contrarily opposed to each other, and their mutual relation is called Contrary Opposition.

The relation of A and O, to each other, as well as that of E and I to each other, is called Contradictory Opposition. That is, two propositions having the same subject and predicate, but differing both in quality and quantity, are said to be contradictorily opposed to each other, and their mutual relation is called Contradictory Opposi tion.

A .Contraries.. E

Subalterns.

...Contra

.Contradictories...

dictories...

.Subalterns...

I..... Subcontraries....O

The relation of I and O to each other is called Subcontrary Opposition. That is, two particular propositions having the same subject and predicate, but differing in quality, are said to be subcontrarily opposed to each other, and their mutual relation is called Subcontrary Opposition.

The relation of A and I to each other, as well as that of E and O to each other, is called Subalternation. That is, two propositions having the same subject and predicate, and the same quality, but differing in quantity, are said to bear to each other the relation of subalternation; the one of universal quantity is called the subalternant, and the other of particular quantity the Subalternate; and both are called Subalterns.

The Opposition is, therefore, of three kinds; (1) Contrary; (2) Contradictory, and (3) Subcontrary. Subalternation is, also, sometimes called a kind of opposition; but there is no opposition between the subalternant and the subalternate, both of which have the same quality and differ in quantity only.

Exercise.

Give the contradictory, the contrary, or subcontrary, and the subalternant or subalternate, of the following propositions :

(1) Every metal conducts heat,

(2) Every planet moves round the sun.

(3) Matter cannot change its own state of motion or of rest.

(4) All plants have not flowers.

(5) Some elements are not metals.

(6) All material bodies are extended.

(7) Heat expands bodies,

(8) Gold is a metal.

(9) A sensation can only be in a sentient being. -
(10) Gases and liquids are perfectly elastic.

(11) Liquids have no shape of their own.

(12) Consciousness is an immediate knowledge.

(13) In nature, relative motion and rest are alone presented to our observation.

(14) If all impeding causes were removed, a body once in motion would continue to move for ever.

(15) Water sometimes contracts by heat.

(16) A sensation is sometimes not accompanied by a perception,

9. Division according to Import1.

The last division of propositions, which we need notice, is founded on the relation of the connotation of the predicate to that of the subject, or, in other words, on the old distinction of Essential and Accidental Predication, and is into (1) Verbal, Analytical, Essential, or Explicative, and (2) Real, Synthetical, Accidental, or Ampliative. When the connotation of the predicate of a proposition is the same as, or a part of, the connotation of the subject, the proposition is called Verbal or Analytical. When, on the other hand, the connotation of the predicate is not a part of that of the subject, the proposition is called Real or Synthetical. In the former case, the predicate merely explains,

1 The division of propositions into (1) Verbal, Analytical, &c., and (2) Real, Synthetical, &c., is here given as founded on their import, for the meaning or import of a proposition is different according as it belongs to one or the other of the two classes. It may also be regarded as founded on the mode of their formation; for an analytical proposition may be regarded as formed by the analysis or resolution into parts of the connotation of the subject, and a synthetical proposition by the synthesis or union of the connotations of the subject and the predicate.

or states the entire meaning, or a part of the meaning, of the subject; and the proposition imparts no new information to those who already know the meaning of the subject. In the latter case, the proposition imparts new information, and the attribute connoted by the predicate is a real addition to that connoted by the subject. Thus the proposition " All men are rational" is verbal, because the attribute 'rationality' is a part of the larger attribute or group of attributes 'humanity,' while the proposition "All men are mortal" is real, because the attribute 'mortality' is not contained in the connotation of the subject 'man'; it is something different from, and new to, humanity; and the proposition expresses the conjunction of these two attributes.

§ 10. The Five Predicables: Genus, Species, Differentia, Proprium, and Accidens :-In a verbal proposition, the predicate, in relation to the subject, is either a genus, a species, or å differentia. In a real proposition, the predicate, in relation to the subject, is either a proprium, or an accidens. In other words, if the predicate of a proposition, in relation to the subject, be a genus, species, or differentia, the proposition is verbal, that is, the connotation of the predicate must be a part of that of the subject. If, on the other hand, the predicate be a proprium, or an accidens, the proposition is real, that is, the connotation of the predicate is not contained in that of the subject.

If the subject of a verbal proposition be an individual, the predicate, in relation to the subject, is called a species. If the subject be a class, the predicate, in relation to it, is called a genus, and the subject, in relation to the predicate, a species. The two terms, genus and species, are thus entirely relative to each other, and one has a meaning only in relation to the other. Given two terms related to each other as genus and species, the connotation of the latter minus the connotation of the former is equivalent to the differentia of the species, that is, to the attribute or group of attributes, which distinguishes that species from others belonging to the same genus. Thus the three terms genus, species, and differentia, implying each the other two, are correlatives. Further, just as a genus implies that there are

species under it, so a species implies that there are individuals under it. And so to the three correlatives mentioned above may be added another, namely, Individual; and the four terms may be thus defined ::

A Genus in extension is a class including smaller classes or species. In comprehension, it is included in the species.

A Species in extension is a class which is included in a larger class or genus, and which includes individuals. In comprehension, it includes the genus and the differentia, and is included in the individual.

A Differentia is an attribute which distinguishes one species from others belonging to the same genus, and which is included in the comprehension of the species. In extension, that is, when taken as a general term, it includes the species and the individual.

An Individual is a particular thing or substance having a unique group of attributes, partly known and partly unknown. In extension, it is included in the species. In comprehension, it includes the species, and consequently also the differentia and genus. The connotation of a species=the connotation of the genus+ the differentia.

.. The differentia=the connotation of the species - the connotation of the genus; and the connotation of the genus = the connotation of the species - the differentia. Example :-Taking 'animal' and 'man' as genus and species we have :-

Humanity = Animality + the Differentia; .. the Differentia= Humanity - Animality.

But, Humanity=Animality+Rationality, that is, the connotation of man consists of those two attributes.

.. The Differentia = Animality + Rationality - Animality = Rationality. That is, 'rationality' is the differentia of the species 'man' in the relation to the genus 'animal,' and by the attribute 'rationality' the species 'man' is distinguished from others belonging to the same genus 'animal.' Similarly, an individual may have its differentia which is equivalent to the connotation of the individual minus that of the species :

Socraticity = Humanity+the Differentia; .. the Differentia of Socrates=Socraticity - Humanity.

By the Differentia of Socrates' is meant the group of attributes by which he is distinguished from other individuals belonging to the same species man.'

The differentia of a genus, like that of a species, in reference to a higher class, is the connotation of the genus minus the connotation of the higher class. Thus the differentia of ‘animal' in relation to the higher class organic being' animality - the attribute of being organized=sentiency; animal being defined as a sentient organized being.

In extension, a species is included in the genus, and an individual in the species. Thus 'animal' contains 'man'; and 'man' contains 'Socrates'; 'metal' contains 'gold'; 'organism' contains animal.' A differentia, when taken in extension, is a larger whole than the species. Sometimes, however, it coincides with the extension of the species; but the comprehension of the differentia being smaller than that of the species, its extent is theoretically greater than that of the latter.

The relation of individual, differentia, species, and genus may thus be represented by diagrams:

The dot in the centre stands for Socrates. The inner circle for man. The outer circle for rational in the first diagram, and for animal in the second, the relation of animal and rational is shown in the third.