Rectangle. In like manner a Rectangle is a Parallelogram having all its angles right angles. A Parallelogram is a Quadrilateral figure having its opposite sides parallel.

And following the same system, if the term be a particular one, we are directed, in defining it, to join to the name of the species specialissima the numerical difference. But definitions of individuals are more properly called Descriptions.

Divested of the logical phraseology, and extending a little the application of the term Definition, we may represent it to be a statement of those parts or properties of a thing, or circumstances respecting it, which distinguish it from all others. In some cases we can only define by a negation of properties; for instance the terms, infinite, cold, &c. admit of no positive definition. Other terms are explicable only by the use of synonymous expressions, or by referring to the things denoted by them: but these are best termed Explanations.

A good definition must be applicable to all the particular species or individuals included under the term defined, and at the same time exclusive of all other species or individuals. A definition of Man which should exclude the Hottentot, and another which should include the Oran Otan, would, in a logical point of view, be equally exceptionable.-In proportion to the species and varieties included under the generic term defined, must, of course, be the diminution of its comprehension; and it becomes extremely difficult, in many cases, to obtain such a selection of properties, as shall include every individual which ought to be included, and yet be sufficiently exclusive. Plato's definition of Man, (viz. a featherless biped,) was justly made by Diogenes the object of ridicule; yet we do not learn that the Cynic gave any better.

A definition ought to be itself clear and plain. The terms employed should be precise and intelligible; and they should bring the import forcibly and distinctly before the view of the mind, so that good sense alone should be requisite to make it properly understood. If the terms employed in a definition

are not in common use, they should themselves be first clearly defined: but, in general, if definitions are designed for those who are beginning any science, it is better to err on the side of diffuseness, than to employ terms which are not familiar. Thus for a learner it is surely best that the square should be defined, a four sided figure having all its sides equal, and all its angles right angles: yet the same thing, as already mentioned, may be denoted by two words. Though, however, that degree of brevity should be carefully avoided in a definition, which may make its import obscure, no unnecessary terms should be used; and the sole object should be, to give a distinct, clear, and forcible representation or discrimination of the thing signified.

We shall close this chapter with a few connected maxims.

(1.) Do not allow in yourself the employment of words which have, as commonly employed, no meaning at all, or a very loose and indeterminate one, or even one absolutely false. Many persons write and speak nonsense, from inattention to this simple principle.

(2.) In all your private investigations, and in the communication of your ideas to others, accustom yourself to employ words in a precise and determinate sense. Careful attention to the import of words, is necessary to success in the search after knowledge, even when the internal operations of the mind are alone employed. We cannot carry on any long train of thought, without the internal use of words; and we are liable to the influence of their ambiguities, as well in those mental processes, as when engaged in the communication of our ideas. In this last employment, it should be our object carefully to avoid all needless ambiguity; and without entering too much into formal statements of our meaning, it will usu ally be easy to limit the acceptation of those leading words, on which the correctness and intelligibility of the whole reasoning may depend.

(3.) When engaged on the productions of others, aim to ascertain in what way precisely the author employs his terms,

especially those which are of a somewhat ambiguous nature, and on which the stress of his argument may rest. If it were the object of the reader to ascertain the real meaning of the author, rather than to try his words by his own ideas, which may be incorrect, numberless volumes of wrangling controversy, in every department of knowledge, would never have been written.

(4.) Where distinctions have been laid down by writers of good authority in the use of words, before considered as synonymous, aim to observe the distinction, and to extend its use. We may sometimes lose in rhetorical effect by such niceties; and undoubtedly they may be carried to an extreme: but it is only by affixing distinct and definite ideas to terms, that we can reasonably hope to carry out of the sphere of mathematics and physics, that precision and certainty which distinguish those sciences.

* Genuineness and Authenticity were formerly confounded by writers of eminence. The present venerable and enlightened Bishop of Llandaff probably first introduced the distinction now universally adopted; making genuineness refer to the author, authenticity to his statements. A book is genuine, if written by the person to whom it is ascribed; authentic, if the facts contained in it are true.

CHAP. XXII.

PROPOSITIONS-EVIDENCE-SYLLOGISMS-OBSERVATIONS ON THE PURSUIT OF TRUTH.

PROPOSITIONS:-Subject-Predicate-Copula-Various kinds of Proposi

tions. EVIDENCE:-Certainty-Sense-Consciousness-Intuition-Ex

perience-Reasoning-Testimony-Divine Authority. SYLLOGISMS:→→ Utility of the Syllogism-Moods-Figures-Complex Syllogisms-Epichirema― Dilemma-Sorites-Enthymeme-Indirect Arguments-Sophisms. PURSUIT OF TRUTH :— :-Analysis-Synthesis-GeneralizationInduction—Analogy-Causes of Error-Qualifications for ascertaining Truth. ADVICE TO THE Student.

A PROPOSITION is an assemblage of words, in which one thing is affirmed or denied of another: for instance, Gold is heavy, Some men are not wicked. The term is extended, in the mathematical sciences, to include not only the statement of a truth which it is proposed to demonstrate, but also that of some construction which it is proposed to make: in the former case the proposition is called a Theorem, in the latter a Problem.

Respecting the mental operations which accompany the statement of a proposition, in the mind of the speaker, and of the hearer, we have had occasion to make a few observations in p. 305-308; and we beg to refer the reader to them before he proceeds.

However complex a sentence may appear, yet if there be but one affirmation or negation throughout, it is only one proposition.

That concerning which any thing is affirmed or denied, is the Subject of the proposition. The Predicate is that which is affirmed or denied of the subject. And the word by which the assertion is completed, is called the Copula. Thus in the proposition Gold is yellow, gold is the subject, yellow the predi cate, and is the copula. The word expressing the negation, is considered as a part of the copula; as in the proposition Man is not immortal, is not is the copula. Some would also make the negative word a part of the copula, even where it is connected with the subject: thus in the proposition, No man is without sin, they make man alone the subject. But it is much more simple and natural to regard the negative word as a part of the copula, or of the subject, or even of the predicate, according to its connexion in sense; and it causes no perplexity in logical distinctions to follow this arrangement.

It is not necessary that there should be three separate words to form a proposition. The asserting word, or verb (see vol. I. p. 66), may include, in its peculiar form, the subject and the predicate; and there is no verb, except be and the corresponding words in other languages, which does not include a part at least of the predicate. Thus amo includes I the subject, am the copula, and loving the predicate: in our own language, the subject is never included in the verb, (though sometimes it is left to be supplied from the preceding sentence,) but the predicate is continually included; thus, Troy was, means Troy was once existing. The interesting inference, is merely inference.

When the subject and predicate express precisely the same idea, the proposition is called identical. The terms may be the same, and yet the ideas different: as, Home is home: meaning that the place where we usually reside, possesses those comforts and delights which give it an exclusive right to the appellation home.