Sometimes though, it is easier said then done.  Especially when we aren’t sure what makes for a good definition.

There are several guidelines, but today I want to talk about 2 characteristics in particular which assist in obtaining clarity. Communicating a definition means that your audience is left better off after listening to you – there is LESS confusion.

First things first!

When you create a definition, you need to include both a genus (the big category to which it belongs) and a differentia (the ‘what about it details’ that make IT different from other members in the category/genus).  Hence, a GooD definition – capital G for genus and capital D for differentia, includes both parts, the genus and the differential.

For example, what is a car?

Car

The ‘genus’ is the large family of motorized vehicles.

And what distinguishes a car from a truck from an airplane could be stated like this:

a member of the motorized vehicle genus which has 4 wheels and has as its primary design function that of transporting 1-6 people on a road.

What’s highlighted in red makes up the differentia.  Now here is the tricky part and what I want to convey in this blog post.  When we attempt accurately to describe the differentia, we have to be both inclusive AND exclusive in a sufficient manner so that:

  • the differentia could not apply to more than one member of the differentia

For example, if we had suggested a differentia that went like this….which has as its primary function that of transporting people and not cargo on a road..then how would we tell whether this included or EXcluded a van or  a bus or even a motorcycle?

A definition has to be ‘mutually exclusive’, meaning that there be NO confusion whether something fits into a car slot or a bus slot or a motorcycle slot or a pickup truck slot.

  • AND the genus and differentia have to provide for all potential members so that you don’t exclude a possible member, leaving them unassigned.

For example, if I had not intentionally selected the number ONE as the lower end of passenger carrying capacity, I might have left out the possibility of a really tiny one-person vehicle from being considered a car.

One passenger car

What got me thinking about the importance of ‘GooD’ definitions and the proper use of categories was the opening of a sermon in which the pastor was describing Mexican food.  He had grown up in California and argued that when you boiled down this style of cuisine, there were basically MEAT tacos and BEAN tacos.  The varieties are endless, but by his thinking, a GooD definition of Mexican food would be this:

Mexican food is a style of cooking (genus) using tacos as a base for filling with either meat or beans in various combinations combined with many possible add-ons. (differentia)

Mexican Food

After tantalizing his congregation with mouthwatering thoughts of a tasty lunch, he delivered his punch line: 

There are only 2 kinds of people in the world:

  • those who live according to the Holy Spirit and are therefore born-again Christians with a happy future
  • those who live according to their own agenda and are therefore enemies of God with a depressing future

If you think about it, every single person on Earth who ever has lived, is living or will live fits into either one or the other group. Therefore, this categorization is considered ‘jointly exhaustive’.

And no one can have a foot in one category AND the other at the same time. Therefore, this description is ‘mutually exclusive’.

It’s sobering, isn’t it!

But truth is like that.  I’m reminded of another area where there are only 2 categories:  a woman is either pregnant or she is not pregnant.  The logic law that states that limitation of reality is called the Law of the Excluded Middle.

Even though Truth can be as bracing as a bucket of ice water, there is Good News.  And it is this:

  • Although EVERYONE starts off in that 2nd category (or trajectory toward remaining an enemy of God), no one is doomed to stay there.  God’s offer of salvation by grace alone through faith alone in Christ alone is available to all those who are willing to accept the gift.

Question: what are other categories with only 2 possibilities? 

And for an explanation of how you can be adopted into God’s forever family, How to become a Christian

 

 

 

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