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the former are capable of being univocally and mechanically expressed, of being preci, ely distinguished from each other, and from those of other kinds, and of being exactly measured; and they are ready, at first, to be defined, and SYLLOGISTICALLY compared: whereas the latter can never be so univocally and artfully exprefled; nor distinguished with fucb precision, (defects which no expedients can remedyk) nor exactly measured; neither can they be logically defined at all or compared syllogistically, till their general ideas are formed by INDUCTION and general Propositions made.
So that, in Mathematics the Method of Reasoning begins where it ends in Ethics, and is contrary throughout. In the one, it begins with Definitions and general Propofitions, and advances from Syllogism to Syllogisın, in which the minor as well as the major Propositions are always general truths ; which generality is indispensable to Demonftration. In the other, the chief labour of Reafoning, by which many personal observa
See Mr. Lacke's Attempt, B. IV. C. iii. 9. 26.
tions are taken, accurate investigations pursued, and fine distinctions drawn, and by which many particular comparisons are formed, necessarily precedes the logical Definition. And, when the general Office or Duty with its correspondent quality, has been Inductively established into a general proposition, Definition, by reducing particular actions under their general head, will itself terminate the logical process : Or, if Syllogisms must be used, the minor propositions will be particular ; so that there can be no Demonstration: and, to the mortification of disputants, one, or however a very few syllogisms, will, be sufficient.
ETHICAL Truth is, therefore, totally different from Mathematical ; and, logically considered, and put in a comparative point of view, it bears a nearer resemblance to Phyfcal, and Phyfical to Mathematical.'
' Physics and Mathematics have the same First Principle, the External Senses; and, when Physical Forms are generalized, Mathematic can lend its Reasoning; and they both te: minate in speculative, not practical, use. Ethics differ from both in its First Principle the Internal Sense, and from MATHEMATICs in the Method of Rea
· Locke was that bold and adventurous philosopher, who, led on by a candid impartiality and a reverence for troth, with a strong and liberal mind, left the beaten track of science, and took a new and untrodden path, in which he walked with great honour to himself, and great advantage to the learned. To subvert doctrines of philosophy sanctioned by authority, to break through systems of education made venerable by time, and to remove habits and prejudices by which the mind has been long enslaved, is a task which has ever been reserved for those few champions of philosophy, who are bleft with superior talents. His Essay produced an useful revolution in the republic of learning; and he may fairly be considered as the second to Bacon in improving the pursuit, and in promoting the interests, of general knowledge. When the navigator of an unknown sea, for
foning, but in this they agree with Physics, the subject of both being individuals: and they differ from both in their End which is practical, not speculative, use: So that ETHICS and MATHEMATICS differ in toto.
the purpose of new discoveries, involves himself in difficulty, and perplexes himself in error, it is what we readily pardon, because it is what we naturally expect : and both he and the philosopher, who embark in the fpirit of improvement, in order to correct what was before erroneously adopted or imperfectly known, will not only commend but honour the fame spirit in others, by which they themselves are corrected or improved.
The opinion, however, which he entertained in his Essay, of the demonstrability of Ethics, he himself doubted of afterwards, and in part retracted in his Familiar Letters." Philosophers as well as navigators derive great advantages from being well informed of the works and observations of those who have gone before them: and he would have neither entertained the opinion in the first instance, nor have doubted about it in the second, had he not been unacquainted with
• Though by the view of moral ideas, whilft I was confidering that subject, I thought I saw that Morality might be demonstrably made out; yet whether I am able to make it out is another question. Locke's Fam. Let. p. 10.
the philosophy of Demonstrative and Syllogistic reasoning, for want of having studied with attention the Analytics of Aristotle, in which that deep philosophy is so particularly investigated ; and had he not likewise been mistaken in regard both to the Principles and Reasoning of Morality, of which the book of Topics, however defective that part of the órganon may be, would have fufficiently informed him, by distinguishing those subjects which are capable of Probability from those which admit of Demonstration. Above all, the Metaphysics of Aristotle, which should be most attentively studied by every future metaphysician, would have taught him, that
* The attempt which Mr. Locke has fhewn, in different parts of his Essay, to make Morality demonstrable like Ma. thematics, is a sufficient proof that he was unacquainted with the old Logic derived originally from Aristotle : And the method by which he hoped to make the attempt fucceed, viz. by proving the agreement or disagreement of ethical ideas by the application and mensuration of a third or medium, is an additional proof that the Logic he espoused was the new one, founded on the first Axiom of Euclid, which is more partial and imperfect than the old. And this is, indeed, strongly apparent in every part of his Essay.