Objects, Advantages, And Pleasures Of Science.

We have mentioned one distinction between Mathematics and Natural Philosop hy , that the former does not depend on the nature and existence of bodies , which the latter entirely does . Another distinction , and one closely connected with thisis that the truths which Mathematics

, teach us , are necessarily such , —they are truths of themselves , and wholly independent of facts and experiments , —they depend only upon reasoning ; and it is utterly impossible they should be otherwise than true . Mathematics teaches by

reasoning , step by step , from the most p lain and evident things , that we arrive at the knowledge of other things which seem at first not true , or at least not generally true ; but when we do arrive at them , we perceive that they are just as true , and for

the same reasons , as the first and most obvious matters , that their truth is absolute and necessary , and that it would be as absurd and self-contradictory to suppose they ever could , under any circumstances , be not true , as to sujipose that 2 added to 2 could ever make 3 , or 5 , or 100 , or anything but I , or which is the same thing , that 4 should ever be equal to 3 , or 5 , or

100 , or anything but 4 . To find out these reasonings , to pursue them to their consequences , and thereby to discover the truths which are not immediately evident , is what science teachesus ; but when thetruth is once discovered , it is as certain and plain by the

reasoning , as the first truths themselves from which all the reasoning takes its rise , on which it all depends , and which require no proof , because they are selfevident at once , and must be assented to the instant they are understood .

But it is quite different with the truths which Natural Philosophy teaches . All these depend upon matter of fact ; and that is learnt by observation and experiment , and never could be discovered "y reasoning at all . If a man were shut

U P in a room with pen , ink , and paper , he might b y thinking discover any of the truths in arithmetic , algebra , or geometry ; lt is possible , at least , there would be lotting absolutely impossible in his discovering all that is now known of these

sciences ; and if his memory were as good as We supposing his judgment and conception to be , he might discover it all Without pen , ink , and paper , and in a dark

room . But we cannot discover a single one of the fundamental properties of matter without observing what goes on around us , and trying experiments upon the nature and motion of bodies . Thus , the man whom we have supposed shut up , coidd

not possibly find out beyond one or two of the very first properties of matter , and those only in a very few cases ; so that he could not tell if these were general properties of all matter or not . He could tell that the objects he touched in the dark

were hard and resisted his touch ; that they were extended and were solid—that is , that they had three dimensions , length , breadth , and thickness . He might guess that other things existed beside those he felt , and that those other things resembled

what he felt in these properties ; but he could know nothing for certain , aud could not even conjecture much beyond this very limited number of qualities . He must remain utterl y ignorant of what really exists in natureand of what properties matter

, in general has . These properties , therefore , we learn by experience ; they are such ' as we know bodies to have , they happen to have them—they are so formed by

Divine Providence as to have them—but they might have been otherwise formed ; the groat Author of Nature might have thought fit to make all bodies different in every respect . We see that a stone dropped from our hand falls to the ground

—this is a fact which we can only know by experience ; before observing it , we could not have guessed it , and it is quite conceivable that it should be otherwise : for instance , that when we remove our hand from the body it should stand still in

the air , or fly upward , or go forward , or backward , or sideways ; there is nothing at all absurd , contradictory , or inconceivable in any of these suppositions ; there is nothing impossible in any of them , as there would be in supposing the stone

equal to half of itself , or double of itself , or both falling down or rising upwards at once ; or going to the ri ght and the left at one and the same time . Our onl y reason for not at once thinking it cjuite conceivable that the stene should stan d

still in the air , or fly upwards , is that we have never seen it do so , and have become accustomed to see it do otherwise . Bat for that , we should at onee think it as G 2