ETHICS. Examiner . . PROFESSOR SETH, ADRIL 13TH, 10 A. M. to 1 P. M. 1. Describe the scope and method of Ethics, and its relation to Psychology. 2. What do Intuitionalists mean by (a) the self-evidence, (b) the absoluteness of moral law's ? How do they answer the objection that moral laws conflict in practice ? Compare the Utilitarian position on this question. 3. Describe precisely the nature of Conscience according to the Intuitional Theory; and compare Bain's account of its growth. 4. State and estimate the Hedonistic view of the ethical End; and critically examine the transition from Egoistic to Altruistic Hedonism. 5. Is the distinction of quality in pleasures consistent with the fundamental position of Hedonism? Explain the grounds of your answer. 6. State briefly the Libertarian Solution of the problem of the Will, and examine its adequacy. 7. Sketch the ethical teaching of Socrates, and indicate his relation to the Socratic Schools. 8. Give Plato's account of the Cardinal Virtues in relation to his triple division of human nature. 9. State and explain Aristotle's definition of the End of life. METAPHYSICS. Examiner .PROFESSOR SETH. APRIL 15TH, 3 TO 6 P. M. 1, Describe the task of Philosophy as (a) Ontology ; (b) Epistemology. Distinguish the latter from Psychology. 2. Compare the views of Descartes and Locke with regard to Mind and Matter and their mutual relation. 3. With what amont of justice may Locke be called a Sensationalist? Combare his tcaching in Books Il. and IV. of the Essay. 4. Give Locke's distinction between the Primary and Secondary Qualities of Matter, with Berkeley's criticism, and your own view as to its validity. 5. How does Berkeley construe (a) the Substantiality, (b) the Causality of the material world ? Give Berkeley's account of Space, comparing it with Hume's and Kant's. 7. Explain and estimate Berkeley's view that the Esse of sensible things is Percipi. 6. 8. How, and with what right, does Hume extend Berkeley's teaching? 9. Indicate briefly the general lesson as to the interpretation of Experience, drawn by Kant from the development of modern philosophy in Locke, Berkeley, and Hume. 1. On what ground would you vindicate the intuitive action of Mind, against the Empirical view, which derives all our ideas from Experience ? Mention the intuitions, and justify the Intuition of Uniformity. 2. Show why a mental identification and judgment are the same. What is the co-relate of identification ? Trace the other laws of mind to these two, and show how all thought takes place within, or by virtue of, these laws. 3. Give some account of the Practical Processes, with examples of their action. 4. How may memory be regarded ? What practical uses may this view subserve ? To what single law may the laws of Association be reduced ? 5. What is the grand peculiarity in Imagination ? Find Sir William Hamilton's Reproductive and Representative Faculties among these, In what respects is Imagination, in its higher function, or exercise, different from the Representative faculty ? 6. To what does Sir Wm. Hamilton's Regulative Faculty correspond in our view of mind ? WEDNESDAY, 12TH JANUARY, 1887. FROM 3 O'CLOCK TO 5.30. 1. On what principles of classification have the Emotions hitherto been regarded ? How have we proposed to regard, and classify, them? 2. What is meant by the Elevated Emotions ? Give some particular account of these states, and find the Æsthetic Emotion among them. What is Adoration ? -3. What considerations may be urged in favour of the Association theory of Beauty? Whose theory is this? What other view has been taken? What are the sensible qualities, according to Burke, in which the Beautiful and Sublime respectively may be said to consist? Show how this view is reconcilable with the Association theory, in fact supposes it. Beauty,” says Cousin, is expression : Art is the seeking after Expression. What is Cousin's enumeration of the Arts accordingly. How do we propose to classify them, at once retaining Cousin's principle of arrangement, and introducing a true ground of classification as such ? LOGIC. FRIDAY, 15TH APRIL, FROM 10 A. M. TILL 1 P. M. 1. From what different points of view may Logic be regarded, and how, accordingly, has it been divided ? 2. Distinguish been Pure Logic and Modified Logic-between Stoicheiology, or the Doctrine of Elements, and Methodology, or the Doctrine of Method: 3. Under what two quantities may Concepts be considered, and what two kinds of reasoning, in Hamilton's account of the process, are based upon this distinction ? 4. How does Mill regard the process of Reasoning, and how may Dr. Brown's view of Reasoning be said to correspond with this ? Distinguish this view of the process from true Reasoning. 5. Give Sir Wm. Hamilton's definition of Reasoning, and show wherein it is defective. How do we propose to supplement it? 6. What are the rules of the Extensive Syllogism ? What those of the Intensive? How do they differ, and why? 7. What do you understand by the Moods and Figures of the Syllogism? Explain the purport and uses of the 2nd and 3rd Figures particularly. 8. Give a scheme of the Fallacies, showing the relation of the Formal Fallacies to the rules of the extensive syllogism--and how the Material Fallacies may be brought under the one class of “Quaternio terminorum,” and “Ambiguous Middle. What Fallacies may be considered not only as Extra dictionem, but as Extra Logical? 9. Give the Laws of Definition and Division. Give those of Probation, and specify the Fallacies more incident to an extended argument. MATHEMATICS. Examiner... ...C. MACDONALD, M. A. GEOMETRY - FIRST YEAR. APRIL 18.-10 A. M. TO 1 P. M. 1. If a straight line be divided internally so that the rectangle of its two parts may be equal to a given square, there is, in order that the problem be possible, a limit to the magnitude of the square : but if divided externally there is no limit. Shew why. 2. The sum of the squares of two sides of a triangle is equal to twice the sum of the squares of half the other side and of the corres, ponding median. Prore. 3. One circle cannot touch another either internally or externally n more points than one. 4. The angle in a segment of a circle greater than a semi-circle is less than a right angle: and the angle in a segment less than a semicircle is greater than a right angle. Either prove this in the Euclidian method, or deduce it from a previous proposition and the principle of “continuity.” 5. If a point be taken without a circle and from it any secant be drawn, the rectangle of the secant and its external segment is equal to the difference of the squares of two constanč lines. Name them and prove the proposition. 6. Describe a triangle about a circle equiangular to a given triangle. 7. Give the construction necessary to find a triangle each of whose angles at the base is double the vertical angle : and add the proof as far as that the base of the triangle you have constructed is a tangent to one of the circles you have drawn. 8. If the sides about the angles of two triangles are proportionals, the triangles must be equiangular. 9. Find a mean proportional between two given lines. 10. Find the magnitude in Degrees of an angle of a regular polygon of n sides, and show from your formula that the greater the irumber of sides, the greater is the angle. 11. Shew that the greatest line drawn through the intersection of two circles, and terminated by their circumferences is that which is parallel to the line joining their centres. 12. Describe a circle to touch a given straight line in a given point, and also touch another circle. (Two solutions.). 13. AB is divided in any point C, and on AB, AC, CB, semicircles are described towards the same parts, and CP is drawn at right angles to AB, meeting the outer circle in P, and PA, PB cut the inner circles in R and Q: prove the following properties (1) RQ is a tangent to the inner circle : (2) PC and RQ sect each other : (3) if AB and RQ meet in T, AT. TB = RT. TQ. GEOMETRY AND MENSURATION-SECOND YEAR. APRIL 18.-10 A, M. TO 1 P. M. 1. Explain “duplicate ratio " and prove that, “similar trangles are to one another in the duplicate ratio of their homologous sides." 2. If four straight lines be proportionals, the similar rectilineal figures descrit ed on them shall also be proportionals. 3. In equal circles, sectors have the same ratio which the arcs on which they stand have to one another. 4. Show that the ratio of the distance of a point from the focus of a parabola to its distance from the directrix is equal to, less than, or greater than unity, according as the point is on, within or without the parabola, the point being in the plane of the parabola. 5. The locus of the feet of perpendiculars on tangents of a parabola, drawn from the focus the tangent at the vertex. 6. The chord of contact of two tangents to a parabola drawn from any point, is bisected by the diameter passing through that point. 7. If P (A BCI) be a pencil, A B C D bein; any line cutting it, and if RQ, drawn through C parallel to PA, meeting PD and PB in R and Q, is bisected in C: then the pencil is Harmonic. 8. Define a pole and polar with respect to a circle : and prove a proposition regarding them that you think remarkable. 9. A circle is inscribed in a triangle. Use a fundamental proposition in the theory of transversals to prove that the straight lines joining the angles of the triangle with the points of contact, pass through the same point. 10. Given two circles that intersect, and a third exterior to both : find the point from which the six tangents drawn to the circles are equal to one another. 11. A right cone of lead, the diameter of whose base is 6 inches and height 4 inches, is cast afresh into another right cone whose base is only 4 inches in diameter : find the height. 12. The longer of the parallel sides of a trapezoid is 20 feet, the distance betwee them is 5 feet, the perpendicular let fal the longer of the parallel sides, from the point of intersection of the other two sides produced is 25 feet : find the area of the trapezoid. on ALGEBRA.-FIRST YEAR. APRIL 18.-3 TO 6 P. M. 1. Shew that Vñ=a +Vm is impossible, Vm and Vn being true and different surds: and prove m (x + m + V22 - m2) =x+ Væ2 – m2, 2 + m - V«? – m2 2. Describe the method of solving a group of, say, three equations, containing three unknown quantities of the form, ax+by+cz=d: and write the values of x, y, z, in “determinant” form. 3. Solve the equation 22n + ax"=b. Is the solution complete ? Describe also the methods of solving the following groups of equations : (1) ax + by=cl (2) ax?+ bya=c xy 1 (3) 2 – yra a,2c2 + 6,42=,?] a,+by=d ac" y'=d) 4. A farmer went to market and sold a number of pigs and oxen : the pigs at $12 apiece, the oxen at $75. It is certain that he sold more than one pig and that he had not 50 oxen to dispose of: further, he received $771 for his sales. Find the number of each kind of animals in the groups he sold. n 12 |