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Not Exactly Vagueness as Original Sin?

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 Exactly Vagueness as Original Sin?

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

  2. 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? van Deemter, WORD, May 2010

  3. 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? van Deemter, WORD, May 2010

  4. 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 van Deemter, WORD, May 2010

  5. 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 van Deemter, WORD, May 2010

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

  7. 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 van Deemter, WORD, May 2010

  8. escholtziii xi pi oi ciklauberi For example,not i(eschscholtzii,klauberi) Interbreeding predicts overlappingspecies: {esch,x} {x,p} {p,o} {o,c} {c,klau} van Deemter, WORD, May 2010

  9. Our own ancestry • you stand in relation i with your parents, grandparents, ... • Let a = the first ancestor such that noti(a,you) • Do you and a belong to same species? van Deemter, WORD, May 2010

  10. 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 van Deemter, WORD, May 2010

  11. 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” van Deemter, WORD, May 2010

  12. 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 van Deemter, WORD, May 2010

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

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

  15. 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: van Deemter, WORD, May 2010

  16. 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” van Deemter, WORD, May 2010

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  18. The numbers use an old-fashioned scale (inches of Mercury) • Words like Very Dry and Much Rainhelp us to understand the scale • These words are vague: Does 22.8 count as Rainor Much Rain? van Deemter, WORD, May 2010

  19. 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: What’s best understood? Remembered? Acted on? (Peters et al. 2009, Zikmund-Fisher et al 2007) van Deemter, WORD, May 2010

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

  21. 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” van Deemter, WORD, May 2010

  22. 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 van Deemter, WORD, May 2010

  23. 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 van Deemter, WORD, May 2010

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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 van Deemter, WORD, May 2010

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

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

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

  44. 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 !! van Deemter, WORD, May 2010

  45. 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 van Deemter, WORD, May 2010

  46. We’re 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? van Deemter, WORD, May 2010

  47. So, … • Vagueness is not just a matter of ignorance • Models of logic and language ought to embrace vagueness van Deemter, WORD, May 2010

  48. 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: Boole’s paradise van Deemter, WORD, May 2010

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

  50. “audible” in classical logic audible xdB inaudible van Deemter, WORD, May 2010

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