Main.VaguenessFuzzy History

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March 05, 2007, at 11:43 PM by 219.78.20.232 -
Changed lines 7-9 from:
@@@If a man with n hairs on his head is bald, then a man with n + 1 hairs on his
head is also bald.@@@
to:
@@@If a man with n hairs on his head is bald, then a man with n + 1 hairs on his head is also bald.@@@
Changed lines 11-24 from:
* For one thing, the fuzzy-theoretic machinery appears to replace vagueness
with extremely refined precision. To what degree, exactly, is it true that Jones is
bald? To degree 0.6? Perhaps to degree 0.59? Or maybe 0.5999? Second, the as-
sumption of a totally ordered set of truth-values is itself problematic. How does the
degree to which Jones is bald compare to the degree to which Smith is tall? How
does it compare to the degree to which a certain borderline rock is part of Everest?
Third, there is the embarrassing presupposition that a point must still exist where
one goes from fully fledged truth to partial truth, or from partial truth to fully
fledged falsehood. What is the maximum value of n such that a person with n hairs
is truly bald, i.e., bald to degree 1? What is the last rock, along a continuous path
descending from the peak of Everest, which is definitely part of the mountain? All of
these are questions which may not have practical relevance but which appear to un-
dermine the theoretical force of the account
.
to:
* Truth-value is still precise even if not identical to 1.
* There is still a sharp line in moving from 1 to less than 1
.
March 05, 2007, at 11:42 PM by 219.78.20.232 -
Added lines 3-25:
* Truth is a matter of degree.
* Continuum of truth-values represented by real numbers in the interval [0,1]
* The conditional premise in the Sorites is not completely true.

@@@If a man with n hairs on his head is bald, then a man with n + 1 hairs on his
head is also bald.@@@

!!Problems

* For one thing, the fuzzy-theoretic machinery appears to replace vagueness
with extremely refined precision. To what degree, exactly, is it true that Jones is
bald? To degree 0.6? Perhaps to degree 0.59? Or maybe 0.5999? Second, the as-
sumption of a totally ordered set of truth-values is itself problematic. How does the
degree to which Jones is bald compare to the degree to which Smith is tall? How
does it compare to the degree to which a certain borderline rock is part of Everest?
Third, there is the embarrassing presupposition that a point must still exist where
one goes from fully fledged truth to partial truth, or from partial truth to fully
fledged falsehood. What is the maximum value of n such that a person with n hairs
is truly bald, i.e., bald to degree 1? What is the last rock, along a continuous path
descending from the peak of Everest, which is definitely part of the mountain? All of
these are questions which may not have practical relevance but which appear to un-
dermine the theoretical force of the account.

March 05, 2007, at 10:25 PM by 219.78.20.232 -
Added lines 1-3:
!Fuzzy logic and vagueness

[[Category.LogicAndMaths]]