Page images
PDF
EPUB

judge of truth, to which common sense muft continually act in fubordination. But this I cannot admit; because I am able to prove the contrary by the most incontestable evidence. I am able to prove, that

[ocr errors]
[ocr errors]

66

[ocr errors]

except we believe many things without "proof, we never can believe any thing at all; for that all found reafoning muft ultimately rest on the principles of common sense, that is, on principles intuitively certain, or intuitively probable; and, confequently, that common fenfe is "the ultimate judge of truth, to which " reason must continually act in fubordi"nation."-This I fhall prove by a fair induction of particulars.

[ocr errors]
[blocks in formation]

All reafoning terminates in first principles. All evidence ultimately intuitive. Common Senfe the Standard of Truth.

[ocr errors]

N this induction, we cannot propofe to comprehend every fort of evidence, and every mode of reafoning; but we shall

[blocks in formation]

endeavour to inveftigate the origin of thofe kinds of evidence* which are the moft important, and of the most exten

*That the induction here given is fufficiently comprehenfive, will appear from the following analyfis.

All the objects of the human understanding have been reduced to two claffes, viz. Abstract Ideas, and Things really exifting.

Of Abstract Ideas, and their Relations, all our knowledge is certain, being founded on MATHEMATICAL EVIDENCE (a); which comprehends, 1. Intuitive Evidence, and, 2. The Evidence of frict demonstration.

We judge of Things really exifting, either, 1. from our own experience; or, 2. from the experience of other men.

--

1. Judging of Real Exiftences from our own experience, we attain either Certainty or Probability. Our knowledge is certain when fupported by the evidence, 1. Of SENSE EXTERNAL (b) and INTERNAL (c); 2. Of MEMORY (d); and, 3. Of LEGITIMATE INFERENCES OF THE CAUSE FROM THE EFFECT (e). Our knowledge is probable, when, from facts already experienced, we argue, 1. to facts OF THE SAME KIND (f) not experienced; and, 2. to facts OF A SIMILAR KIND (g) not experienced. This knowledge, though called probable, often rifes to moral certainty.

2. Judging of Real Exiftences from the experience of other men, we have the EVIDENCE OF THEIR TESTIMONY (b). The mode of underflanding produced by that evidence is properly called Faith; and, this faith fometimes amounts to probable opinion, and fometimes rifes even to abfolute certainty.

[blocks in formation]

five influence in fcience, and in common life; beginning with the fimpleft and cleareft, and advancing gradually to thofe which are more complicated, or lefs perfpicuous.

SECTION I

Of Mathematical Reafoning.

THE evidence which takes place in pure mathematics, produceth the highest affurance and certainty in the mind of him who attends to it, and understands it; for no principles are admitted into this fcience, but fuch as are either felf-evident, or fufceptible of demonftration. Should a man refufe to believe a demonftrated conclufion, the world would impute his obftinacy, either to want of understanding, or to want of honesty: for every person of understanding feels, that by mathematical demonftration he must be convinced whether he will of not. There are two kinds of mathematical demonftration. The firft is called direct; and takes place when a conclufion is

inferred

inferred from premifes which render it ne¬ ceffarily true: and this perhaps is a more perfect, or at least a fimpler, kind of proof, than the other; but both are equally convincing. The other kind is called indirect, apagogical, or ducens ad abfurdum; and takes place when, by fuppofing a propofition falfe, we are neceffarily led into an abfurdity, which there is no other way to avoid, than by supposing the proposition true. In this manner it is proved, that the propofition is not, and cannot be, false; or, in other words, that it is certainly true. Every step in a mathematical proof either is felf-evident, or must have been formerly demonftrated; and every demonstration doth finally refolve itself into intuitive or felf-evident principles, which it is impoffible to prove, and equally impoffible to disbelieve. Thefe first principles conftitute the foundation of mathematical fcience: if you can difprove them, you overturn the whole fcience; if you refufe to believe them, you cannot, confiftently with this refufal, acquiefce in any mathematical truth whatfoever. But you may as well attempt to blow out the fun with a pair of bellows,

as

as to difprove thefe principles: and if you fay, that you do not believe them *. , you will be charged either with falfehood or with folly; you may as well hold your hand in the fire, and fay that you feel no pain. By the law of our nature, we must feel in the one cafe, and believe in the other; even as, by the fame law, we must adhere to the earth, and cannot poffibly fall headlong to the clouds.

But who will pretend to prove a mathematical axiom, That a whole is greater than a part, or, That things equal to one and the fame thing are equal to one another? Every proof must be clearer and more evident than the thing to be proved. Can you then affume any more evident principle, from which the truth of thefe axioms may be confequentially inferred ? It is impoffible; because they are already

*Si quelque opiniaftre les nie de la voix, on ne l'en fçauroit empefcher; mais cela ne luy eft pas permis interieurement en fon efprit, parce que fa lumiere naturelle y repugne, qui eft la partie où se rapporte la demonftration et le fyllogifme, et non aux paroles externes. Au moyen de quoy s'il fe trouve quelqu'un qui ne les puiffe entendre, cettuy-là eft incapable de difcipline.

Dialectique de Boujou, liv. 3. ch. 3.

as

« PreviousContinue »