embl forum, dec 2010 not exactly vagueness as original sin? kees van deemter university of aberdeen
TRANSCRIPT
EMBL Forum, Dec 2010
Not ExactlyVagueness as Original Sin?
Kees van Deemter
University of Aberdeen
EMBL Forum, Dec 2010
Plan of the talk
1. Vagueness is hard to avoid
2. We are often vague for good reasons
3. Vagueness is a problem
4. How to model vagueness formally?
EMBL Forum, Dec 2010
1. Vagueness is hard to avoid
Vague words have borderline cases
An Aberdeen afternoon in December
-2 C cold
12 C not cold
5 C ¿cold?
EMBL Forum, Dec 2010
Vague adjectives: warm, cold, large, ... Vague nouns: girl, giant, island, ...
and so on …
Most words in English or German are vague
Vagueness is prevalent in science too
Example: species terms
EMBL Forum, Dec 2010
What makes a species?
Long thought unproblematic (e.g. Linnaeus 1750)
The interbreeding criterion(Mayr, Dobzhansky, 1940)
x is same species as y x interbreeds with y
EMBL Forum, Dec 2010
Ensatina (Stebbins 1949, Dawkins 2004)
EMBL Forum, Dec 2010
Ensatina’s habitat and interbreeding
Called a ring species. Logically:
eschscholtzii i x i p i o i c i klauberi
c
o
px
eschscholtzii
klauberi
CENTRAL VALLEY
EMBL Forum, Dec 2010
escholtzii i x i p i o i c i klauberi
For example, not i(eschscholtzii,klauberi)
interbreeding predicts overlapping species:
{esch,x} {x,p} {p,o} {o,c} {c,klau}
“same species” is not transitive: same(esch,x) same(x,p), not same(esch,p)
EMBL Forum, Dec 2010
Our own ancestry
you stand in relation I to your parents, grandparents, ...
Let a = the first ancestor such that not i(a,you)
Do you and a belong to same species?
EMBL Forum, Dec 2010
Are you and a the same species?
Formal Response: “No; the interbreeding criterion should be used”
Many overlapping species
s..s6
s5s4
s3s2
s1
time
EMBL Forum, Dec 2010
Are you and a the same species?
Formal Response: “No; the interbreeding criterion should be used”
Many overlapping species
Standard Response: “Yes; species should be defined via the transitive closure of i”
EMBL Forum, Dec 2010
Are you and a the same species?
Formal Response: “No; the interbreeding criterion should be used”
Many overlapping species
Standard Response: “Yes; species should be defined via the transitive closure of i”
All living beings are one species
EMBL Forum, Dec 2010
Interim conclusion
Key concepts of science resist precise definition
EMBL Forum, Dec 2010
Dawkins on species terms
“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”.
“Tyranny of the discontinuous mind”.
(Dawkins 2004, “The Ancestor’s Tale”)
EMBL Forum, Dec 2010
Why is the fiction of species convenient?
Links between species have gone extinct
When xan and oreg are extinct:
esch i xan i pi i oreg i cro i klau
Result: three separate species: {esch}, {pi}, {cro,klau}
EMBL Forum, Dec 2010
Vagueness as original sin? (with thanks to Tintoretto)
EMBL Forum, Dec 2010
2. We are often vague for good reasons
Why are we often more vague than we need to be? (Game theorists, e.g., B. Lipman 2000, 2006)
Can vagueness be used strategically?
Some tentative answers ..
EMBL Forum, Dec 2010
A practical perspective: computers speaking vaguely
Input: numbers or formulas (15 C, …)
Output: “Mild, … A nice Spring day’’
Input: Time-series data on babies in IC
Output: “Slight fever, … Usually, …’’
What’s best understood? Remembered? Acted on? (Peters et al. 2009, Zikmund-Fisher et al 2007)
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]
EMBL Forum, Dec 2010
First (tentative) answer to Lipman
Vague expressions are easy to produce & digest
They allow us to omit irrelevant info They tend to be brief and efficient They add interpretation to the facts
EMBL Forum, Dec 2010
We’re not the first to see this …
Edwardian “banjo” barometer
very drymuch rain
EMBL Forum, Dec 2010
Second answer
11m 12m
EMBL Forum, Dec 2010
Height of house 1 =11m Height of house 2 =12m
- “the 12m house needs to be demolished”- “the tall house needs to be demolished”
Comparison is easier than measurement
Therefore, we might prefer “the tall house”
EMBL Forum, Dec 2010
Third answer
A politician promising “low unemployment”, or “stable government”
Game-theory models predict benefits from vague promises (Aragones & Neeman 2000) Unforeseen contingencies could make
concrete promises difficult to honour Disappointed voters could hold politician
to account
EMBL Forum, Dec 2010
3. Vagueness is a problem
Sorites puzzle (Eubulides, 450 BC)
One of the top ten unsolved problems of science (“The list universe”, 2007 AD)
0 hairs is bold (x hairs is bold) (x+1 hairs is bold) therefore, 106 hairs is bold Yet 106 hairs is not bold
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
EMBL Forum, Dec 2010
Sorites enhanced by science
Eubulides in the audio lab
Decibel (dB): measures the loudness of sounds
-30dB is inaudible 100dB is very loud differences of 0.5dB cannot be discerned
EMBL Forum, Dec 2010
Eubulides in the audio lab
-30dB is inaudible
-30dB is indistinguishable from -29.5dB, so
-29.5dB is inaudible
EMBL Forum, Dec 2010
Eubulides in the audio lab
-29.5dB is inaudible
-29.5dB is indistinguishable from -29dB, so
-29dB is inaudible
EMBL Forum, Dec 2010
Eubulides in the audio lab
...........
99.5dB is inaudible
99.5dB is indistinguishable from 100dB, so
100dB is inaudible !!
EMBL Forum, Dec 2010
The new sorites argument as a whole
-30dB is inaudible-30dB is indistinguishable from -29.5dB, so
-29.5dB is inaudible-29.5dB is indistinguishable from -29dB, so
-29dB is inaudible
...........
99.5dB is inaudible99.5dB is indistinguishable from 100dB, so
100dB is inaudible !!
EMBL Forum, Dec 2010
A further complication:we’re all different
Colour terms like “red” (Hilbert 1987) People cannot distinguish the same colours
pigment on lens and retina; sensitivity of photo receptors
Time words like “evening” (Reiter et al. 2005)
Is dinner time relevant? The time of year?
EMBL Forum, Dec 2010
For analysing the meaning of language, mathematical logic is the tool of choice
Classical logic is built on crisp dichotomies George Boole (1815-1864) gave
the first algebraic account A statement is either true or false (1 or 0) Nice and simple: Boole’s paradise
EMBL Forum, Dec 2010
“audible” in classical logic
audible
inaudible
x dB
EMBL Forum, Dec 2010
“audible” in classical logic
x dB
audible
inaudible
Indistinguishable
x+
x-
EMBL Forum, Dec 2010
Semi-classical logics use dichotomies too
Context-aware logics (Kamp 1981) use Just-Noticeable Difference
E.g., loudness: JND 1dB
JNDs mistakenly modelled as crisp
Crispness contradicted by empirical evidence
Subtler models are needed
EMBL Forum, Dec 2010
We have seen:
1. Vagueness is everywhere
2. We are vague for a reason
3. Vagueness is a problem
EMBL Forum, Dec 2010
4. How to model vagueness?
EMBL Forum, Dec 2010
Some like it crisp
Blastland & Dilnot (2008): false clarity Substances that are “poisonous” Genes that “cause” a condition
Dawkins (2004): tyranny of the discontinuous mind
C.P. Snow’s Rede Lecture (1959) The Two Cultures
C.P.Snow talked about the gulf separating Scientists & engineers Scholars in the humanities
They do not know each other
and do not speak with each other
SELLC banquet, Guangzhou, Dec 2010
EMBL Forum, Dec 2010
Two approaches to continuous data
Engineers & psychophysicists: approximations, real numbers,Gaussian distributions,
Philosophers, linguists, and most logicians: crisp dichotomies (true/false, 1/0).
They inhabit Boole’s Paradise!
EMBL Forum, Dec 2010
“Continuous” logics
Date back to J.Łukasiewicz 1920 and M.Black 1937
Map statements to numbers between 0 and 1
EMBL Forum, Dec 2010
Fuzzy logic (L.Zadeh 1975)
[φ] = degree of truth of φ
[1000 hairs is bald] < [100 hairs bald]
Negation: [not φ] = 1- [φ]
Disjunction: [φ or ] = max([φ],[])
Conjunction: [φ & ] = min([φ],[])
EMBL Forum, Dec 2010
sorites paradox in Fuzzy Logic
As x increases, Bald(x) becomes less true:
[Bald(0)] = 1
[Bald(103)] 0.5
[Bald(106)] 0
Each premiss
Bald(x) Bald(x+1)is almost true
EMBL Forum, Dec 2010
Problems for Fuzzy Logic
Is 1000 hairs bald or somewhat bald?
[Bald(1000)] = 0.5
[SwBald(1000)] = 0.5
Consider Bald(1000) or SwBald(1000)
Fuzzy Logic assigns a strangely low value:
EMBL Forum, Dec 2010
Problems for Fuzzy Logic
Is 1000 hairs bald or somewhat bald?
[Bald(1000)] = 0.5
[SwBald(1000)] = 0.5
Consider Bald(1000) or SwBald(1000)
Fuzzy Logic assigns a strangely low value:
[Bald(1000) or SwBald(1000)] = max(0.5, 0.5) = 0.5
EMBL Forum, Dec 2010
A better way (e.g., Edgington 1992,1996)
[] = probability of someone agreeing with
[ or ] = [] + [] - [&]
[Bald(1000) or SwBald(1000)] = 0.5 + 0.5 - 0 = 1
EMBL Forum, Dec 2010
Boole’s 2-valued paradise was such an attractive place
EMBL Forum, Dec 2010
When vagueness is taken seriously ...
Truthfulness becomes problematic
“We didn’t know that smoking causes cancer” Not exactly true
Falsification & Belief Revision
“Are all ravens black? What about this grey-black one?” Not exactly black
EMBL Forum, Dec 2010
Questions for linguists, logicians, philosophers, psycho-physicists, computer scientists, biologists
A clear need for collaboration between academic disciplines
EMBL Forum, Dec 2010
The End
www.csd.abdn.ac.uk/~kvdeemte/NotExactly
With thanks to
Judith Masthoff (for Homer Simpson’s coiffure)
EMBL Forum, Dec 2010
“Not Exactly: in Praise of Vagueness” Oxford University Press, Jan. 2010
Part 1: Vagueness in science and daily life
Part 2: Theories of vagueness
Part 3: Vagueness in Artificial Intelligence
EMBL Forum, Dec 2010