Logical Gal and the Source of Misunderstandings

19 Nov

Consider the assumptions below: are they true?

  • The French are snobs
  • Southerners are lazy
  • Kids don’t read much
  • Americans are generous
  • Women feel guilty
  • Schools are failing students

It depends

We often treat these particular statements as true JUST because we know some cases where:

  • SOME French people behave as though they were better than us
  • SOME Southerners lack drive
  • SOME kids prefer video games to reading
  • SOME Americans open their wallets for every world misery
  • SOME women confess their conflicting views about motherhood, marriage and working
  • SOME schools routinely turn out students unprepared to take up adult roles in society

An effective and accurate (truthful) communicator does not assume that the qualities pertaining to certain cases equally apply in EVERY case.   This is the difference between the Universal (ALL) and the Particular (SOME).

When we apply the characteristics of the few or even the many to every, we are going beyond what is logically correct.  Logical thinking is, after all, using language correctly.

EXTENSION is the term to note the particular details of one exemplar of a category.  The term to identify all those members of a category that also carry the same ‘extension’ is COMPREHENSION.  And ABSTRACTION is the term that pulls together the descriptive characteristics that EVERY single member of of the category holds in common.

Take a house, for example:

House - Ranch House - shack House - Victorian

The 3 houses above are all very different.  To get the idea of ‘house’, we abstract what they have in common:

  • a roof
  • 4 walls
  • shelter for living
  • space enough to protect some personal belongings of inhabitants

A particular house, say the rancher on the left, has all 4 of the above features plus we can say that it is:

  • on one floor and noticeably longer than it is wide

But if we took that particular rancher which is a sum of the ‘applies to all’ features (the abstracted idea of house) + a particular characteristic (long and on one floor) and said

  • Houses are easy for handicapped people to access

We would be guilty of taking an extension and applying it across the board to all houses.

To be logical, we would have to supply the correct quantifier and say SOME houses make it easy for handicapped people to access.  A mansion might not have a way for a wheel chair to reach higher floors.

Ramp on rancher

If extension means the particular characteristics beyond the abstracted or general idea of a concept, then what is comprehension?  Think about extension as the details.  Think about comprehension as the number or sum total of all the members of a category to which this description applies.

And when we add more particular details, then a category member can be said to have a ‘greater’ extension.  But, conversely, there are fewer members that can be said to share that extension.

Here are 3 houses again, but this time they are:

a) a general, abstracted house

b) an abstracted house considered a ranch

c) an abstracted house that is ranch-style and has a handicap ramp

The latter, house C, shows the greatest extension because it has the most detail (hence, there are fewer houses that are accurately said to be that kind of house)

The first, house A, has the greatest comprehension because more houses qualify to be that kind of house (basic house) without all the extra details.

See Saw

The seesaw picture shows the inverse relationship between extension and comprehension.  The greater the details (greater extension), the fewer items that meet that description (smaller comprehension) and vice versa.

Bottom line?  Committing ourselves to take the time AND think clearly and then express ourselves honestly can ease the tension and conflict that characterizes our world.  It’s either laziness or pure disingenuousness to paint people or institutions with a broad brush.

Language is the source of misunderstandings Language is the source of...in French

 

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