is included in the admitted equality of the two angles. Our assent is governed by this discovery alone.

A process, similar to what we have already investigated, is repeated to show that the point C must coincide with the point. F; wherefore, says the demonstration, as the point B also coincides with the point E, the base BC shall coincide with the base EF. Why? Because, says Euclid, if the base BC does not coincide with the base EF, two straight lines would inclose a space. And how do you prove that two straight lines cannot inclose a space? By an admission in the tenth axiom that they Two straight lines, says the axiom, cannot en

cannot.

close a space.

In this theorem, then, the proofs arc effected by showing, that the points in debate are admitted either by the premises of the proposition, or by axioms, &c. I know that I have operated on a theorem which is more easily analyzed than any other in Euclid, because the subsequent theorems are domonstrated by preceding ones: still the same principle will be found in all.

I have now shown, that we assent to a proposition when we discover that the premises affirm the conclusion; and that proofs and arguments have no effect, but to show us that such an affirmation exists. I have investigated this subject far too cursorily, but I will leave it, and proceed to show why certain premises affirm certain conclusions for instance, why the word half implies that it is less than the whole. Perhaps you will say, that the meaning of the word half admits that it is less than the whole; but I ask how it acquires this meaning? If you say, that common consent concurs in attaching this signification to the word, I ask how common consent came to

:

this resolution? Finally, is it an arbitrary conclusion, forced on us by the framers of language, that a half is less than a whole; or does it depend on some principle which is superior to any such dictation? The answer to this question will constitute the subject of my next lec

ture.

LECTURE VII.

THERE is a region called the valley of imagination that I occasionally visit, for the eccentric adventures with which it abounds. In a recent excursion thither, I noted a young woman, who was fleeing, as for her life. Her speed was impeded by an infant, which she held with some tenderness, while her face was suffused with tears. The object from which she fled was a monster, whose body was luminous and deformed. He seemed confident of his victim, and pursued her with increasing ardour. She arrived at a river, and turning to ascertain the proximity of her pursuer, plunged the infant in the stream, in the apparent hope, when unincumbered, of avoiding her

enemy.

Whether she succeeded in her retreat I did not discover, for my attention was arrested by two young men, who were preparing to encounter each other in mortal combat. I could perceive that both would gladly have

suspended their intent; but no sooner did a relenting thought occur to either, than the monster whom I lately saw, appeared again, and with threatening gestures frightened the youth from his parific contemplations.

I became anxious to know who this potent being is who can urge a mother, to immolate her recent infant, and terrify two gallant youths to the sacrifice of life. I therefore besought one, who was loitering like myself, to yield me the information. The monster whom you saw first, he replied, is SHAME; the second is an impostor, who bears the name only of the former. True shame is the offspring of crime; but false shame is the descendant of folly. The first is justly feared, for whoever falls within his power be impresses with a mark which burns more intensely than cautery, and more durably than life. The second also affixes his mark on those whom he overtakes, but though it pains for a period, it eventually assuages, and the subject of his malice learns to contemn the monster, and his impotent assaults.

This allegory has not much bearing on our subject; but I suspect these lectures would long since have yielded to the distractions of business, and the absence of extrinsic impulse, did not the fear of one of thesc monsters deter me from abandoning a labour publicly undertaken. The motive for perseverance is therefore not very alluring, but, as it is, proceed we with our discussions.

Why cannot the same thing both be and not be? Because the proposition contains two assertions which negative each other. How came the propositions by meanings so opposite? By the consent of mankind. But what united on this proposition the consent of mankind? We

may proceed thus in an endless train of trifling assertions, without arriving at any satisfactory result. You will, however, remember that I promised to show in this Lecture the reasons which compel us to yield our assent to propositions like the above. I now proceed to the undertaking.

The necessity for our assent to such propositions is founded on the phenomena to which the propositions refer: thus, I can show you a knife, and tell you that the knife is visible. I can remove the knife, and tell you' that it is invisible. But why cannot the knife be both visible and invisible at the same time? Try if you can effect such a coincidence, and you will discover why. The impossibility is precisely what you will experience, nor has it any other meaning.

Why cannot the same spot be, at the same time, both white and black? Because the word white implies that the spot is not black. But how came white by this implication? Was it arbitrarily imposed by the framers of our language? No. They called one sight white and The another black, merely to name what they saw. proposition is a result of experience. If I assert that the same spot cannot be both white and hard, the proWhy? Because my senses position will be untrue. can discover such a coincidence. There is

reason.

no other

All the axioms of geometry depend for their authority on similar principles. Why are things which are equal to the same, equal to one another? Because, says Mr. Campbell, the two expressions are equivalent to cach other. But what makes them equivalent? The latter part of the phrase being a definition only of the former.