Deductive Logic Part 30

All C is B.

.'. all C is A.

.'. some C is A.

Similarly in EAO in figure 1, instead of arguing that the whole of C is excluded from A, we draw a conclusion which really involves a further inference, namely that part of C is excluded from A.

[Ill.u.s.tration]

No B is A.

All C is B.

.'. no C is A.

.'. some C is not A.

-- 639. The reason why the canons have been expressed in so c.u.mbrous a form is to render the validity of all the moods in each figure at once apparent from the statement. For purposes of general convenience they admit of a much more compendious mode of expression.

-- 640. The canon of the first figure is known as the Dictum de Omni et Nullo--

What is true (distributively) of a whole term is true of all that it includes.

-- 641. The canon of the second figure is known as the Dictum de Diverse--

If one term is contained in, and another excluded from a third term, they are mutually excluded.

-- 642. The canon of the third figure is known as the Dictum de Exemplo et de Excepto--

Two terms which contain a common part partly agree, or, if one contains a part which the other does not, they partly differ.

-- 643. The canon of the fourth figure has had no name a.s.signed to it, and does not seem to admit of any simple expression. Another mode of formulating it is as follows:--

Whatever is affirmed of a whole term may have partially affirmed of it whatever is included in that term (Bramantip, Dimaris), and partially denied of it whatever is excluded (Fesapo); whatever is affirmed of part of a term may have partially denied of it whatever is wholly excluded from that term (Fresison); and whatever is denied of a whole term may have wholly denied of it whatever is wholly included in that term (Camenes).

-- 644. From the point of view of intension the canons of the first three figures may be expressed as follows.

-- 645. Canon of the first figure. Dictum de Omni et Nullo--

An attribute of an attribute of anything is an attribute of the thing itself.

-- 646. Canon of the second figure. Dictum de Diverso--

If a subject has an attribute which a cla.s.s has not, or vice versa, the subject does not belong to the cla.s.s.

-- 647. Canon of the third figure.

1. Dictum de Exemplo--

If a certain attribute can be affirmed of any portion of the members of a cla.s.s, it is not incompatible with the distinctive attributes of that cla.s.s.

2. Dictum de Excepto--

If a certain attribute can be denied of any portion of the members of a cla.s.s, it is not inseparable from the distinctive attributes of that cla.s.s.

CHAPTER XVI.

_Of the Special Uses of the Four Figures._

-- 648. The first figure is useful for proving the properties of a thing.

-- 649. The second figure is useful for proving distinctions between things.

-- 650. The third figure is useful for proving instances or exceptions.

-- 651. The fourth figure is useful for proving the species of a genus.

FIGURE 1.

-- 652.

B is or is not A.

C is B.

.'. C is or is not A.

We prove that C has or has not the property A by predicating of it B, which we know to possess or not to possess that property.

Luminous objects are material.

Comets are luminous.

.'. Comets are material.

No moths are b.u.t.terflies.

The Death's head is a moth.

.'. The Death's head is not a b.u.t.terfly.

FIGURE II.

-- 653.

A is B. A is not B.

C is not B. C is B.

.'. C is not A. .'. C is not A.

We establish the distinction between C and A by showing that A has an attribute which C is devoid of, or is devoid of an attribute which C has.

All fishes are cold-blooded.

A whale is not cold-blooded.

.'. A whale is not a fish.

No fishes give milk.