van Deemter, Riga, Jan Not Exactly Vagueness as Original Sin? Kees van Deemter University of Aberdeen Scotland

van Deemter, Riga, Jan Plan of the talk 1. Vagueness is everywhere

van Deemter, Riga, Jan Plan of the talk 1. Vagueness is everywhere 2. Vagueness is a problem

van Deemter, Riga, Jan Plan of the talk 1. Vagueness is everywhere 2. Vagueness is a problem 3. We are vague for a reason

van Deemter, Riga, Jan 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 Vagueness is everywhere Example doctors informing doctors about a baby in intensive care

van Deemter, Riga, Jan 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 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 Johns income is £20,000...

van Deemter, Riga, Jan 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 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 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 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 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 The judge argued that this is no longer the original car

van Deemter, Riga, Jan The judge argued that this is no longer the original car nor the genuine Old Number One

van Deemter, Riga, Jan 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 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 What is the judge saying? What if further repairs/replacements are performed, so none of the original parts remains?

van Deemter, Riga, Jan. 2010

Successive changes are common the cells in your body renew themselves a book changes constantly when its 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 How about the concepts that we use to categorize things? Lets 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 Vagueness is everywhere Second example: the fiction of species

van Deemter, Riga, Jan The fiction of species Surely, species-denoting terms are crisp?

van Deemter, Riga, Jan What makes a species? Thought unproblematic until late 1800s 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 Ensatina salamanders Salamanders living in the hills around Californias Central Valley Studied by Stebbins (1949), popularised by Dawkins (2004), The Ancestors Tale. Ensatina salamanders look different, depending on where they live

van Deemter, Riga, Jan. 2010

Ensatinas 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 p x eschscholtzii klauberi CENTRAL VALLEY

van Deemter, Riga, Jan 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 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 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 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 Ancestors Tale)

van Deemter, Riga, Jan 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 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 Vagueness is a problem

van Deemter, Riga, Jan Vagueness is a problem Caveat: Ill paint with a very broad brush!

van Deemter, Riga, Jan 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 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 dB is indisc. from 150dB, so 150dB is inaudible

van Deemter, Riga, Jan Scientifically enhanced version of an ancient paradox known as sorites invented by Aristotles contemporary Eubulides (approx. 450 bC) One of the original versions: 0 hairs is bold x hairs is bold x+1 hairs is bold therefore, 10 6 hairs is bold Yet 10 6 hairs is not bold

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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 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 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 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 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 Problems for logicians Booles 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 ( ) Minor variants include Partial Logic (e.g. K.Fine 1975)) Context-aware logics (e.g., H.Kamp 1981)

van Deemter, Riga, Jan Window in Lincoln Cathedral

van Deemter, Riga, Jan Classical Logic: a dichotomy 20,000 hairs (?) Not bald Bald

van Deemter, Riga, Jan Partial Logic: two dichotomies 50,000 hairs Not bald Bald Undecided 1,000 hairs

van Deemter, Riga, Jan 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 We have seen: Vagueness is everywhere Vagueness is a problem

van Deemter, Riga, Jan We are vague for a reason

van Deemter, Riga, Jan Vagueness as original sin? (with thanks to Tintoretto)

van Deemter, Riga, Jan We are vague for a reason (The topic of my talk on Friday) Game theorists are studying language: Whats the utility of a statement? utility = expected payoff

van Deemter, Riga, Jan 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 Here: just one example 11m 12m

van Deemter, Riga, Jan One house of 11m height one house of 12m height 1.the house thats 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 A need for empirical work! (Were looking for a postdoc to work on this for 21 months in Aberdeen...)

van Deemter, Riga, Jan Modelling vagueness

van Deemter, Riga, Jan 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 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 Booles Paradise!

van Deemter, Riga, Jan 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 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 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(10 6 )] 0

van Deemter, Riga, Jan 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 disjunction a value that is uncomfortably low: [Bald(1000) or SwBald(1000)] = max(0.5, 0.5) = 0.5

van Deemter, Riga, Jan A better way (Edgington 1992,1996) [ ] = probability of someone agreeing with For example, [ or ] = [ ] + [ ] - [ & ] Consequences: [Bald(1000) or SwBald(1000)] = = 1 [Bald(i) or ¬Bald(i)] = = 1

van Deemter, Riga, Jan These remarks about probabilistic logic are only indicative Lets reflect briefly on the broader implications of degree theories

van Deemter, Riga, Jan Booles Paradise was such a pleasant place

van Deemter, Riga, Jan Booles 2-valued paradise was an attractive place If were expelled, life becomes harder!

van Deemter, Riga, Jan Expulsion from Booles Paradise

van Deemter, Riga, Jan When vagueness is taken seriously... Truthfulness and lying become problematic We didnt 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 Difficult questions for linguists, philosophers, logicians, and mathematicians

van Deemter, Riga, Jan Difficult questions for linguists, philosophers, logicians, and mathematicians Wed better rise to the challenge!

van Deemter, Riga, Jan Not Exactly: in Praise of Vagueness Oxford University Press, 28 Jan Part 1: Vagueness in science and daily life Part 2: Theories of vagueness Part 3: Vagueness in Artificial Intelligence

van Deemter, Riga, Jan The End With thanks to my Aberdeen colleagues Judith Masthoff (illustrations) Ehud Reiter ( BABYTALK corpus) Advaith Siddharthan (lit. suggestions)