Anomalies of Language

Language can impede reasoning

Multiple Senses of Words
  • Words often have more than one meaning.  The first entry of Merriam-Webster’s definition of sound, for example, defines three senses:
    • a: a particular auditory impression
    • b: the sensation perceived by the sense of hearing
    • c: mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium (such as air) and is the objective cause of hearing
  • BTW, Merriam-Webster’s definition of sound solves the age-old riddle: if a tree falls in the forest with no one around, does it make a sound? The answer: Yes in sense (c), No in sense (b).
  • Multiple senses of words sometimes follow a pattern. An example is the distinction between the process and product senses of words, e.g. of decision, construction, and explanation:
  • Symbolic logic uses grammar to distinguish different senses of the verb to be:
    1. The is of predication ascribes an attribute to something or someone.
      • Barack Obama is a Democrat. 
        • Symbolic Representation
          • Db, meaning b has property D
    2. The is of identity asserts that ‘two’ things are the same thing.
      • Mark Twain is Samuel Clemens
        • Symbolic Representation
          • m = s, meaning m and s are the very same thing
      • The sum of 5 and 7 is 12. 
        • Symbolic Representation
          • 5 + 7 = 12, meaning the sum of 5 and 7 is the same thing as 12
    3. The is of existence asserts the existence of something.
      • There are ghosts
        • Symbolic Representation
          • (Ex)Gx, meaning there is at least one thing x such that x is a ghost
  • A fourth sense of to be is the is of definition
    • A square is a rectangle with four equal sides
      • i.e. square means rectangle with four equal sides.
  • A word acquires meaning either naturally, as language evolves, or by stipulation, whereby its meaning is established by fiat.  
  • The word knife, for example, has evolved to mean “a cutting instrument consisting of a sharp blade fastened to a handle,” per Merriam-Webster.  Merriam-Webster’s definition is a lexical or reportive definition, an empirical hypothesis about word usage subject to confirmation and refutation. 
  • By contrast, The Texas Penal Code defines knife as “any bladed hand instrument that is capable of inflicting serious bodily injury or death by cutting or stabbing a person with the instrument.” This definition is stipulative, decreeing what knife is to mean, as if to say “the word knife hereby means any bladed hand instrument …”  Stipulative definitions are true by fiat rather than by virtue of usage. Thus, the Penal Code’s definition of knife is not refuted by a pair scissors, which is not a knife in the ordinary sense yet is still “a bladed instrument capable of inflicting injury or death…”
  • Since it’s an empirical hypothesis, a reportive definition can be wrong.  Consider the American Heritage’s definition of chair: 
    • A piece of furniture designed to accommodate one sitting or reclining person, providing support for the back and often the arms and typically standing on four legs.
  • The definition is correct only if:
    1. anything that’s a chair satisfies the definition and
    2. anything that satisfies the definition is a chair. 
  • But kneeling chairs don’t satisfy condition #1, since they lack backs:
  • A word, phrase, or sentence is used ambiguously if it can be plausibly understood in more than one way.  Thus Matt eats only fresh vegetables is ambiguous between:
    • The only foods Matt eats are fresh vegetables. 
    • The only vegetables Matt eats are fresh vegetables. 
  • Ambiguity is a property, not of words, phrases, and sentences, but of their use on particular occasions. Consider sentences with the word funny:
    • The Daily Show is usually funny, but not last night.
    • At first I thought the problem was the router but now I think there’s something funny going on with the network card.
    • Sherry met the new math teacher yesterday and said he’s a funny guy.
  • The first two sentences would ordinarily be used unambiguously, the Daily Show being on the Comedy Channel and network cards not known for their humor.  The third sentence has greater potential for ambiguity.  Knowing nothing about the new math teacher, you may be uncertain whether Sherry meant humorous fellow or a strange character.  
  • Ambiguity is lexical or syntactic according as it’s due to multiple senses of words or grammatical structure.  Examples:
    • Lexical
      • He’s a poor student.
      • Driver: Should I go left at the light?  Passenger: Right!
      • The duchess can’t bear children.
      • Male barn swallows attract females with long tail feathers.
    • Syntactic
      • I said I would see you on Tuesday.
      • Visiting relatives can be boring.
      • There’s a guard on duty at all times.
      • I know she killed him because she wanted the insurance money.
  • The ambiguities of the lexical group derive from multiple senses of
    • poor, i.e. bad versus impoverished,
    • right, i.e. non-left versus correct,
    • bear, i.e. stand versus give birth to,
    • with, i.e. by means of versus having. 
  • The sentences of the syntactic group are ambiguous because of grammar. 
    • On Tuesday can modify either I said or I would see you
    • Visiting can be understood as a present participle modifying relatives (i.e. relatives who are visiting) or as part of the gerund visiting relatives (i.e. the act of visiting relatives). 
    • There’s a guard can mean there’s the same guard and there’s some guard or other.
    • Because she wanted the insurance money could be why she killed him or how I know.
  • Words and sentences with multiple meanings are a common source of humor.
    • I don’t want to achieve immortality through my work; I want to achieve immortality through not dying. (Woody Allen)
    • I’m feeling great, and I have sex almost every day.  Almost on Monday, almost on Tuesday, almost on Wednesday. (Jack Lalanne)
    • I told the doctor I broke my leg in two places. He told me to quit going to those places. (Henny Youngman)
Literal and Figurative Language
  • A word, phrase or sentence is used or understood figuratively if it is not used or understood literally.  Examples:
Figure of SpeechLiteral Meaning
She’s under the weather.She’s sick.
He’s between a rock and a hard place.He’s in a difficult situation.
I’m starving.I’m very hungry.
Curiosity killed the cat.Satisfying one’s curiosity can have unfortunate consequences.
We have to tighten our belts.We have to reduce expenses.
Bill’s not hurting for money.Bill’s financially well off.
We were packed like sardines.We were packed tightly together.
Her car loves gas.Her car uses a lot of gas.
The White House denied the report.The administration denied the report.
I was so mad I could have eaten nails.I was very mad.
How can I thank you?Thank you.
Nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb.No person shall be prosecuted for the same offense twice.
  • Figures of speech are of many kinds: metaphor, simile, personification, metonymy, litotes, hyperbole, and rhetorical question, to name a few (all represented in the table).  
  • Figures of speech can be a source of ambiguity. Her car loves gas is potentially ambiguous between her car uses a lot of gas and her car literally feels love toward gas.
  • It’s typically evident from context and common knowledge whether a sentence is used figuratively or literally.  Her car loves gas is clearly figurative, motor vehicles being incapable of love.  But occasionally there’s a need to explicitly indicate how a sentence should be understood.  Your remark that the groom has cold feet is liable to be misunderstood if you’ve just seen him walking barefoot in the snow.  In such cases, words and phrases such as literally, figuratively, in a manner of speaking, as it were, so to speak and if you will come to the rescue.  The groom literally had cold feet, not as it were or in a manner of speaking. These phrases aren’t foolproof, though: I’m literally starving is sometimes used to mean I’m famished.
Vague and Precise Language
  • A linguistic expression is vague if it is subject to borderline cases, possible scenarios where its truth is indeterminate though all the relevant facts are known. 
  • Take the word short. Select a random sample of a thousand adult males, line them up by height, start from the short end, and try to determine who’s short.  As the men become taller their shortness becomes less obvious.  Eventually you reach a nebulous range where you’re unable to decide whether the men are short or not.  The problem isn’t a lack of evidence, since the men are directly before you and their heights can be measured.  The problem, rather, is that the meaning of short yields no precise demarcation between shortness and non-shortness. The dictionary definition of short, “having little height,” is of no help. For men in the hazy zone, the truth or falsehood of the sentence “he is short” is indeterminate.
  • You can always stipulate a meaning for short, say, “less than 5 feet in height.”  But your stipulated sense is not the ordinary sense, which remains indeterminate in borderline cases.
  • The opposite of vague is precise, meaning “sharply defined.”   For example, “less than 5 feet in height” versus “short.”
  • Vagueness permeates language. For example, like “short,” lots of words are vague because of indeterminate minimums and maximums. The following are indeterminate:
    • the minimum height a tall male adult can be
    • the maximum height a short male adult can be
    • the minimum net worth a rich person can have
    • the maximum net worth a poor person can have
    • the minimum age an old person can be
    • the maximum age a young person can be
  • Vagueness is useful.  As you wait at a crossing for a 200-car train to pass by, you can later describe the train as having a huge number of cars, though you didn’t keep count, and taking an incredibly long time to go by, though you didn’t look at your watch.  We usually don’t know enough to be precise.
  • Vagueness isn’t always desirable, for example in law and science.  A law prohibiting driving at an “excessive speed” is an invitation to chaos. Newton’s theory of gravity does not vaguely predict that an object dropped at sea level picks up speed as it falls. It predicts, rather, that the object accelerates at the rate of 32 feet per second, each second, enabling objective confirmation or refutation.
Obscure and Clear Language
  • A text is obscure if it’s “not readily understood or clearly expressed” (MW obscure) and clear if it’s “free from obscurity or ambiguity, easily understood” (MW clear).
  • G.W.F Hegel’s 1812 book Science of Logic opens with this paragraph:
    • BEING, pure Being — without any further determination. In its indeterminate immediacy it is similar to itself alone, and also not dissimilar from any other; it has no differentiation either within itself or relatively to anything external; nor would it remain fixed in its purity, were there any determination or content which could be distinguished within it, or whereby it could be posited as distinct from an Other. It is pure indeterminateness and vacuity. – Nothing can be intuited in it, if there is any question here of intuition, or again it is merely this pure and empty intuition itself; equally there is in it no object for thought, or again it is just this empty thought. In fact, Being, indeterminate immediacy, is Nothing, neither more nor less.
  • Hegel’s text is clearly obscure, being neither “readily understood nor clearly expressed.”
  • It may be obscure because Hegel’s thoughts, though clear, are obscurely expressed.  Perhaps he uses words in technical senses.  Perhaps he assumes a certain level of knowledge, e.g. a familiarity with other of his works. 
  • Or it may be that Hegel’s thoughts themselves are obscure, however expressed.  In this case the text is nonsense
  • Advice from Alfred E. Kahn, the “Father of Airline Deregulation:”
    • “If you can’t explain what you’re doing in plain English, you’re probably doing something wrong.”