Tag Archives: Differentia

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

 

 

 

Of Bouncers and Secret Servicemen

16 Jul

What do bouncers do?  I’ve never been to a skanky private nightclub guarded by a big burly bouncer, but I’ve seen them in the movies.

The function of a bouncer is to let in ONLY those authorized to enter – same job description of the President’s Secret Service.

We started to define ‘meal’ last time when our imaginary Susie opined, “It’s not healthy to eat between meals!”

We identified a GooD definition as one having a clearly identified genus or a broad category (think family) that contains different members easily distinguished one from another.  If you can picture a Venn diagram, then the boundary of the diagram delineates the genus and individual points within the genus circle are the differentia.

We thought deeply and decided that meals belong to the genus that WE called,

“Food prepared for human consumption”

And besides meals, we proposed other ‘family members’ such as –

  • a single edible item like a CARROT that is seasoned, cooked, cut or arranged in such a way as to have been ‘prepared’
  • a potable drink that is either poured from a container or created from ingredients or seasoned or heated/iced

So now the question is, are we done?  If we include ‘meals’, we have 3 participants in our category.  Are we ready to finish describing and distinguishing a meal?

Almost, but not quite:   We need to run our genus through a grid to insure a complete & accurate definition.

Consider this question –

  • Does our genus contain ALL possibilities?  Can we say, that with our 3 described differentia, we have exhausted ALL possibilities?  (I AM aware that we have YET to describe the differentia that separates ‘meals’ from its other 2 ‘siblings’.)  The way to answer this is to think of any and all ‘foods prepared for human consumption’ and see if they fit into one of the 3 sub-groups.

How about a container of yogurt that I buy at the store – Where does that fit?

Is it a ‘single food item that is seasoned, cooked, cut or arranged’?  NO!!!

Woops, then we need to add another member to the food category.  How about

  • Food or drink that comes pre-packaged, ready to be consumed.

Now we ask our 2nd detailed question “Is there any ambiguity or possible confusion among our differentia?  Could a potential member be assigned to more than one of our differentia?” If so, then we have to be more specific in limiting/ describing the differentia.  If we can’t think of any possibilities, then we can say with confidence that our definition is:   ‘mutually exclusive’.

Let’s return to our Bouncer/ Secret Servicemen analogy.  Imagine two different functions occurring at the White House on the same night.  One might be a reception welcoming the National Spelling Bee finalists and the other a state dinner for UN ambassadors.   The President is going to mingle and congratulate the young people before going into the international soirée.  Invitees to both are filing through security under the scrutiny of Secret Service and Protocol officials.  You can be sure that the lists for each event are VERY detailed.  And I doubt that any of the ambassadors and their spouses are good enough spellers in English OR young enough to be on the elite guest list of Spelling Bee-ers and family.  The 2 lists ARE mutually exclusive.  There will be no confusion.

And if those are the only 2 events hosting outside guests, the two lists are also ‘ jointly exhaustive’.  They take care of ALL guests that night.  In summary, there ARE no other possibilities, there IS no confusion, no one admitted to the White House can be on both lists or on NEITHER list.  Protocol has done its job correctly.

So must we be as accurate when we define a term.

Let’s return to our term ‘meal’.  If we look at the other 3 differentia, I think we can confidently define a meal as:

A food prepared for human consumption that is composed of two or more edible/potable items previously packaged and/or presently seasoned, cooked, cut or arranged.

Food genus

Whew !  So what’s the point of all that?   Well, there’s no sense in engaging in a discussion with Susie UNTIL we reach agreement WITH her on what constitutes a meal.  Once we all accept the definition of terms, then we can turn to the propositions and evaluate whether they are true or not and then examine the deduction that Susie undergoes to arrive at her conclusion.

Your ongoing assignment is to pick a term and draw it out, placing it in its larger family or genus.

It all depends on what you mean by…..

15 Jul

I know you probably are thinking, “Enough with these terms – get on with the argumentation part of your logic blog!”

I tell you, terms are where it’s at!  Real progress down the road CAN be had in direct proportion to the amount of effective work you do at clearing up and coming to an agreement regarding terms.

When Susie uses a word or words to refer to a single concept (hence a ‘term’), we’ve got to pin her down on what she has in her mind’s eye!

She might say, “It’s not healthy to eat between meals!”

* *

Before launching in with a self-righteous volley right back at Susie like:

“Wait a second, what do you mean it’s not healthy!  Why I think that ….”

..we must clarify with Susie what she means by “meals”

I like to practice creating GooD definitions.  A ‘good’ definition has a genus and a differentia, hence my large and emboldened G, D.

A genus is the family or category the term fits into and the differentia is what makes the family members distinguishable one from the other.

Here’s how to create a definition.  Ask yourself this first question

1)    What is the larger group of things we are talking about, the broader category that meal could belong to?

In this case, it’s probably ‘food’, but that could be food for sale in the grocery store, or food that is used for photographers, or food on display in restaurant counters.

2)    How can I narrow down the category without compromising a full-orbed picture of possible distinctions?

In this example, let’s say that the broader category or genus is “Food prepared for human consumption”

Once we have the genus taken care of we can write:

  • A meal is food prepared for human consumption that________________

Now our task is to think of all the possible items that would fit in that category, kind of like the brothers and sisters of ‘meal’, members of the family of ‘food prepared for human consumption.’

What else might be a food prepared for human consumption that is NOT a meal?

I would suggest these 2 possibilities besides ‘meal’:

  • a single edible item like a CARROT that is seasoned or cooked or cut or arranged in such a way as to have been ‘prepared’
  • a potable drink that is either poured from a container or created from ingredients or seasoned or heated/iced

Now we can describe the differentia for meal to make it DISTINGUISHABLE from these 2 family members.  Here goes:

  • a combination of 2 or more food and/or drink items that is seasoned or cooked or cut or arranged

And our FULL and COMPLETE GooD definition of meal would be thus,

A meal is food prepared for human consumption that is a combination of 2 or more food and/or drink items that is seasoned or cooked or cut or arranged.

*

Well, speaking about food,  it’s lunch time and I’m going to make us each a meal of roast beef & Swiss sandwiches together with pop corn and Diet Dr. Pepper!    

Next time we’ll run our definition through one more diagnostic test to be sure that it is complete.

Your homework to practice creating GooD definitions?  Pick out some terms that you hear this week and ask yourself what is the broader category to which they belong.