Essential logic - I lesson

Lets begin with the following set of logically arranged statements or logical scheme:

• Dolphins are mammals.
• Dolphins inhabit the sea.
• Some denizens of the sea are mammals.

There are three essential terms in this set of statements that bear consideration: “Dolphins”, “denizens of the sea”, and “mammals”.

Three is also the number of statements or propositions making up the scheme. The first two statements (“Dolphins are mammals” and “Dolphins inhabit the sea”) are known as premises, while the last statement (“Some denizens of the sea are mammals”) is called the conclusion.

We can see the principle of identity fully at work in this scheme, and namely when two items in a triad are equivalent to the third they are equivalent to each other.

There is a corollary to the principle of identity, and that is the principle of discrepancy: two items of a triad having nothing in common with the third or even in the case of only one of them having something in common cannot be said to be identical, that is, they are different one from the other.

Clearly, in all these cases the threesome scheme is essential to the reasoning process. Lets now take a closer look at this threesome.

The three propositions or terms of any reasoning process as afore-described (henceforth also referred to as “ratiocination”) are called the major term, the minor term, and the middle term.

The logical operation entailed in such formal reasoning is to first compare the major and then the minor term with the middle term.

Having successfully acted as an intermediary, so to speak, the middle term does not appear at all in the conclusive statement, leaving the major and the minor terms to directly face up to each other without any go-between.

ADDITIONAL REMARKS

Here is a very concise rendition of the syllogism coined by a follower of the renowned Medieval scholar, John Dun Scotus (nicknamed Doctor Subtilis for his fine powers of reasoning), who, as a champion of the doctrine of the Blessed Virgin Mary’s Immaculate Conception, summed up the immaculist thesis with the following formula:

Potuit,

Decuit,

(Ergo) Fecit.

It was possible.

It was convenient.

It was done.

Triplicity, then, is an essential feature of the syllogism, as the following formulation by the Schoolmen succinctly reminds us : Terminus esto triples: maior mediusque minorque (The terms must be three: major, middle and minor).