Sorites Applied to Composition

The sorites paradox arises frequently when the property in question appeals to some
manner of degree. Above, it was demonstrated that properties that fall under the sorites paradox cannot be natural. This is because such a property, if it is to be coherent at all, is vague. Since there is no vagueness in the world, such a property does not, in the final metaphysical picture, exist.

(1) If a property falls under the sorites paradox, then it is not a natural property.

There are, of course, a plethora of answers to the Special Composition Question. The aim of this section is only to eliminate one type of answer. Under compatibilst answers to SCQ, there are those that appeal to some degree of contact between parts. Prima facie, this type of answer is promising. Consider again our ham sandwich. Isn't it just when we take the ham and cheese and place them between the bread that a ham sandwich is formed?

This, certaintly, is a case in which the distance between the parts is relevent. There is no sandwich when the parts are scattered across the kitchen counter. But what about the parts getting closer allows for a sandwich to form? Perhaps they need to be touching. But if that were the answer to SCQ, then every time two people shake hands, they form a new object. Surely this is not the case.

1) If CONTACT is true, then every time two people shake hands, an object is formed.
2) It is not the case that every time two people shake hands, an object is formed.
3) CONTACT is not true.

A similar line of reasoning denies all answers that appeal to some connectedness between the parts (call these fusion-type answers).

Now what of an appeal direct to distance of parts? Our ham sandwich does not come into existence until all the parts are some distance away from each other. But recall the argument given against baldness. Where would one mark the distinction between ham sandwich and no ham sandwich? One meter? One centimeter? One micrometer? Surely my sandwich is allowed some measure of shifting without falling out of existence.

(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.

Unfortunetly, this is sufficient to run a sorites paradox.

(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.
(2) Two parts 0 units apart form an object. (If there is any distance that permits composition, it is this)
(3) Two parts 1 unit apart form an object. (From 1 and 2)
(4) Two parts 2 units apart form an object. (From 1 and 3)
...
(100,001) Two parts 99,999 units apart form an object. (From 1 and 100,000)
(100,002) Two parts 99,999 units apart do not form an object. (From common sense)
(100,003) Contradiction!

Thus, any answer to the Special Composition question cannot appeal only to the spacial relations that hold between objects. The argument can be run analogously to time, and likely any other quantitative relation. Note, however, that this argument is vulnerable if space is discrete. More on this will be said later.