Wednesday, July 16, 2014

Logic Lessons pt 11 - Rules for Definitions

At our last session we discussed the nature of definitions.  Now here are the rules.

     Definitions must be:

  1. Coextensive with thing defined (neither too narrow nor too broad)
    To define "triangle" as "plane figure" or human as "animal" is problematic because, while true, the definition is too broad.  "Plane figure" could include non-triangles like squares and trapezoids.  "Animal" could include non-humans like orangoutangs, armadillos, and duck-billed platypuses.  

    But to define "triangle" as "3-sided, enclosed plane figure whose interior angles equal 180 degrees and lines are equal to each other," is also problematic because it excludes triangles whose 3 lines are not equal (e.g. right triangles).  To define "human" as "rational male animals" is too limiting because it excludes women from the definition of human.  

    Definitions need to be precise so as not to confuse.  The more precise we are in our definitions, the easier time we will have in talking with each other.  

    This is the hardest of the rules to obey.

    In fact, I just had a phone call from Rick O., who criticized my inclusion of Clerks: The Animated Series into my top 25 sitcoms of all time.  

    The thrust of the argument centered around my criteria (i.e. definition) of what makes a great TV sitcom.  He thought my definition was too broad because Clerks had only 6 episodes and was less in total length than most movies.  I said his definition was too narrow, because there were many great shows that only last a short amount of time (Firefly, Freaks and Geeks).  

    By the end of the discussion, he understood my reasoning a little better.  "Your thinking is consistent," he concluded, "but awful."  The point is that even though we disagreed, we at least understood each other better because we were better able to define more precisely our definitions and articulate how we thought the other violated this first rule.

  2. Clear, not obscure
    Clarity in definition is important.  If you say that a "quarvat" is "an 8523rd century version of a Gravity Rod," you have a coextensive definition, but unless you are fan of James Robinson's writing, the definition is too obscure to matter.  Clarity requires you to put the commons sense of the definition as plainly as possible and as accessibly as possible.

  3. Literal, not metaphorical
    "Writing a novel is like giving birth."  There is great truth in that statement, but that is a terrible definition of novel writing.  "Lies are a tangled web."  Again, a true aphorism, but it is a bad definition because it uses metaphor.  I know now what writing a novel and lies are like, but I don't, from these definition, know what they are.

  4. Brief, not long
    This may not always be possible.  But you want to give the simplest version of the definition because it will be the easiest to understand and therefore the easiest to either accept of refute.

  5. Positive, not negative (if possible)
    Negative definitions tend to be too broad.  If you say "human" is "any creature that is not rational" becomes problematic because it excludes angels.  

    The only time to use a negative definition is for something negative.  "Darkness" can only be defined by a negative: "Absence of light."  "Never" = "Not ever."

  6. Not Circular: term defined cannot appear in the definition
    If I were to say that a "quarvat" is a "quarvat-shaped object," you will not have learned anything because you are using the word you are trying to define inside of your definition.  You need to predicate something new about your subject in a definition in order for it to have any meaning.

    Next time we will go over kinds of definitions.

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