2.1: Breakdown of meaning
- Page ID
- 223809
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)What’s a concept? A concept is something we use in thought, like an idea. We combine concepts to form new concepts, we think about the world through concepts, and we form new concepts. For example, when we see a bunch of striped horse-like animals running around we can use the concept zebra to group them together and then learn more things about them. When we see a bunch of different people betting on the price of commodities, we use the concept futures trading to understand these disparate activities under one idea. One way of putting the point is that concepts are the things expressed by words or phrases. The phrase “futures trading” expresses a concept (an abstract meaning, or an idea in our mind). The word “zebra” expresses a different concept. I can form whole thoughts in my mind by putting concepts together to form propositions.
Zebras are striped
Futures trading is risky and morally suspect
Here we have the concepts Zebra, Striped, Futures Trading, Risky, and Morally Suspect. We can recombine these to make new thoughts:
Zebras are morally suspect
If a thing is striped, then it’s risky
Futures trading is striped
These aren’t very good thoughts or propositions, but they’re thoughts or propositions nonetheless.
The communication of concepts (expressed using words or phrases) breaks down in many ways. That is, when we try to communicate our ideas to other people, we often mess up. We leave ambiguity or speak vaguely and therefore don’t effectively communicate what we intend to communicate. Two such breakdowns are especially important to be able to distinguish: Vagueness and Ambiguity.
Vagueness
Vagueness is problematic unspecificity. Meaning the concept or word or phrase admits of borderline cases (has fuzzy boundaries), and/or doesn’t tell us enough to mean much of anything.
If you can’t easily pinpoint where a concept start and stops—if you can’t draw a clean line around all of the things the concept applies to, excluding all of the things the concept doesn’t apply to—then you have a vague concept. It’s not necessarily a problem to have a vague concept, though, unless you need a more sharp or specific concept.
- That man is tall!
- 1 inch taller than average? 2 inches taller than average? 7?
- Water is “hot” just in cases where it feels much warmer than room temperature.
- “much warmer” isn’t any more specific than “hot”
- You’re no friend of mine unless you’ve been there for me.
- Does that mean being available when you call me? Does that mean going out of my way to comfort you? What degree of support are you expecting? The boundaries aren’t clear.
- We’ll do whatever is prudent to help the victims of this natural disaster.
- Does that mean donate some money to mercy corps? Does that mean spare no expense? What degree of support are you offering? There are many borderline cases for which this statement won’t help us predict what support will be offered. I like to call these “weasel statements” because they allow one to weasel out of obligations later by saying “I said we’d do whatever is prudent and it turned out not to be prudent to do much of anything, so I never lied.”
- The winner is whoever dances the best.
- Wait, what does that mean? How do we measure “goodness” of dancing? It might be better to say that the winner is whoever the judges score the highest. That’s specific and quantitative—it’s easy to measure.
- I have lots of stuff to do, so I won’t be able to make it.
- Look, we all have lots of stuff to do. If you truly have so much stuff to do that it justifies cancelling our plans, then I’d want to know how much you have to do. Do you have to take the dogs for a walk? Or do you have to rewrite an entire term paper in an evening because your hard drive crashed the day before the paper was due? These are very different scenarios.
Ambiguity
Ambiguity is problematic in that the ambiguous word or phrase admits of multiple distinct interpretations. A sentence could be read in different ways based on how we interpret a word or phrase. There is grammatical ambiguity, and also semantic ambiguity.
Grammatical ambiguity is where the structure of a sentence (like a dangling modifier or a poorly-placed pronoun) make the sentence compatible with more than one reading.
Semantic or Lexical Ambiguity is where a word or phrase could mean multiple different things, each of which makes the sentence as a whole have very different interpretations.
- John went to the park to meet Bob, but he never arrived.
- Pronoun ambiguity: to whom does “he” refer? Grammatical Ambiguity
- It’s difficult to walk a dog wearing a dress because of all the funny looks.
- Who is wearing the dress? The dog? The Person? This is a dangling modifier. So it’s Grammatical ambiguity.
- I believe in freedom, so I believe the government should do nothing but protect me from threats foreign and domestic.
- “Freedom” is ambiguous between positive freedom and negative freedom (freedom from constraint vs. freedom to accomplish one’s goals). Semantic ambiguity.
- Headline: Prostitutes appeal to Pope
- What does “appeal” mean here? Appeal as in “attract” or appeal as in “plead with”? Semantic ambiguity.
- She critiqued them for playing soccer poorly.
- This is a little tricky to identify, but it is a dangling modifier because it’s ambiguous between “she critiqued them poorly” and “playing soccer poorly.” The modifier “poorly” doesn’t clearly attach to the critique or the soccer playing because it could attach to either.
- He fed her cat food
- Did he feed a woman cat food? Did he feed a female cat cat food? Did he feed a woman’s cat with food? Grammatical ambiguity.
- We all saw her duck.
- We saw a duck that belongs to her? Or we saw her perform the action of ducking? The word “duck” is ambiguous here.
We need to be able to distinguish between these two breakdowns in meaning to fully understand each of them. Sometimes meaning breaks down because someone is trying to express a concept but uses ambiguous wording which leaves us uncertain which concept they’re trying to communicate. Other times, someone is trying to use a concept to make a point, but the concept they choose is vague, which leaves us uncertain how to apply the concept to the concrete cases because the concept is indeterminate—we’re not sure what to do with certain borderline cases.