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van Deemter, Riga, Jan. 2010
Not ExactlyVagueness as Original Sin?
Kees van Deemter
University of Aberdeen
Scotland
van Deemter, Riga, Jan. 2010
Plan of the talk
1. Vagueness is everywhere
van Deemter, Riga, Jan. 2010
Plan of the talk
1. Vagueness is everywhere
2. Vagueness is a problem
van Deemter, Riga, Jan. 2010
Plan of the talk
1. Vagueness is everywhere
2. Vagueness is a problem
3. We are vague for a reason
van Deemter, Riga, Jan. 2010
Plan of the talk
1. Vagueness is everywhere
2. Vagueness is a problem
3. We are vague for a reason
4. How to model vagueness
van Deemter, Riga, Jan. 2010
1. Vagueness is everywhere
Example
doctors informing doctors about a baby in intensive care
van Deemter, Riga, Jan. 2010
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]
van Deemter, Riga, Jan. 2010
“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 ...
van Deemter, Riga, Jan. 2010
Example: Is John poor?
£19,000 p/a
£21,000 (Threshold A)
£17,5000 (Threshold B)
John
John is poor
John is not poor
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
1. Vagueness is everywhere
First example: vague identity
A car undergoes a series of repairs.
At what stage does it become a different car?
van Deemter, Riga, Jan. 2010
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)
van Deemter, Riga, Jan. 2010
The judge argued ...
... that this is no longer the “original” car
van Deemter, Riga, Jan. 2010
The judge argued ...
... that this is no longer the “original” car nor the “genuine” Old Number One
van Deemter, Riga, Jan. 2010
The judge argued ...
... 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”
van Deemter, Riga, Jan. 2010
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.”
van Deemter, Riga, Jan. 2010
What is the judge saying?
What if further repairs/replacements are performed, so none of the original parts remains?
van Deemter, Riga, Jan. 2010
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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
van Deemter, Riga, Jan. 2010
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.
van Deemter, Riga, Jan. 2010
1. Vagueness is everywhere
Second example: the fiction of species
van Deemter, Riga, Jan. 2010
The fiction of species
Surely, species-denoting terms are crisp?
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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} }
van Deemter, Riga, Jan. 2010
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?
van Deemter, Riga, Jan. 2010
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!
van Deemter, Riga, Jan. 2010
“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”)
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
2. Vagueness is a problem
van Deemter, Riga, Jan. 2010
2. Vagueness is a problem
Caveat: I’ll paint with a very broad brush!
van Deemter, Riga, Jan. 2010
2. Vagueness is a problem
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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[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) ...
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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)?
van Deemter, Riga, Jan. 2010
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?
van Deemter, Riga, Jan. 2010
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]
van Deemter, Riga, Jan. 2010
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)
van Deemter, Riga, Jan. 2010
Window in Lincoln Cathedral
van Deemter, Riga, Jan. 2010
Classical Logic: a dichotomy
20,000 hairs (?)
Not bald
Bald
van Deemter, Riga, Jan. 2010
Partial Logic: two dichotomies
50,000 hairs
Not bald
Bald
Undecided
1,000 hairs
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
We have seen:
Vagueness is everywhere
Vagueness is a problem
van Deemter, Riga, Jan. 2010
3. We are vague for a reason
van Deemter, Riga, Jan. 2010
Vagueness as original sin? (with thanks to Tintoretto)
van Deemter, Riga, Jan. 2010
3. We are vague for a reason
(The topic of my talk on Friday)
Game theorists are studying language:
What’s the “utility” of a statement?utility = expected payoff
van Deemter, Riga, Jan. 2010
“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)
van Deemter, Riga, Jan. 2010
Here: just one example
11m 12m
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
A need for empirical work!
(We’re looking for a postdoc to work on this for 21 months in Aberdeen ...)
van Deemter, Riga, Jan. 2010
4. Modelling vagueness
van Deemter, Riga, Jan. 2010
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)
van Deemter, Riga, Jan. 2010
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!
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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],[])
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
These remarks about probabilistic logic are only indicative
Let’s reflect briefly on the broader implications of degree theories
van Deemter, Riga, Jan. 2010
Boole’s Paradise was such a pleasant place
van Deemter, Riga, Jan. 2010
Boole’s 2-valued paradise was an attractive place
If we’re expelled, life becomes harder!
van Deemter, Riga, Jan. 2010
Expulsion from Boole’s Paradise
van Deemter, Riga, Jan. 2010
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
van Deemter, Riga, Jan. 2010
Difficult questions for linguists, philosophers, logicians, and mathematicians
van Deemter, Riga, Jan. 2010
Difficult questions for linguists, philosophers, logicians, and mathematicians
We’d better rise to the challenge!
van Deemter, Riga, Jan. 2010
“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
van Deemter, Riga, Jan. 2010
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)