Althouse: "Some philosophers argued that vagueness was a form of ignorance: that there is a precise number of grains separating a heap from a nonheap..."

December 28, 2017

"Some philosophers argued that vagueness was a form of ignorance: that there is a precise number of grains separating a heap from a nonheap..."

"... but we don’t know what it is. Others argued that vagueness was a result of semantic indecision: that there are lots of possible things we could mean by 'heap,' each of which would establish a precise number of grains for heap-hood, but we haven’t taken the trouble to specify that meaning. Still others, looking to avoid a sharp distinction between heaps and nonheaps, sought to develop nonclassical or 'fuzzy' logics, which experimented with degrees of truth... Fara’s theory [was] that vagueness was an expression of our ever-changing purposes: that there is a precise point at which a heap becomes a nonheap, but it 'shifts around' as our objectives do. In fact, because the act of considering two comparable heaps accentuates their similarity, 'the boundary can never be where we are looking.' No wonder we think it doesn’t exist."

From the entry Delia Graff Fara in the NYT compilation of essays, "The Lives They Lived," about people who died this year.

40 comments:

rhhardin said...: What a chair is is vague. Everybody pretty much agrees what's a chair and what isn't a chair and what's a doubtful case but don't know what it is that they're knowing when they do that.

Cavell What a chair is.

The vagueness, so called, is fairly precisely shaped in order to say stuff that we're interested in saying.; 12/28/17, 8:51 AM
tcrosse said...: Sen Warren heap big deal.; 12/28/17, 8:56 AM
Michael K said...: "Heap" was a computer science term. I don't know if it still is.; 12/28/17, 8:59 AM
mockturtle said...: Thomas Aquinas would approve.; 12/28/17, 9:01 AM
Fernandinande said...: Fara’s theory [was] that vagueness was an expression of our ever-changing purposes: that there is a precise point at which a heap becomes a nonheap, but it 'shifts around' as our objectives do.

The theory that the meanings of poorly defined words can change is so obvious that it's only .015 of an interesting theory.; 12/28/17, 9:02 AM
Wince said...: Thus political language has to consist largely of euphemism, question-begging and sheer cloudy vagueness...

Phrases like "a not unjustifiable assumption" ...are a continuous temptation, a packet of aspirins always at one's elbow.
Look back through this essay, and for certain you will find that I have again and again committed the very faults I am protesting against.

- George Orwell; 12/28/17, 9:04 AM
MikeR said...: Wow - quite an article over there. Big effort by NYT to convince us that the kind of people they consider Elites really are important and worthy of emulating. Mostly a lot of media folks. For instance, the one who discovered how to do PR on behalf of vicious murderers so that people wouldn't kill them, just keep them in jail forever. Quite an accomplishment, that, but it course it was _important_.; 12/28/17, 9:17 AM
Wilbur said...: In high school, they called this the fallacy of the beard: we can all agree that one hair cannot constitute a beard and that 10,000 hairs does constitute a beard. What is the numerical cutoff point between beard and non-beard?

I just took it to mean that some things cannot be measured numerically or precisely.; 12/28/17, 9:23 AM
Dust Bunny Queen said...: "How long is something considered "new"?"

And...is something only considered "new" if it hasn't been pre-owned?

Or... is it "new" to you because you just obtained it from a thrift store or garage sale? Even though the object is very old and probably had been owned by multiple people? See my new antique clock?

Is it considered "new" even if never owned but has sat on the shelf for 30 years. New Old Stock?; 12/28/17, 9:27 AM
tcrosse said...: "How long is something considered "new"?"

Like New York ?; 12/28/17, 9:29 AM
Anonymous said...: The truth is that mortals are not capable of accurately quantifying every 'heap' they encounter, so they take a visual shortcut to a usable, but imprecise, description. To think that you have to try to accurately quantify everything in view -to avoid being vague- would make you an obsessive-compulsive.; 12/28/17, 9:30 AM
Wince said...: "In addressing for the assembly this morning... I am recalling the words of the foundry-founder of More Science High School, Eukipha Heap, who pressed the first bricks with his own hands. Knowledge for the pupil-the people, he said: 'Give them a light and they'll follow it anywhere'. We think that is a fair and a wise guy-kind of rule to be guided by..."

"That's the spirits we have here!"; 12/28/17, 9:32 AM
Original Mike said...: "Give them a light and they'll follow it anywhere"

Numen Lumen; 12/28/17, 9:39 AM
Michael said...: It seems to me that a "heap" is a loose pile, of any size. Ten grains could be in a heap, as opposed to scattered about, and 10,000 grains would not be a heap if they were in a container or spread evenly across an area. A heap is a vaguely conical pile formed by dropping things from a single point and letting them spread out naturally (or pushing them up from the sides into a similar shape). No dictionaries were disturbed in the production of this comment.; 12/28/17, 9:46 AM
The Godfather said...: Harvey Weinstein got in a heap of trouble for sexual harassment, and Donald Trump didn’t. Discuss.; 12/28/17, 9:53 AM
tcrosse said...: Not to be confused with La Nouvelle Vague.; 12/28/17, 9:59 AM
Rick.T. said...: I worked with a CIO who when asked how long a project would take would always answer: "How long is a piece of string?" Then following with: "Fast, cheap, good. Pick two."; 12/28/17, 10:09 AM
William said...: How many heaps make a pile?.......Do you heap certain things and pile others?.....It doesn't take much to keep philosophers entertained for hours.; 12/28/17, 10:16 AM
buwaya said...: The problem is language, but also the urge to taxonomize.
Nature doesnt taxonomize.
Humans argue about systems in nature in terms of human manias.
This really doesnt help humans control nature.

Arguing about terms to use in describing nature isnt science.
Feynman had a pet peeve about this. Knowing the name of something has nothing to do with understanding it.; 12/28/17, 10:43 AM
Fernandinande said...: How many heaps make a pile?

The pile is the only natural enemy of the hole.; 12/28/17, 11:23 AM
SeanF said...: Michael: It seems to me that a "heap" is a loose pile, of any size.

And what constitutes a pile? :); 12/28/17, 11:26 AM
mockturtle said...: And what constitutes a pile? :)

A hemorrhoid?; 12/28/17, 11:29 AM
Red Devil said...: "♫...Have a heapin helpin of our hospitality...♫" Jed Clempett; 12/28/17, 11:31 AM
Fernandinande said...: SeanF said...
And what constitutes a pile? :)

It's an inside-out hole.; 12/28/17, 11:32 AM
Char Char Binks, Esq. said...: Now we know how many angels can dance on the head of a pin -- a heap.; 12/28/17, 12:09 PM
William said...: In discussions like this, a wise man is always mindful that time flies like an arrow, but fruit flys like a banana.; 12/28/17, 12:18 PM
mockturtle said...: I worked with a CIO who when asked how long a project would take would always answer: "How long is a piece of string?" Then following with: "Fast, cheap, good. Pick two."

Meal planning is similar. You can have economy, elegance or ease or any two of the three but not all three.; 12/28/17, 12:34 PM
Richard Dolan said...: Odd how some people find ordinary language so puzzling, isn't it? According to the article, Ms. Fara was "a skilled practitioner of logic and formal semantics" -- sounds like Quine and Chomsky put together -- and approached her study of such puzzles from that perspective. Her solution to the 'heap' puzzle ultimately focused on the purpose for which the word was being used in a particular context, but only to a certain point. There was still all that talk about imprecision and vagueness, trying to measure the use of a word like 'heap' by standards created for other purposes.

Wittgenstein, too, started out as a logician but ultimately dropped that approach in studying language by focusing on purpose, context and usage. For him, the collective experience of lived lives, rather than formal logic, provided a better way of understanding language and its various rules of usage. He used to complain that a lot of philosophical puzzles were created by very smart people staring at words for too long, trying to make them do a job they weren't intended for. Imagining that the use of a word like 'heap' presents such a puzzle -- because we can't say precisely when a heap becomes a non-heap -- is a good example of what W was talking about. It's not so much that the word is imprecise -- we all know precisely what it means -- but different speakers still might disagree about when and whether it fits a particular context. In part, it's just definitional -- we don't have a mathematical calculation in mind when using words like 'heap', but instead something more like a picture, because we all have a visual idea of what a heap looks like. That's not a problem or a puzzle, but only a fact of life, like knowing when a person passes from young to middle-aged (you know what that difference looks like, too).

No doubt, Fara was well aware of that view, and I'd be curious to see what she had to say about it. I suspect her answer would have been that her interests lay elsewhere and she wanted to see how far she could get by applying the tools of formal logic to issues in semantics, while still taking as her starting point ordinary language rather than some artificial substitute. Fair enough.; 12/28/17, 12:36 PM
Char Char Binks, Esq. said...: "Knowing the name of something has nothing to do with understanding it."

Much the way Antifa doesn't understand the meaning of fascism, or just as likely, exploits the vagueness of the term while pretending to oppose what they're actually engaging in.; 12/28/17, 12:56 PM
n.n said...: Pro-Choice, selective and opportunistic, including color diversity, congruence, witch hunts, elective wars, selective-child, recycled-child, and conflation of logical domains (i.e. accuracy outside a limit frame of reference in time and space), are religious doctrines promoted, pleaded out of ignorance for political, social, and fiscal progress.; 12/28/17, 1:33 PM
buwaya said...: "Much the way Antifa doesn't understand the meaning of fascism"

That's something else. That is just verbal warfare, calling their opponents names.
Its the verbal equivalent of flinging dung.

Very ancient tactic. I'm sure that among the first uses of language was to call the enemy clan poopyheads.; 12/28/17, 1:47 PM
Fernandinande said...: Michael K pontificated..
"Heap" was a computer science term. I don't know if it still is.

Yay! Now you're getting the "humble" part of the humble brag.; 12/28/17, 2:03 PM
Nancy said...: A man had 20 odds and ends and he got rid of 19 of them. What was left? Classic response: The end.; 12/28/17, 2:22 PM
Jupiter said...: A mathematician would say that if twenty grains of sand are a heap, then so is one grain. In fact, no grains of sand is the empty heap.; 12/28/17, 3:32 PM
Jupiter said...: Blogger Michael K said...
"Heap" was a computer science term. I don't know if it still is.

In computer science, it is called a "priority queue". Programmers still call it a "heap".; 12/28/17, 3:36 PM
n.n said...: Heap is still a computer science term, which simply refers to an unstructured class of memory.; 12/28/17, 4:35 PM
n.n said...: Another form of vagueness, or ambiguity, that is designed to promote ignorance, or at least personal comfort, is the use of a medical term of art, "fetus", to dehumanize a human life early in her evolution, in order to rationalize selective-child (and recycled-child) for political, social, and economic progress. A practice normalized by liberal feminists.; 12/28/17, 4:42 PM
Josephbleau said...: The importance of heap, the way I see it, is that a heap is too large to easily carry with you. A heap is a store of future value, leading to savings for the future and the need to defend property. Hunter gatherers have no heaps, or if they do they desert them after getting their fill.; 12/28/17, 5:12 PM
campy said...: What differentiates bric-a-brac from knickknacks?; 12/28/17, 5:28 PM
Ken B said...: Jupiter is correct.; 12/28/17, 9:44 PM