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):
Fa*1*
If Fa*1* then Fa*2*
If Fa*2* then Fa*3*
…
If Fa*i-1* then Fa*i*
Therefore,
Fa*i* (where i can be arbitrarily large)

- {a
*1*, ... a*i*} is initially ordered, with each adjacent pair indiscriminable with respect to F. - Fa
*1* is intuitively true. - Fa
*i* is intuitively false.

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

## No comments:

## Post a Comment