Two-term reasoning

1. Transductive reasoning

The concept of transductive reasoning is developed by Piaget ([1924], 185) to analyze the development of children’s intelligence. Transductive reasoning is characterized as the prelogical and intuitive way of thinking of the young child, which goes directly from an individual or a particular fact to another individual or particular fact, without the intermediary 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 [reasons by transduction]”(1996, p. 107).

Transductive reasoning seems to be the product of a conditioned association “nap = afternoon”, which gives, by application of the scheme of the opposites: “no siesta = no afternoon”. From this perspective, napping is a defining feature of the afternoon.

Grize observes that adults are also likely to 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 stop” (ibid.).

In the latter case, the statement has the form of a “semantic block” (Carel 2011), “Answer because Stimulus”. Yet the adult does not apply the negation in the same way as the child; saying “it is not a red light since 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 Traffic Act refused to believe that he collided head on with another vehicle because he was driving down a one-way street, implying the material impossibility of a fact from its legal prohibition.

2. Two-term reasoning

In a very different context, Gardet and Anawati speak of, “two-term reasoning” which is characteristic of “a specifically Semitic 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, connatural to 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 medium term], not explicitly understood, is nevertheless explicit in the reasoning mind? We don’t think so. Undoubtedly, two-term reasoning can be ‘translated’ into a three-term syllogism […]. Yet in the logical mechanism of thought, it is indeed the confrontation, by contrast, similarity or inclusion, of the two terms of the reasoning that gives the ‘proof’ its power of conviction. The universal middle term is not present in the mind, even in an implicit form. This is not about establishing a discursive proof, but about promoting a self-evident certainty. (Bouamrane & Gardet 1984, p. 75; my emphasis)

The Arab logician and theologian al-Sumnani has distinguished five rational processes, that is five argument schemes, which are characteristic of two-term reasoning. These five processes are based on

Findings, and then, by a movement of the mind operating either by elimination or by analogy from the same to the contrary, or from the same to the same. It is always a question of passing from the present, actual fact, the “witness” (shâhid) [the argument, cp], to the absent, (gha’ib) [the conclusion, cp]. There is no abstract search for a universal principle. (Gardet and Anawati [1948], pp. 365-367; my emphasis).