TERM to TERM REASONING
Two types of term to term reasoning have been observed in very different contexts, transductive reasoning in psychology and two-term reasoning in Arabic culture.
Both are described as immediate projections, directly from one term to another, corresponding to a kind of conditioned « associative reflex ». Such reasoning looks like an automatic association between the form and content of two terms, as such, dispensing with predication, judgment, and any law-like connection (« backing« ).
1. Transductive Reasoning
The concept of transductive reasoning was developed by Piaget ([1924], 185) to analyze the development of children’s intelligence. Transductive reasoning is characterized as the pre-logical and intuitive way of thinking of the young child, which goes directly from one individual or a particular fact to another individual or particular fact, without the mediation of a general law. According to Grize,
The young child who says, ‘It’s not afternoon because there was no nap’ is based on the daily experience of napping as an ingredient of the afternoon [transductive reasoning].(1996, p. 107).
Transductive reasoning appears to be the product of a conditioned association “nap = afternoon”, that results from the application of the scheme of opposites to “no siesta = no afternoon”. From this perspective, napping is a decisive defining characteristic of the afternoon.
Grize notes that adults also use this kind of reasoning:
When we say that we stopped at the traffic light because it was red, […] our thinking does not go through a general law of the kind: “any red traffic light implies stopping” (ibid.).
In the latter case, the statement takes the form of a “semantic block” (Carel 2011), « answer because stimulus ». However, the adult does not use the negation in the same way as the child to say “it is not a red light because I did not stop” would be considered as a denial of reality.
However, it is said that a motorist deeply imbued with respect for the Highway Code refused to believe that he had collided head-on with another vehicle because he (the victim) was driving down a one-way street. According to this belief, the legal prohibition of a fact implies its material impossibility.
2. Two-Term Reasoning
In a very different context, Gardet and Anawati speak of, “two-term reasoning” which is characteristic of “a specific rhythm of thought which the Arab mind knew how to use with a rare happiness of expression” (Gardet and Anawati [1967], p. 89). This type of reasoning seems to be similar in nature to transductive reasoning.
The ‘dialectical’ logic associated with the Arab genius, is organized according to modes of reasoning with two terms that proceed from the singular to the singular, by affirmation or negation, without a universal middle term. Should we say, as has sometimes been said before, that [this universal middle term], not explicitly understood, is nevertheless explicit in the thinking mind? We don’t think so. Undoubtedly, a two-term argument can be ‘translated’ into a three-term syllogism […]. But in the logical mechanism of thought, it is actually the confrontation, the contrast, the similarity or the inclusion, of the two terms of the argument that gives the ‘proof’ its persuasiveness. The universal middle term is not present in the mind, even in an implicit form. It is not a matter of establishing a discursive proof, but of promoting a self-evident certainty. (Bouamrane & Gardet 1984, p. 75; my emphasis)
The Arab logician and theologian al-Sumnani has distinguished five rational processes, i.e. five schemes of argument, that are characteristic of two-term reasoning. These five processes,
are based on observations, and then, on a movement of the mind which operates either by elimination or by analogy from the same to the opposite, or from the same to the same. It is always a matter of moving from the present, actual fact, the “witness” (shâhid), to the absent, (gha’ib). There is no abstract search for a universal principle. (Gardet and Anawati [1948], pp. 365-367; my emphasis).