Besides the terms explained above, the older logicians use the term summum genus to mean a highest genus or a genus which cannot be a species, being the highest and most general of its kind, and the term infima species to mean a lowest species or a class which cannot be a genus to another, being the lowest of its kind, while the intermediate genera and species are called by them subaltern genera and species. Substance,' for example, is regarded by them as a summum genus, 'man' as an infima species, incapable of further subdivision into species, and 'body,' 'living being,' and 'animal' as subaltern genera and species.

The two terms 'genus' and 'species' express the relation of containing and contained. Any class containing another is popularly called a genus in relation to the latter, which is called a species. In the Sciences of Classification, in Botany and Zoology, for example, groups of a particular description are called genera in relation to others of an equally definite nature, which are called species. In order to express the relation of containing and contained, we not only use the two old terms, genus and species, but also many others according to the position of the groups in a system of division or classification. For example, the terms kingdom and sub-kingdom, class and sub-class, order and sub-order, genus and sub-genus, species and subspecies, variety and sub-variety, used in Zoology and Botany, mark as clearly the relation of containing and contained as the two words, genus and species.

Exercises.

I. State whether the following propositions are verbal or real, analytical or synthetical, and whether the predicate in relation to the subject is a genus, species, differentia, proprium, or accidens:—

1. Oxygen is an elementary gas.

2. Water boils at 100o C., under a pressure of 760 mm.

3. Platinum is a rare metal.

4. Sugar is sweet.

5. The atmospheric air is a mixture of nitrogen and oxygen.

6. Copper conducts heat as well as electricity.

7. All men have the power of thinking.

8. All animals are sentient beings.

9. All the flowering plants have fruits. 10. Heat expands bodies.

11. The leaves of plants are green.

12. Spring-water contains many salts in solution. 13. Hydrogen is the lightest substance known.

14. London is the largest city in England.

15. Milton was blind when he composed the “Paradise Lost.” II. Give the genus, species, differentia, proprium, and accidens of each of the following terms:

(1) Triangle, (2) Circle, (3) Straight line, (4) Square, (5) Right angle, (6) Element, (7) Force, (8) Material Body, (9) Animal, (10) Chalk, (11) Rock, (12) Virtue, (13) Volition, (14) Knowledge, (15) Pleasure.

§ 11. Miscellaneous Exercises on Propositions.

In describing the logical characters of a proposition, the following method should be followed:

I. What is given is a sentence. Ascertain whether the sentence consists of a single proposition or of a plurality of propositions.

II. In the former case, state whether it is—

i. Categorical, Hypothetical, or Disjunctive.
ii. Affirmative or Negative.

iii. Necessary, Assertory, or Problematic.

iv. Universal, Particular, or Indesignate; Singular and Universal, or Singular and Particular.

v. Verbal (or Analytical) or Real (or Synthetical).

Both the quality and quantity of a proposition may also be stated at once by saying whether it is A, E, I, or O.

III. In the latter case, state the propositions of which it consists, and treat each of them as detailed above.

IV. Sometimes the quality, quantity, and other characters of a proposition are not quite evident from its form or the manner of its statement. In such cases, verbal changes should be made in order to state it in the logical form, keeping the meaning the same. It is always safe first to ascertain, as in the case of the term, the meaning

of the proposition, or, where this is not practicable, to see, before attempting to describe the logical characters of the proposition, whether the subject be a general term taken distributively or not, whether there be any negative particle attached to the copula or to the predicate, whether there are any signs of universality or negation before the subject, &c.

Examples.

1. "No man is perfect": categorical, negative, assertory, universal, and real.

2. "The three angles of a triangle are together equal to two right angles": categorical, affirmative, assertory in form, but really necessary, universal, and real.

3. "Some elements are not metals": categorical, negative, assertory, particular, and real.

4. "None but material bodies have weight": this proposition really means that "all things having weight are material bodies." In this form it is an A proposition. In the original form, it may be regarded as an E proposition, "no not-material bodies have weight,” signifying that having weight is denied of all things other than, or except, material bodies, that none that have weight are other than material bodies, and this last is the same as "all things having weight are material bodies,” the proposition we have substituted above for the original one. It should be noted that the proposition does not mean that every material body has weight.

5. "All metals except mercury are solids.”—In this proposition 'solids' is affirmed of all metals except mercury, and the proposition may, therefore, be regarded as an A proposition and described as categorical, affirmative, assertory, universal, and real. Or it may be taken as an I proposition, 'some metals are solids,' but in this degraded form, the full meaning of the original proposition is not expressed. Or we might state the names of all the metals except mercury, and form a proposition with them all as the subject and 'solids' as the predicate as before. For example, 'gold, copper, iron, silver, &c., are solids.' Such a proposition would be a combination of the several propositions, having each a certain metal for its subject, and 'is a solid' for its copula and predicate. Thus, 'gold is a solid,' 'copper is a solid,' 'iron is a solid,' and so forth.

6. "All is not gold that glitters,"="All that glitters is not gold." This proposition is really O, though it has the form of E. It really means that at least some thing that glitters is not gold.

7. "If mercury be heated, it will expand": conditional, affirmative, assertory, universal, real.

8. "All men are rational, but all are not wise": this sentence is a combination of the two propositions-(1) 'All men are rational ' (A), and (2) ‘All men are not wise' (O).

9. "Gravity as well as heat can produce motion": a combination of the two propositions, (1) 'Gravity can produce motion' (A), and (2) 'Heat can produce motion' (A).

Examples for Solution.

Treat the propositions1 given below as follows:

I.-Describe the logical characters of each of them.

II.-Give the contradictory, the contrary or subcontrary, and the subalternant or subalternate of each of them.

III.-State the relation of the predicate to the subject in each of the affirmative propositions.

IV. In the case of a disjunctive proposition, state the hypothetical propositions, one or other of which is equivalent to it.

1. Every pure substance consists of similar moleculcs.

2. Some animals have no power of locomotion.

3. Sensations are passive states of the mind.

4. Nothing is annihilated.

5. All metals except one are solid.

Benevolence is a virtue.

6.

10. Uneasy rests the head that wears a crown.

1 Most of the propositions given here are taken from Ganot's Popular Natural Philosophy, Roscoe's Chemistry, and Reid's Inquiry, exactly in the form in which they are expressed by the authors. They are kept in that form in order that students may acquire the habit of describing the characters of propositions as they actually occur in the works of authors, instead of the contracted and artificial propositions of the Logician.

11. None were there.

12. None but sensations can resemble sensations.

13. Metals conduct heat and electricity.

14. Oxygen is a colourless, invisible gas, possessing neither taste nor smell.

15.

Hydrogen is the lightest body known.

16. Matter is indestructible.

17. Most of the acids are soluble in water.

18. All acids contain hydrogen and always contain also oxygen. 19. The passage of water to the state of ice, and the return of the latter to the liquid state, are physical phenomena.

20. The mass of a body is the quantity of matter contained in the body.

21. The elementary atoms can unite with each other to form compounds, but cannot be destroyed by any known process. 22. If molecular attraction were the only force acting upon the small particles of which bodies are composed, they would come into complete contact.

23. All bodies are extended, impenetrable, divisible, porous, compressible, and elastic.

24. Strictly speaking, impenetrability only applies to the atoms of bodies.

25. Divisibility, porosity, compressibility, and elasticity do not apply to atoms, but only to bodies or aggregates of atoms. 26. Two portions of matter cannot simultaneously occupy the same portion of space.

27. Compressibility is both a consequence and a proof of porosity. 28. Both rest and motion are either absolute or relative.

29. Bodies are either opaque or transparent.

30. If a small quantity of manganese di-oxide be mixed with the potassium chlorate, the oxygen is given off from the chlorate at a much lower temperature.

31. Oxygen can be prepared by heating powdered potassium chlorate in a small thin glass flask.

32. All the elements with the single exception of fluorine combine with oxygen to form oxides.

33. Sulphur exists in three modifications.

34. Many organic bodies are completely decomposed and charred

by strong sulphuric acid.