van deemter, riga, jan. 2010 not exactly vagueness as original sin? kees van deemter university of...

van Deemter, Riga, Jan. 2010

Not ExactlyVagueness as Original Sin?

Kees van Deemter

University of Aberdeen

Scotland


Plan of the talk

1. Vagueness is everywhere


Plan of the talk


2. Vagueness is a problem


Plan of the talk



3. We are vague for a reason


Plan of the talk




4. How to model vagueness



Example

doctors informing doctors about a baby in intensive care


From the BABYTALK corpus

“BREATHING – Today he managed 1½ hours off CPAP in about 0.3 litres nasal prong oxygen, and was put back onto CPAP after a desaturation with bradycardia. However, over the day his oxygen requirements generally have come down from 30% to 25%. Oxygen saturation is very variable. Usually the desaturations are down to the 60s or 70s; some are accompanied by bradycardia and mostly they resolve spontaneously, though a few times his saturation has dipped to the 50s with bradycardia and gentle stimulation was given. He has needed oral suction 3 or 4 times today, oral secretions are thick.”

[BT-Nurse scenario 1]


“Vagueness”

A technical sense of the word:• An expression is vague

if it allows borderline cases • Example: poverty can be defined

in different ways, e.g.,• Threshold A: income < 60% of median• Threshold B: income < 50% of median

• Suppose median income is £35,000, and John’s income is £20,000 ...


Example: Is John poor?

£19,000 p/a

£21,000 (Threshold A)

£17,5000 (Threshold B)

John

John is poor

John is not poor


Some sources of vagueness

Vague adjectives: ‘large’, ‘small’, ... Vague adverbs: ‘often’, ‘slowly’, ... Vague determiners: ‘many’, ‘few’, ... Vague nouns: ‘girl’, ‘giant’, ‘island’, ... ...

Not just in everyday conversation, but in science and business too



First example: vague identity

A car undergoes a series of repairs.

At what stage does it become a different car?


A London court case(with thanks to Graeme Forbes)

High Court of Justice, July 1990 Vintage Bentley racing car, named

“Old Number One”, sold for £10 million Many repairs since its victories in 1929-30

“none of the 1929 Speed 6 survives with the exception

of fittings (...). Of the 1930 Speed 6 (...) only the

following exist on the car (...), namely pedal shaft, gear

box casing and steering column.” (From expert report)


The judge argued ...

... that this is no longer the “original” car



... that this is no longer the “original” car nor the “genuine” Old Number One



... that this is no longer the “original” car nor the “genuine” Old Number One

But neither is it a mere “reconstruction” or “resurrection”.

It is “authentic”


The judge wrote:

“At any one stage in its evolution it had indubitably retained its characteristics. Any new parts (...) never caused the car to lose its identity (...) There is no other Bentley (...) which could legitimately lay claim to the title of Old Number One or its reputation. It was this history and reputation, as well as its metal, which was for sale on 7th April 1990.”


What is the judge saying?

What if further repairs/replacements are performed, so none of the original parts remains?


Successive changes are common

the cells in your body renew themselves a book changes constantly when it’s written languages change through place and time

The conclusion seems hard to avoid:

Object identity is an incoherent concept A concession to mental laziness


How about the concepts that we use to categorize things?

Let’s look at one of the corner stones of biology: the concept of a species

species-denoting terms: e.g.(common) Chimpanzee, Homo sapiens, etc.



Second example: the fiction of species


The fiction of species

Surely, species-denoting terms are crisp?


What makes a species?

Thought unproblematic until late 1800’s Platonic view: there “just are” different species

(e.g. Linnaeus 1750) Evolution theory: species evolve gradually (Mayr, Dobzhansky, 1940) Modern theory of

species, based on interbreeding:

same-species(x,y) x interbreeds with y


Ensatina salamanders

Salamanders living in the hills around California’s Central Valley

Studied by Stebbins (1949), popularised by Dawkins (2004), “The Ancestor’s Tale”.

Ensatina salamanders look different, depending on where they live


Ensatina’s habitat and interbreeding

Ensatina is called a ring species. Logically, the ordering is not ring-like:

eschscholtzii i x i p i o i c i klauberi

c

o

px

eschscholtzii

klauberi

CENTRAL VALLEY


escholtzii i x i p i o i c i klauberi

i(eschscholtzii,klauberi) does not hold

The interbreeding criterion predicts a proliferation of overlapping species:

{ {esch,x}, {x,p}, {p,o}, {o, c}, {c,klau} }


Dawkins also asks:

How about our own ancestry?

You stand in relation i with your parents, grandparents, etc. ...

But at some time there was an ancestor a such that i(a,you)

Do you and a belong to same species?


Are you and a the same species?

Formal Response: “No; interbreeding should be used as in the original definition”

Implication: many overlapping species

Standard Response: “Yes; species should be defined via the transitive closure of i”

Implication: All living beings are one species. The species concept becomes meaningless!


“Let us use names as if they really reflected a discontinuous reality, but let's privately remember that (...) it is no more than a convenient fiction, a pandering to our own limitations”.

(Dawkins 2004, “The Ancestor’s Tale”)


Why is the fiction of species convenient? Many of the links between different species have

gone extinct

Ensatina in the year 2000:

Ensatina in 3000, when xan and oreg are extinct:

esch i xan i pi i oreg i cro i klau

Three separate species!

esch i xan i pi i oreg i cro i klau


A cultural theme

Dawkins (2004): Thinking in crisp terms is a “tyranny of the discontinuous mind” A tyranny ... or a convenience?

Blastland & Dilnot (2008): “false clarity” Substances that are poisonous; genes

that “cause” a medical condition More about this later



Caveat: I’ll paint with a very broad brush!



Eubulides in the audio lab

Decibel (dB) is a metric of sound, aimed at

measuring the experience of loudness:

-30dB is too soft to be audible differences of 0.5dB cannot be discerned 100dB is experienced as very loud


Consider this argument:

-30dB is inaudible-30dB is indiscernible from -29.5dB, so

-29.5dB is inaudible-29.5dB is indiscernible from -29dB, so

-29dB is inaudible...0dB is indiscernible from 0.5dB, so

0.5dB is inaudible...149.5dB is indisc. from 150dB, so

150dB is inaudible


Scientifically enhanced version of an ancient paradox known as sorites invented by Aristotle’s contemporary

Eubulides (approx. 450 bC) One of the original versions:

0 hairs is bold x hairs is bold x+1 hairs is bold therefore, 106 hairs is bold Yet 106 hairs is not bold


[Aside: Vagueness as ignorance]

“bald” does have sharp boundaries, but speakers do not know these boundaries

Vagueness is only apparent

A surprisingly popular view (Williamson 1994, Bonini et al 1999, Sorensen 2001, Tuck 2009) ...


First objection against “vagueness as ignorance”

Objection A: Inconsistent usage

First, we differ in terms of our senses

Example: Colour (Hilbert 1987): People do not distinguish the same colours Density of pigment on lens and retina;

sensitivity of photo receptors


Secondly, we differ culturally:

Reiter et al (2005): weather forecasters use the word evening in different ways. Interviews suggest cultural differences:

Is dinner time relevant? Does the season matter (sunset)?


Second objection

Objection B: “New usage cannot be crisp”

Example: the new word flibbery:

Rhubarb in your mouth I now decide to call this fibberiness:

“My mouth feels flibbery now”. Have I defined the threshold?


Given these objections ...

“Vagueness as ignorance” is not tenable

A theory of meaning ought to take vagueness seriously

[End of Aside on vagueness as ignorance]


Problems for logicians

Boole’s Paradise

For analysing the meaning of language, mathematical logic is the tool of choice

Classical logic is built on crisp dichotomies a statement is either true or false George Boole (1815-1864)

“Minor” variants include Partial Logic (e.g. K.Fine 1975)) Context-aware logics (e.g., H.Kamp 1981)


Window in Lincoln Cathedral


Classical Logic: a dichotomy

20,000 hairs (?)

Not bald

Bald


Partial Logic: two dichotomies

50,000 hairs

Not bald

Bald

Undecided

1,000 hairs


Context-aware logics rely on dichotomies too

Context-aware logics use the notion of a Just-Noticeable Difference (JND), e.g., loudness of sounds: 1dB temperature: 2 degrees Celsius

JNDs modelled as a crisp interval

Crispness contradicted by empirical evidence

More sophisticated models are needed


We have seen:

Vagueness is everywhere

Vagueness is a problem


Vagueness as original sin? (with thanks to Tintoretto)



(The topic of my talk on Friday)

Game theorists are studying language:

What’s the “utility” of a statement?utility = expected payoff


“Why have we tolerated a world-wide several-thousand-year efficiency loss?” (Lipman 2000, 2006)

Survey article : “Utility and Language Generation: the case of vagueness”(van Deemter, J. Philosophical Logic 2009)


Here: just one example

11m 12m


One house of 11m height one house of 12m height

1. “the house that’s 12m tall needs to be demolished”

2. “the tall house needs to be demolished”

Comparison is easier and more reliable than measurement prefer utterance 2

Measurable as likelihood of incorrect action


A need for empirical work!

(We’re looking for a postdoc to work on this for 21 months in Aberdeen ...)


4. Modelling vagueness


C.P. Snow (1959): “Two Cultures”

Rede Lecture, Cambridge

Arts and Sciences do not understand each other Students of the Arts know little about science Postmodernism has caused the gap to widen

We saw earlier: Tyranny of the discontinuous mind (Dawkins)

and false clarity (Blastland & Dilnot)


A similar rift between

1. Engineers & psychophysicists designing theories of measurement and perception

2. Philosophers and linguists studying communication and language

Engineers are comfortable with approximations (typically using Real numbers)

Philosophers want crisp dichotomies (e.g. true/false). They live in Boole’s Paradise!


Engineers design “continuous” logics

Known as degree theories

Variety of approaches, starting with J.Łukasiewicz 1920, and M.Black 1937

Mapping statements to numbers between 0 and 1, to say “how true” they are


Best known example:Fuzzy logic (Zadeh 1975)

[φ] < [] φ is less true than

[Denmark is large] < [Sweden is large]

[Sweden is small] < [Denmark is small]

Negation: [¬φ] = 1- [φ] Disjunction: [φ or ] = max([φ],[]) Conjunction: [φ & ] = min([φ],[])


Analysis of sorites paradox

Each premisse of the form Bald(x) Bald(x+1)

is almost completely true

Bald(x) becomes “less true”

as x increases. E.g., [Bald(106)] 0


Problems for Fuzzy Logic

Suppose we hesitate whether to call a person with 1000 hairs “bald” or “somewhat bald”:

[Bald(1000)] = 0.5 and[SomewhatBald(1000)] = 0.5

Fuzzy Logic assigns to the disjunctiona value that is uncomfortably low:

[Bald(1000) or SwBald(1000)] = max(0.5, 0.5) = 0.5


A better way (Edgington 1992,1996)

[] = probability of someone agreeing with

For example, [ or ] = [] + [] - [&]

Consequences:

[Bald(1000) or SwBald(1000)] = 0.5+0.5 =1[Bald(i) or ¬Bald(i)] = 0.5+0.5 = 1


These remarks about probabilistic logic are only indicative

Let’s reflect briefly on the broader implications of degree theories


Boole’s Paradise was such a pleasant place


Boole’s 2-valued paradise was an attractive place

If we’re expelled, life becomes harder!


Expulsion from Boole’s Paradise


When vagueness is taken seriously ...

Truthfulness and lying become problematic “We didn’t know there was a link between

smoking and cancer” – Not exactly true

Verification and falsification “All ravens black?

What about this grey-black one?” – Not exactly black

Belief revision No longer just the removal of possible worlds


Difficult questions for linguists, philosophers, logicians, and mathematicians


Difficult questions for linguists, philosophers, logicians, and mathematicians

We’d better rise to the challenge!


“Not Exactly: in Praise of Vagueness” Oxford University Press, 28 Jan. 2010

Part 1: Vagueness in science and daily life

Part 2: Theories of vagueness

Part 3: Vagueness in Artificial Intelligence


The End

www.csd.abdn.ac.uk/~kvdeemte/NotExactly

With thanks to my Aberdeen colleagues

Judith Masthoff (illustrations)

Ehud Reiter (BABYTALK corpus)

Advaith Siddharthan (lit. suggestions)

van deemter, riga, jan. 2010 not exactly vagueness as original sin? kees van deemter university of...

Documents

vagueness slide

poor slide

problem slide

y slide

reason slide

authentic slide

original car slide

mental laziness slide