The word sorite comes from the Greek word soros, meaning, “heap”.
A sorite is a discourse progressing by reiteration of the same syntactic form.
1. Sorite paradox
The sorite of the heap is one of the famous paradoxes proposed by Eubulide, a Greek philosopher, contemporary of Aristotle:
A grain of wheat is not enough to make a heap of wheat, nor two grains, nor three grains, etc.
In other words, if n grains do not make a heap, n + 1 do not make a heap either.
So no amount of grains of wheat can make up a pile of wheat.
Similarly, and if you take a grain out of a heap of wheat, you still have a heap of wheat, and so on, down to the last grain. So, a grain of wheat is itself a heap of wheat. [1]
This paradox can be illustrated by any collective name: cluster, crowd, flock, army, collection, bouquet, collective…
2. Rhetorical sorite
A rhetorical sorite (gradatio, climax) is a discourse progressing by the reiteration of the same cause-effect, begetter-begotten relation, or simply temporal succession of linked events, building up to a climax, as in the following poem:
Cursed be
The father of the wife
Of the blacksmith who forged the iron of the ax
With which the woodcutter fell the oak
In which was carved the bed
Where was born the great-grandfather
Of the man who drove the car
In which your mother
Met your father!
Robert Desnos, [The Dove of the Ark], [1923]. [2]
3. Logical sorite: a chain of syllogisms
In logic, the term sorite refers to a chain of syllogisms such that the conclusion of the first serves as a premise for the following one.
The sorite is also called polysyllogism:
A polysyllogism is a series of syllogisms chained together in such a way that the conclusion of one serves as a premise for the next. (Chenique 1975, p. 255).
Serial or subordinate argumentation are other names for polysyllogistic argument, and for this kind of sorite, S. Serial Argumentation.
The term sorite may also refer to an abbreviated polysyllogism “in which the conclusion of each syllogism is not expressed, except the last” (Chenique 1975, pp. 256-257).
The critical problem with the polysyllogism is the stability and reliability of the reiterated inference. In a formal system, the transmission of the truth is flawless, while in a default argument chain, as the reasoning progresses the cogency of the conclusions weakens. In such series, everything happens as if the weights of the rebuttals grow exponentially, up to the point where the chain will break.
Other kinds of reasoning engage in the sorite paradox, for example:
— Analogy: A is analogous to B, B to C, … and Y to Z. But is Z always analogous to A? S. Analogy.
— Causal chains, when the expected, theoretically perfect, “domino effect” is counteracted.
— Interpretive reasoning; which is why some Arabic legal schools refuse to interpret the sacred text of the Koran. They consider that only the starting point, the letter of the Sacred Text can be considered certain, and that engaging in interpretation would trigger a slippery slope process, leading to some unpredictable result, potentially contradictory with the undisputable content of the Sacred Text.
3. Chinese sorite
The expression « Chinese sorite » or « Confucian sorite » is used by Masson-Oursel ([1912], p. 17) to designate « arguments [argumentations] expressing a sequence of means implemented by human activity in view of an end » (1912, p. 20). Eno (2016, p.11) speaks of “sorite” or “chain syllogism”[2].
The sorite posits a desirable state and considers the stages along the way to achieving it. The progressive sorite starts from the first stage and proceeds to the ultimate goal. The spring of the progression can be considered as causal, instrumental or indeterminate, in this case the succession seems purely temporal. The regressive sorite states the goal and enumerates the stages backwards to the first, basic stage.
In the brief Confucian treatise The Great Learning (Dàxué), a regressive sorite is immediately followed by a progressive sorite on identical contents. Regressive sorite:
In ancient times, those who wished to make bright virtue brilliant in the world first ordered their states; those who wished to order their states first aligned their households; those who wished to align their households first refined their persons; those who wished to refine their persons first balanced their minds; those who wished to balance their minds first perfected the genuineness of their intentions; those who wished to perfect the genuineness of their intentions first extended their understanding; extending one’s understanding lies in aligning affairs.
The Great learning, R. Eno, p. 12
In the progressive sorite, « the first condition spreads, so to speak, into new conditions which arise from each other. Thus, in Mencius IV, 1, § 27, each term unites with the next by the expression: ‘the main fruit (chĕu) of A is B’. » (Id., p. 19). The previous regressive sorite corresponds to the following progressive sorite:
Only after affairs have been aligned may one’s understanding be fully extended. Only after one’s understanding is fully extended may one’s intentions be perfectly genuine. Only after one’s intentions are perfectly genuine may one’s mind be balanced. Only after one’s mind is balanced may one’s person be refined. Only after one’s person is refined may one’s household be aligned. Only after one’s household is aligned may one’s state be ordered. Only after one’s state is ordered may the world be set at peace.
The Great Learning. R. Eno, p. 12
The difference between progressive and regressive sorite is purely in the textual organization of the stages that compose them. These steps are listed in the form of a parallelism: « when A, then B« . This expression belongs to the « if… then… » family, used to note the logical implication, which gives the sorite an appearance of reasoning. Masson-Oursel proposes a second formulation expressing the progression (or regression) characteristic of the sorite:
Each step forward represents an anticipation that is justified afterwards, thanks to the formula: « in view of B, there is a way, a path to follow (yeou tao); A being given, then (seu) B is given. (Masson Oursel, 1912, p. 20).
The sorite proposes a path to follow, a way on which successive stages are marked. It would be more a question of method or path to follow than a logical or causal inference.
[1] The concept of a heap is three-dimensional, typically pyramid-shaped. Two or three grains cannot constitute a heap because they do not fit, or fit badly, on top of each other, the heap is not stable. On the other hand, it is possible to constitute a heap of four grains, from a base of three grains. We could therefore say that the heap is possible from four objects on.
[2] Robert Desnos, La Colombe de l’Arche, 1923. In Œuvres [Works]. Paris: Gallimard, Quarto, 1999, p. 536.
[3] http://hdl.handle.net/2022/234242