1. EMBL Forum, Dec 2010 Not Exactly Vagueness as Original Sin? Kees van Deemter University of Aberdeen

2. 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?

3. 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?

4. 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

5. 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 i nterbreeds with y

6. EMBL Forum, Dec 2010 Ensatina (Stebbins 1949, Dawkins 2004)

7. EMBL Forum, Dec 2010 Ensatinas habitat and interbreeding Called a ring species. Logically: eschscholtzii i x i p i o i c i klauberi c o p x eschscholtzii klauberi CENTRAL VALLEY

8. 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)

9. 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?

10. 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 s5 s4 s3 s2 s1 time

11. 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

12. 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

13. EMBL Forum, Dec 2010 Interim conclusion Key concepts of science resist precise definition

14. 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 Ancestors Tale)

15. 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}

16. EMBL Forum, Dec 2010 Vagueness as original sin? (with thanks to Tintoretto)

17. 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..

18. 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, … Whats best understood? Remembered? Acted on? (Peters et al. 2009, Zikmund-Fisher et al 2007)

19. 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]

20. 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

21. EMBL Forum, Dec 2010 Were not the first to see this … Edwardian banjo barometer very dry much rain

22. EMBL Forum, Dec 2010 Second answer 11m 12m

23. 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

24. 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

25. 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, 10 6 hairs is bold Yet 10 6 hairs is not bold

26. EMBL Forum, Dec 2010

41. 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

42. EMBL Forum, Dec 2010 Eubulides in the audio lab -30dB is inaudible -30dB is indistinguishable from -29.5dB, so -29.5dB is inaudible

43. EMBL Forum, Dec 2010 Eubulides in the audio lab -29.5dB is inaudible -29.5dB is indistinguishable from -29dB, so -29dB is inaudible

44. EMBL Forum, Dec 2010 Eubulides in the audio lab........... 99.5dB is inaudible 99.5dB is indistinguishable from 100dB, so 100dB is inaudible !!

45. 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 !!

46. EMBL Forum, Dec 2010 A further complication: were 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?

47. 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: Booles paradise

48. EMBL Forum, Dec 2010 audible in classical logic audible inaudible x dB

49. EMBL Forum, Dec 2010 audible in classical logic x dB audible inaudible Indistinguishable x+ x-

50. 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

51. EMBL Forum, Dec 2010 We have seen: 1. Vagueness is everywhere 2. We are vague for a reason 3. Vagueness is a problem

52. EMBL Forum, Dec 2010 4. How to model vagueness?

53. 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

54. C.P. Snows 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

55. 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 Booles Paradise!

56. EMBL Forum, Dec 2010 Continuous logics Date back to J.Łukasiewicz 1920 and M.Black 1937 Map statements to numbers between 0 and 1

57. 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],[ ])

58. EMBL Forum, Dec 2010 sorites paradox in Fuzzy Logic As x increases, Bald(x) becomes less true: [Bald(0)] = 1 [Bald(10 3 )] 0.5 [Bald(10 6 )] 0 Each premiss Bald(x) Bald(x+1) is almost true

59. 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:

60. 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

61. 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

62. EMBL Forum, Dec 2010 Booles 2-valued paradise was such an attractive place

63. EMBL Forum, Dec 2010 When vagueness is taken seriously... Truthfulness becomes problematic We didnt know that smoking causes cancer Not exactly true Falsification & Belief Revision Are all ravens black? What about this grey-black one? Not exactly black

64. EMBL Forum, Dec 2010 Questions for linguists, logicians, philosophers, psycho-physicists, computer scientists, biologists A clear need for collaboration between academic disciplines

65. EMBL Forum, Dec 2010 The End www.csd.abdn.ac.uk/~kvdeemte/NotExactly With thanks to Judith Masthoff (for Homer Simpsons coiffure)

66. 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

67. EMBL Forum, Dec 2010