Philosophical Buzzwords: Sorites

About Philosophical Buzzwords posts. Todd asked for a definition of a sorites argument. I know what a sorites argument is, but I'm not entirely sure I can give an uncontroversial account. But I'll try. Luckily, I have a candidate handy, from my paper on the sorites paradox and the aggregation of harms. The following argument is prototypically a sorites paradox:

1. A single grain of wheat is not a heap. 2. For any number n, if n grains of wheat are not a heap, then neither are n+1 grains. 3. Therefore, there is no number n such that n grains is enough to make a heap.

An alternative formulation which would also count as a sorites paradox is this:

1. A single grain of wheat is not a heap. 2.1. If 1 grain of wheat is not a heap, then neither is 2 grains. 2.2. If 2 grains of wheat are not a heap, then neither are 3 grains. ... 2.999999. If 999,999 grains of wheat are not a heap, then neither are 1,000,000. 3. Therefore, by a million applications of modus ponens, 1,000,000 grains are not a heap.

What's notable is that the arguments appear valid, each premise is intuitively true, and the conclusion is intuitively false. I think this might be a good formal definition of a sorites:

An argument is soritical if and only if it meets all of the following conditions:

• it is of this form, where F is the soritical predicate (‘is not a heap’, for instance):

  Fa1 If Fa1 then Fa2 If Fa2 then Fa3 … If Fai-1 then Fai Therefore, Fai (where i can be arbitrarily large)

• {a1, ... ai} is initially ordered, with each adjacent pair indiscriminable with respect to F.
• Fa1 is intuitively true.
• Fai is intuitively false.

I think that a formulation very much like this might come from Barnes.