1. van Deemter, WORD, May 2010 Not Exactly Vagueness as Original Sin? Kees van Deemter University of Aberdeen

2. van Deemter, WORD, May 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. van Deemter, WORD, May 2010 1. Vagueness is hard to avoid Vague words have borderline cases An Aberdeen afternoon in May at 3PM 22 C warm 8 C not warm 15 C ¿warm?

4. van Deemter, WORD, May 2010 Vague adjectives: warm, cold, large,... Vague nouns: girl, giant, island,... and so on … Most words in ordinary English are vague Vagueness is prevalent in science too Example: species terms

5. van Deemter, WORD, May 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. van Deemter, WORD, May 2010 Ensatina (Stebbins 1949, Dawkins 2004)

7. van Deemter, WORD, May 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. van Deemter, WORD, May 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}

9. van Deemter, WORD, May 2010 Our own ancestry you stand in relation i with your parents, grandparents,... Let a = the first ancestor such that not i(a,you) Do you and a belong to same species?

10. van Deemter, WORD, May 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. van Deemter, WORD, May 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. van Deemter, WORD, May 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. van Deemter, WORD, May 2010 Interim conclusion Key concepts of science resist precise definition

14. van Deemter, WORD, May 2010 Vagueness as original sin? (with thanks to Tintoretto)

15. van Deemter, WORD, May 2010 2. We are often vague for good reasons Strategic vagueness Why are we often more vague than we need to be? (Game theorists, e.g., B. Lipman 2000, 2006) Some tentative answers:

16. van Deemter, WORD, May 2010 First answer Suppose I say about a day in May: The temperature is 15 C. The rain probability is 20%. Wind speed is 10mph, humidity 55% Easier to digest: A nice-enough Spring day, with light winds and a chance of rain

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18. The numbers use an old-fashioned scale (inches of Mercury) Words like Very Dry and Much Rain help us to understand the scale These words are vague: Does 22.8 count as Rain or Much Rain ?

19. van Deemter, WORD, May 2010 Aberdeen Computing dept. build programs Input: numbers or formulas (15 C, …) Output: words (Mild, … A nice Spring day) Medical applications too (e.g. BABYTALK) Open questions: Whats best understood? Remembered? Acted on? (Peters et al. 2009, Zikmund-Fisher et al 2007)

20. van Deemter, WORD, May 2010 Second answer 11m 12m

21. van Deemter, WORD, May 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

22. van Deemter, WORD, May 2010 Third answer A politician promising drastic budget cuts, 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

23. van Deemter, WORD, May 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

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40. 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

41. van Deemter, WORD, May 2010 Eubulides in the audio lab -30dB is inaudible -30dB is indistinguishable from -29.5dB, so -29.5dB is inaudible

42. van Deemter, WORD, May 2010 Eubulides in the audio lab -29.5dB is inaudible -29.5dB is indistinguishable from -29dB, so -29dB is inaudible

43. van Deemter, WORD, May 2010 Eubulides in the audio lab........... 99.5dB is inaudible 99.5dB is indistinguishable from 100dB, so 100dB is inaudible !!

44. van Deemter, WORD, May 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 !!

45. van Deemter, WORD, May 2010 Vagueness as ignorance The concept bald does have sharp boundaries, but speakers do not know them A surprisingly popular view (Williamson 1994, Sorensen 2001, Tuck 2009) Contradicted by empirical evidence

46. van Deemter, WORD, May 2010 Were all different Colour terms like red (Hilbert 1987, R.Parikh 2000) 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. van Deemter, WORD, May 2010 So, … Vagueness is not just a matter of ignorance Models of logic and language ought to embrace vagueness

48. van Deemter, WORD, May 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 mathematical account A statement is either true or false (1 or 0) Nice and simple: Booles paradise

49. van Deemter, WORD, May 2010 Window in Lincoln Cathedral

50. van Deemter, WORD, May 2010 audible in classical logic audible inaudible x dB

51. van Deemter, WORD, May 2010 audible in classical logic x dB audible inaudible Indistinguishable x+ x-

52. van Deemter, WORD, May 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

53. van Deemter, WORD, May 2010 We have seen: 1. Vagueness is everywhere 2. We are vague for a reason 3. Vagueness is a problem

54. van Deemter, WORD, May 2010 4. How to model vagueness?

55. van Deemter, WORD, May 2010 Some like it crisp Blastland & Dilnot (2008): false clarity Substances that are poisonous Genes that cause a condition Another example: Vagueness as ignorance

56. van Deemter, WORD, May 2010 Two cultures (compare C.P. Snow) Engineers & psychophysicists: approximations, real numbers, Gaussian distributions, Philosophers, linguists, and most logicians: crisp dichotomies (true/false, 1/0). They inhabit Booles Paradise!

57. van Deemter, WORD, May 2010 Continuous logics Date back to J.Łukasiewicz 1920 and M.Black 1937 Map statements to numbers between 0 and 1

58. van Deemter, WORD, May 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],[ ])

59. van Deemter, WORD, May 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

60. van Deemter, WORD, May 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:

61. van Deemter, WORD, May 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

62. van Deemter, WORD, May 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

63. van Deemter, WORD, May 2010 Booles 2-valued paradise was such an attractive place

64. van Deemter, WORD, May 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

65. van Deemter, WORD, May 2010 Questions for linguists, logicians, philosophers, computer scientists Wed better rise to the challenge!

66. van Deemter, WORD, May 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. van Deemter, WORD, May 2010 The End www.csd.abdn.ac.uk/~kvdeemte/NotExactly With thanks to Judith Masthoff (for Homer Simpsons coiffure)

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69. 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)

70. van Deemter, WORD, May 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 Three separate species!