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