their benefit certain of the notes with which I had furnished them, and which consumed much time in dictation.

The peculiar characteristics of the following treatise are (1) the doctrine of extension and intension, (2) the quantification of the predicate, (3) the solution of opposed propositions, (4) the reduction of the thirty-six moods in each figure to nine essential moods, (5) the evolution of all additional moods caused by the introduction of the sign of partial quantity on the one hand, and by the ultratotal quantification of the middle term on the other, and (6) the doctrine of induction. The treatise is likewise characterised by the exclusion therefrom of the doctrine of modals, and of enthymemes and sorites.

In the treatment of syllogisms I have employed no scheme of pictorial notation, for the simple reason that I am thoroughly convinced of the general uselessness of any such, and therefore strongly deprecate its use. I am acquainted with the schemes of Euler, Ploucquet, Lambert, Hamilton, and Boole, of which I take Lambert's to be the best; but I am far from thinking it desirable to trouble the student with it.

In the course of the following pages I have not scrupled to avail myself of the demonstrations of

others; and where I have found such expressed with a truth, clearness, and precision, which I should despair of approaching, I have transplanted into my own work as much as I found necessary, in all cases (except in the statement of the canons of syllogisms, which are taken from Sir William Hamilton's Disquisitions) acknowledging the obligation by annexing the name of the author. But inasmuch as in all such cases I have not unfrequently amended the grammatical construction, I have been unable to indicate the extracts by the usual addition of "".

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I have already stated the immediate design of my work; independently of that, I have sufficient faith in my own labours to entertain the hope that they may not be without influence upon logic as a branch of liberal education in the Universities. This hope will be fully realised, as far as Cambridge is concerned, if I am in the most indirect manner instrumental in giving logic a place in the curriculum of her studies, and thus removing from her a stigma as disgraceful as it is peculiar.

My claims to originality are small: they are confined to the treatment of logical opposition and the principle of the congruity of syllogisms. In stating the thirty-six moods of the syllogism I have not borrowed from any other writer, but have

drawn them up from my own investigation. However, I believe they will be found to agree with those of Sir William Hamilton.

BIRMINGHAM,

July 21st, 1856.

CORRECTIONS.

The following Errata occurred through the negligence entailed on the Author's illness; he trusts they are the only blunders which disfigure this little work.

P. 56. 4th line from the bottom, for 'argument' read agreement. P. 63. 13th line from the top, the word 'All' should be enclosed in []

P. 64.

P. 72.

P. 73.

8th line from the top, the brackets enclosing the word 'Any' should be transferred to the All' of the preceding line.

7th line from the bottom, the word 'Certain' on the right hand should be enclosed in [ ]

8th line from the top, the word Certain' to be preceded by a [

4th line from the bottom, the word 'Certain' to be enclosed in [ ]

N.B. It would be better in pages 72 and 73 to substitute (Certain) for [Certain] wherever the latter occurs, inasmuch as the [ ] have been appropriated to distinguish the redundancy of the sign of quantity 'All.'

In page 57, in the 6th and 9th lines from the bottom, the word 'definite' (which is used by Baynes) is equivocal, and should be replaced by the word 'determinate.'

INTRODUCTION.

OF THE DEFINITION AND SPHERE OF

THEORETICAL LOGIC.

THEORETICAL Logic is the Science of the Laws of Thought.

Thought is conversant with 1 Conception, 2 Judgment, 3 Reasoning, 4 Science.

The mind, in performing the act of conception, forms a Concept of every object of thought.

Conception is the process, the concept is the product.

A Concept is the cognition or idea of the general attribute or attributes in which a plurality of objects coincide (HAMILTON).

This process of conception obviously involves the perception of a number of objects, their comparison, the recognition of their points of similarity, and their subjective union by this common attribute (BAYNES).

Accordingly a concept may either refer to an individual or to a species (that is, a class comprehending several individuals) or to a genus (that is,

I. L.

1

a class comprehending several species) or to higher classes.

Judgment is the action of referring one concept to another. The result of such action put into words is a sentence expressing the relation between two concepts.. The concepts in such a sentence are called the Terms, and the sentence itself is called the Proposition.

A proposition is an expression that two notions or concepts can or cannot be reconciled (THOMSON). Reasoning is concerned with the relation that subsists between two propositions. The two being compared, the result is the generation of a third proposition.

In certain cases (which will be explained in the right place) an inference expressed in words is called a simple Illation; in other cases, a Syllogism.

A system of such illations and syllogisms, concatenated according to the laws of logical progression, is called an Organon.

An organon may be either for the discovery of truth or for imparting it to others.

What logic is not.

Logic is not concerned with the philosophy of language, or in any way with the means of expressing what is thought.

Language expresses all that is thought. Logic is the instrument of which language is the material, and philosophy the result. As the prerequisite of philosophy is logic, so the prerequisite of logic is