Philosophy

Thank you for the magnanimous response; I trust these topics were indeed retrieved from a list of unsolved problems and not from a list of papers you wrote (only kidding!) In any event, I will argue that the Sorites "paradox" is no such thing--and that its arguments can be rejected. DEFINITION: The Sorites paradox describes a number of related problems involving discontinuity, boundary-conditions, parthood, identity, and mereology. For any aggregate entity, suffering the loss of a single constituent compositional sub-entity does not make any difference to the described entity. A heap of one million grains, for example, is still a heap after it has lost one. However, this logic would permit one to subtract (or add--it doesn't matter) to the point of absurdity; if 999,000 grains constitute a heap, then so must a single grain. (All problems of this paradox are additive in nature, even if some aren't expressed in composition--e.g. when does a whisper become a shout?) More formally: N = X; If N = X, --> N - 1 = X; ergo N - 999,999 = X. ARGUMENT I take it as manifestly evident that since the Sorite's paradox proceeds from a true statement to a false conclusion, that it is invalid. I intend to show why. In the first place, there appears to be a logical error in Sorite's paradox--one that inheres in the presentation of the problem itself. The metric of additive (or reductive) iteration is taken to be the minimal unit allowable. But why? Another flaw of Sorite's argument lies in its lexical imprecision. "Heap" is an arbitrary term; its usefulness is contingent on its describing functional relations. I have singled out this word because Sorite's paradox persists only by virtue of ambiguity. By redefining a heap in terms of mass or molarity, one could theoretically avoid such problems, but would forfeit as well any practical conceptual reference. Similarly, "baldness" would lose its potency if its descriptive role were limited to heads having zero hairs. Therefore, in rejecting the paradox, I will show not only that it is false, but will present--out of necessity--a semantics which would allow meaningful discourse of the problematic terms in question. I claim, therefore, that: 1a. Because the argument proceeds from mathematical induction, the addition or subtraction of a single unit from an entity is logically indistinct from the addition or subtraction of any number of units. That is, the common-sense distinction between All but one and All but (All - 1) is not captured by the simplistic logic of the exercise. 1b. The paradox depends on the continuity of an entity in cases of minimal addition or subtraction. If this is no longer a distinct point of essence in the inductive chain, the paradox doesn't hold. 2a. Mass nouns are meaningful only inasmuch as they are regarded contextually. The heapness of any entity is a predicate whose meaning is no more context-invariant than the predicate to the proposition that "I am in Hawaii" is geography-invariant. Heapishness, then, is contextually contingent. 2b. Predicates of extension vary contextually. The word tall, for example, applies differently in different contexts. A short building is taller than a tall person. Likewise a single person can be both tall and not tall depending on the circumstances. Tallness cannot just be an expression of aggregated measurements (presuming--reasonably I think--that space is discontinuous); instead, it is a predicate of extension. Thus boundaries are not static but rather congruent to the context. Furthermore, the context extends not only in relation to comparative entities but to the perspective of the viewer as well. 2c. The truth-value of expressions with extensional predicates is contingent on context. No aggregation of heap sub-entities, by this manner of reckoning, can be meaningfully described as a heap per se.