In a reply to a question about the sorites paradox, Professor Maitzen writes: "Logic requires there to be a sharp cutoff in between those clear cases -- a line that separates having enough leaves to be a head of lettuce from having too few leaves to be a head of lettuce. Or else there couldn't possibly be heads of lettuce." However, there is no justification that clearly leads from his premise to his conclusion: obviously we can have heaps of sand without knowing exactly how many grains of sand are required to distinguish a "heap" from a pile of individual sand grains, or else there would not be a so-called "paradox" in the first place! The premise as he presents it sounds like a tautology, not a logical argument. What makes a "heap" of sand is not only how many grains of sand there are, but also how those grains are arranged. If you took a "heap" of sand and stretched it out in a line, you would have the same number of grains, but it would no longer be a "heap." You could take a head of lettuce and separate it into its individual leaves, but then you'd no longer have a head of lettuce. So you can clearly have a head of lettuce without knowing the exact number of leaves required, since we can easily validate that assertion through an appeal to empirical experience. The sorites paradox tries to impose a degree of precision on a concept that by design is meant to be indeterminate in number. His answer does not address that consideration at all, but merely insists that a heap "must be" determinate in number or else it could not exist.

What makes a "heap" of sand is not only how many grains of sand there are, but also how those grains are arranged. If you took a "heap" of sand and stretched it out in a line, you would have the same number of grains, but it would no longer be a "heap."

Agreed! Even so, there must be a sharp cutoff between (a) enough grains to make a heap of sand if they're arranged properly and (b) too few grains to make a heap of sand no matter how they're arranged. An instance of (a) would be 1 billion; an instance of (b) would be 1.

Why must there be a sharp cutoff between (a) and (b)? Because otherwise (a) can be shown to apply to 1 (which clearly it doesn't) or (b) can be shown to apply to 1 billion (which clearly it doesn't). That's what the sorites argument shows.

...obviously we can have heaps of sand without knowing exactly how many grains of sand are required to distinguish a "heap" from a pile of individual sand grains, or else there would not be a so-called "paradox" in the first place!

You seem to be saying that the sorites paradox is simply that we have heaps of sand without knowing the smallest number of grains that's enough, if arranged properly, to make a heap of sand. I don't see why that gap in our knowledge would itself be paradoxical, any more than it's paradoxical that the moon exists but we don't know its exact mass in grams. Plenty of exact measures elude our knowledge without thereby being paradoxical.

The sorites paradox tries to impose a degree of precision on a concept that by design is meant to be indeterminate in number.

The sorites argument doesn't impose a sharp cutoff between (a) and (b) that can't exist; instead, it reveals that a sharp cutoff must exist. As I suggested in my previous reply, the everyday sorites-prone concepts aren't designed to be indeterminate. They're not designed at all. We're taught those concepts by being shown clear positive cases; our teachers simply don't comment on the other cases. The indeterminacy results from omission rather than by design.

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