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Not Exactly Vagueness as Original Sin?. Kees van Deemter University of Aberdeen. Plan of the talk. Vagueness is hard to avoid We are often vague for good reasons Vagueness is a problem How to model vagueness formally?. 1. Vagueness is hard to avoid.
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Not ExactlyVagueness as Original Sin? Kees van Deemter University of Aberdeen EMBL Forum, Dec 2010
Plan of the talk • Vagueness is hard to avoid • We are often vague for good reasons • Vagueness is a problem • 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 Ccold 12 Cnot 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
x p eschscholtzii o CENTRAL VALLEY klauberi c Ensatina’s habitat and interbreeding Called a ring species. Logically: eschscholtzii i x i p i o i c i klauberi EMBL Forum, Dec 2010
escholtziii xi pi oi ciklauberi For example,not i(eschscholtzii,klauberi) • interbreeding predicts overlappingspecies: {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 noti(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.. time s6 s5 s4 s3 s2 s1 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) EMBL Forum, Dec 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
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 dry much 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 houseneeds 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 isnot bold 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 inaudible 99.5dB 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 xdB inaudible EMBL Forum, Dec 2010
“audible” in classical logic audible x+ Indistinguishable x dB x- inaudible 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
